Line 1 h t t p : slash slash w ww from open parenthesis Update of to Living Rev period period l i v i n g r e v from lrr hyphen 2005 hyphen \ [ \ begin { a l i g n e d } ht tp : //wwwˆ{ ( Update o f } { Living Rev . } . l 7 closing parenthesis to Relativity comma(Updateof sub i to the powerlrr−2005 of− 17) sub11 e to2008 the), power of 1 comma w s open parenthesis period sub o to the http : //wwwLivingRev..livingrevRelativity, ie,ws (. o rg/lrr8 − 2008 − 8 poweri v of 2008 i sub n r g g slash r to the e power v ˆof{ closingl r r parenthesis− 2005 comma− sub7 l rr 8 ) hyphen} { Relativity 20 0 8 hyphen 8 ,Line} { 2 hlinei }ˆ{ 1 }ˆ{ 1 } { e } , Binary{ w .. s and} ..( Millisecond{ . }ˆ{ .. Pulsars2008 } { o }ˆ{ ), } { r g / } { l r r } 8 − 20 0 8 − 8 \\ \ r u l e {3em}{0.4 pt }\end{ a l i g n e d }\ ] Duncan R period Lorimer Binary and Millisecond Pulsars Department of Physics Duncan R . Lorimer West Virginia University \ centerlineP period O{ periodBinary Box\ 63quad 1 5 and \quad MillisecondDepartment of Physics\quad Pulsars } Morgantown West Virginia University \ centerlineWV 26506 comma{Duncan U period R . Lorimer S period A} period P . O . Box 63 1 5 email : Duncan period Lorimer at mail period wvu periodMorgantown edu \ centerlineh ttp : slash{ slashDepartment astro period of w Physics v u period} eduWV slash 26506 people , U . S slash . A . dunc email : Duncan . Lorimer @ mail . wvu . edu Living Reviews in Relativity \ centerline {West Virginia Universityh ttp : / / astro} . w v u . edu / people / dunc ISSN 1433 hyphen 835 1 Living Reviews in Relativity Accepted on 14 October 2008 \ centerlinePublished on{P 4 November .O. Box63 2008 15 } ISSN 1433 - 835 1 Abstract Accepted on 14 October 2008 \ centerlineWe review the{Morgantown main properties} comma demographicsPublished on and 4 November applications 2008 of binary and millisecond Abstract radio pulsars period .. Our knowledge of these exciting obj ects has greatly increased in recent years comma \ centerline {WV26506 ,U . S . A . } mainlyWe due review to successful the main properties surveys which , demographics have brought and applicationsthe known pulsar of binary population and millisecond to over radio pulsars . Our 1 800 period There are now 83 binary and millisecond pulsars associated with the disk of our Galaxy comma \ centerlineknowledge{ email of these : exciting Duncan obj . ects Lorimer has greatly $ increased @ $ mail in recent . wvuyears , . mainly edu } due to successful surveys which and a further 140 pulsars in 26 of thehave Galactic brought globular the known clusters pulsar periodpopulation Recent to over highlights include the discovery of the young relativistic binary system PSR J 1 906 plus 746 comma a rej uvination in globular \ centerline {h ttp : / / astro . wv u . edu / people / dunc } cluster pulsar1 research800 . There including are now growing 83 binary numbers and millisecond of pulsars pulsars with associated masses in with excess the of disk 1 period of our Galaxy 5 M sub , odot comma a precise measurement of relativistic spin precession in the double pulsar system and a Galactic \ centerline { Living Reviews in Relativity } millisecondand a pulsar further in 140 an pulsars eccentric in 26 open of the parenthesis Galactic globular e = 0 period clusters 44 . Recent closing highlights parenthesis include orbit the around discovery an unevolved of the companion period Line 1young hline relativistic Line 2 Attribution binary system hyphen PSR Non J 1906 hyphen + 746 Commercial, a rej uvination hyphen in globular NoDerivs cluster 3 period pulsar 0 Germany research including from h t tp : slash slash cr e a t i v \ centerline {ISSN 1433 − 835 1 } e c o mgrowing mon s numbersperiod o of r pulsarsg slash with l i c masses e n s e in s excessslash by of hyphen1.5M , na c precise hyphen measurement n d slash 3 of to relativistic This review spin is precession licensed underin a Creative Commons License periodthe double 0 slash pulsar d e system slash to and the a Galactic power of millisecond period pulsar in an eccentric (e = 0.44) orbit around an unevolved \ centerline { Accepted on 14 October 2008 } companion . \ centerline { Published on 4 November 2008 }

\ centerline { Abstract } Attribution − Non − Commercial − NoDerivs3.0Germanyhttp://creativecommons.org/licenses/by−nc−nd/3License. \ begin { c e n t e r } ThisreviewislicensedunderaCreativeCommons .0/de/ We review the main properties , demographics and applications of binary and millisecond radio pulsars . \quad Our knowledge of these exciting obj ects has greatly increased in recent years , mainly due to successful surveys which have brought the known pulsar population to over \end{ c e n t e r }

\ centerline {1 800 . There are now 83 binary and millisecond pulsars associated with the disk of our Galaxy , }

\ begin { c e n t e r } and a further 140 pulsars in 26 of the Galactic globular clusters . Recent highlights include the discovery of the young relativistic binary system PSR J $ 1 906 + 746 , $ a rej uvination in globular cluster pulsar research including growing numbers of pulsars with masses in excess of $ 1 . 5 M {\odot } , $ a precise measurement of relativistic spin precession in the double pulsar system and a Galactic millisecond pulsar in an eccentric $ ( e = 0 . 44 ) $ orbit around an unevolved companion . \end{ c e n t e r }

\ [ \ begin { a l i g n e d }\ r u l e {3em}{0.4 pt }\\ Attribution − Non − Commercial − NoDerivs 3 . 0 Germanyˆ{ h t tp : / / creativecommons.org/licenses/ by − n c −{ n } d / 3 } { This review is licensed under a Creative Commons } License { . 0 / d e / }ˆ{ . }\end{ a l i g n e d }\ ] Imprint .. slash .. Terms .. of Use \ centerline { Imprint \quad Imprint/ \quad Terms /\quad Termso f Use } of Use LivingLiving Reviews Reviews in Relativity in Relativity is ais peer a peer reviewed reviewed open open access access j ournal j ournal published published by the byMax the Max Planck Planck Institute for Gravitational Physics comma Am M u-dieresis hlenberg 1 comma 1 4476 Potsdam comma Germany period ISSN 1 433 hyphen \noindentInstituteLiving for Gravitational Reviews Physics in Relativity , Am Mu ¨ hlenberg is a peer 1 , 1 4476reviewed Potsdam open , Germany access . ISSN j ournal 1 433 - published8351 . by the Max Planck 8351 periodThis review is li censed under a Creative Commons Attribution - Non - Commercial - NoDerivs 3 . 0 This review is li censed under a Creative Commons Attribution hyphen Non hyphen Commercial hyphen NoDerivs 3 period 0 \noindentGermanyInstitute License : forhttp Gravitational : / / cre a t Physics iv e com , mo AmM n s . $ org\ddot /{ lu i} c$ en hlenberg s e s / by 1 - , n 1 c 4476 - Potsdam , Germany . ISSN 1 433 − 8351 . Germanyn d / License 3 . 0 : / .. dehttp / : slash slash cre a t iv e com mo n s period org slash l i c en s e s slash by hyphen n c hyphen n d slash 3 period 0 slashBecause de slash a Living Reviews article can evolve over time , we recommend to cite the article as follows : \noindentBecause aThis Living review Reviews article is li can censed evolve overunder time a comma Creative we recommend Commons to Attribution cite the article− asNon follows− Commercial : − NoDerivs 3 . 0 Case 1 Duncan R period Lorimer comma Case 2 Binary and Millisecond Pulsars comma Case 3 Living Rev period Relativity comma 1 1\noindent comma openGermany parenthesis License 2008 closing : \quad parenthesishttp comma : // 8 cre period a topenDuncanR iv square ecommons.Lorimer bracket, Online . org Article / l closing i c en square s e bracket s /by : cited− n open c − n d / 3 . 0 / de / square bracket less date greater closing square bracket comma Case 4 httpBinaryandMillisecondPulsars : slash slash www period livingreviews, period org slash lrr 2008 8 \noindentTheline date− givenBecauseline − asquotedblleft less a date Living greater− hyphen Reviews then− uniquelyquotedblright article identifies can− hyphen the evolve version over of the timearticle ,you we are recommend referring to periodto cite the article as follows : LivingRev. Relativity, 11, (2008), 8. [OnlineArticle] : cited[< date >], Article .. Revisions \ [ \Livingl e f t . Reviews l i n e −l i supports n e −quotedblleft two different− wayshyphen to keep−quotedblright its articles up− hyphenhyphenhttp : to//\ hyphenwwwbegin.livingreviews{ datea l i g : n e d }.org&/lrr20088 Duncan R . Lorimer , \\Fast hyphen track revision A fast hyphen track revision provides the author with the opportunity to add short The date given as < date > then uniquely identifies the version of the article you are referring to . ¬ices Binary of current and research Millisecond results comma trends Pulsars and developments , \\ comma or important publications to &the article Living period Rev .. A fast . hyphen Relativity trackArticle revision , is refereed 1 Revisions 1 by the , responsible ( 2008 subject ) editor , period 8 .. . 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\noindent of the article ’ s online version at ht t p : / /www . l i v i n gre v i ews . org / l rr − 2 0 0 8 − 8 . Contents 1 P r e a m b l e 5 2 P ulsar Ph eno m enolog y 6 2.1 T helig hth ouse m od el ...... 62.2Pulsepe rio ds an dslowdow n rates ...... 6 2.3Pulseprofiles...... 82.4Thepuls ardistancescale...... 11 2.5 Pulsarsin binary syste ms ...... 122.6Evolutionof norm aland milliseco ndp ulsars ...... 12 2.6.1 High -m asssystem s ...... 14 2.6.2 Lo w- mass syste ms ...... 142.7Interme diate m ass binary pulsars ...... 162.8 Isolated recycled puls ars...... 172.9 Ane w classof millisecond p ulsars ? ...... 17 2.10 P ulsar velocities ...... 182.11Pulsar searches...... 192.11.1Al −l sky searches ...... 192.1 1.2 Searc hesclose to th eplane of o ur Gala xy...... 19 2.11.3 Searchesatinterm ediate and hig h G alacticlatitude s ...... 202.11.4 Targeted searches of globular clusters ...... 20 2.11.5 Targetedsearchesofotherregion s ...... 21 2.1 1.6 Extragalactic searc hes ...... 21 2.1 1.7 Surveys with new telescop es...... 21 2.12 G oingfurth er ...... 21 3 P uls ar St atistics and D em ograp hy 23 3.1 Selection effectsin p ulsar search es ...... 233.1.1Theinvers e sq uarelaw an d s urvey th resh olds ...... 233.1.2 Interstellar p ulse dispersio nand m ultipath scatterin g...... 24 3.1.3 Orbital acceleratio n ...... 253.2 Correcting theob served pulsar sam ple ...... 273.2.1 Scalefactor determin ation ...... 273.2.2T hesm all-n um ber bias...... 273.2.3 The beam ing correctio n ...... 283.3 Th e pop ula tio n ofnorma l and millisecon dp uls ars...... 28 3.3.1 Lum inosity distrib utio ns an dlocal num ber estim ates ...... 283.3.2 Galactic pop ul at io n and birth-rates...... 29 Contents \noindent3.4Contents T he pop ula tion ofrelativistic binaries ...... 1 ..... P .r .... . e .... . a . m b . l e ...... 5 ...... 303.4.1Doublene 2 .... P .... u l s a r .... P h .... e n o .... m .... e n o l o g .... y .... 6 \noindentutron1 \ h starbinaries f i l l P r \ h f i l l .e \ .h f i . l l .a m . b . l e.\ .h f i . l l .5 ...... 2 period. . 1 .. . T ... h . e l i . g .. 303.4.2 h t h .. o u s W e .. m hite .. o d .. d e l warf–n .. period .. period eutron .. period star .. period bin .. period aries .. period .. period .. period .. period .. period .. period .. period .. period .. period .. period .. period .. period .. period .. period .. period .. period .. period .. period .. \noindent...... 323.5Goi2 \ h f i l l P \ h f i l l u l s a r \ h f i l l P h \ h f i l l e n o \ h f i l l m \ h f i l l e n o l o g \ h f i l l y \ h f i l l 6 periodngfurther...... period .. period .. period .. period .. period .. period .. period .. period .. period .. period .. 6 2 period. . 2 .. . 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Observing period .. period .. bperiod asics .. period . .. period. . .. . 6 ...... 2 period...... 354.2Thetimi 3 .. 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Ti period ming .. period stability .. period .. period . .. . period . .. period .. 8 2 period...... 4 .. 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T ae r ge\quad t e d sp e o a r p c\ hquad e s o fu o tl h a e\ rquad r e g it o n i o .. s\quad .. periodn \ ..quad periodo .. f period n o .. r periodm a \ ..quad periodl ..\quad perioda .. n d \quad m i l l i s e c o n \quad d p \quad u l s \quad a r s \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad 28 period .. period .. period .. period .. period .. period .. period .. period .. period .. period .. period .. period .. period .. period .. period .. period3 . 3 .. . period 1 \quad .. 2 1L u m \quad i n o s i t y \quad d i s t r i b \quad u t i o \quad n s \quad a n \quad d l o c a l \quad n u m \quad b e r \quad e s t i m \quad a t e s \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad 28 32 . period 3 . 21 ..\quad 1 periodG 6a .. l E a x c t r t a ig a c l\ aquad c t i cp .. o s e p a\ rquad c .. hu e s l ..\ periodquad ..a period t i o ..\quad periodn ..\ periodquad ..a period n d \ ..quad periodb .. i period r t h ..− r a t e s . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad 29 period .. period .. period .. period .. period .. period .. period .. period .. period .. period .. period .. period .. period .. period .. period .. period3 . 4 ..\ periodquad T .. period\quad ..h period e \quad .. periodp o .. p period\quad .. periodu l a .. period\quad ..t 2 i1 o n \quad ofrelativistic \quad b i n a r i e s \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad 30 32 . period 4 . 1 ..\quad 1 periodD 7\quad .. 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ST e l\quad e c t i oh n e ..\ equad ff e c t s i i n m ..\ pquad .. u li s a n r g .. s\quad e a r cm h ..\quad e s .. periodo \quad .. periodd e .. l period . \quad .. period. \quad .. period. \ ..quad period. ..\quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad 36 period4 . 3.. period\quad ..T period i \quad .. periodm i .. n period g \quad .. periods t .. a period b i .. l period i t y ..\ periodquad ... period\quad ... period\quad .. period. \quad .. period. \quad .. period. \ ..quad period. ..\quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad 37 period4 . 4.. period\quad ..T period i \quad .. periodmi .. n period g b i .. n period a r .. y 23\quad p u l s a r s \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad 40 43 . period 5 \quad 1 periodT \ 1quad .. 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I6 n\ tquad e r s tP e\ lquad l a r ..u p ..l u s l a s e r .. t d i s\ pquad e r s imi o .. n n g a n\quad d .. ma ..\ uquad l t i pn a d t h\quad .. s c an t te e\ rquad i n ..u g period t r o .. n s t a r \quad m \quad a s s e s \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad 46 period .. period .. period .. period .. period .. period .. period .. period .. period .. period .. period .. period .. 24 3 period 1 period 3 .. O r b i t a l .. a c c e l e r a t i o .. n .. period .. period .. period .. period .. period .. period .. period .. period .. period .. period .. period .. period .. period .. period .. period .. period .. period .. period .. period .. period .. period .. period .. period .. period .. period .. period .. period .. period .. period .. period .. period .. 25 3 period 2 .. 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T h .. e .. p o p .. u l a .. t io .. n .. o f n o r m a .. l .. a n d .. m i l l i s e c o n .. d p .. u l s .. a r s .. period .. period .. period .. period .. period .. period .. period .. period .. period .. period .. period .. period .. period .. period .. period .. period .. period .. period .. period .. 28 3 period 3 period 1 .. L u m .. i n o s i t y .. d is t r i b .. u t io .. n s .. a n .. d l o c a l .. n u m .. b e r .. e s t i m .. a t e s .. period .. period .. period .. period .. period .. period .. period .. period .. period .. period .. period .. period .. period .. 28 3 period 3 period 2 .. G a l a c t i c .. p o p .. u l .. a t io .. n .. a n d .. b i r t h hyphen r a t e s period .. period .. period .. period .. period .. period .. period .. period .. period .. period .. period .. period .. period .. period .. period .. period .. period .. period .. period .. period .. period .. period .. period .. 29 3 period 4 .. 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T .. e s t i n g g e n e r a l r e l a t i v i t y .. period .. period .. period .. period .. period .. period .. period .. period .. period .. period .. period .. period .. period .. period .. period .. period .. period .. period .. period .. period .. period .. period .. period .. period .. period .. period .. period .. period .. period .. period .. period .. period .. period .. 42 4 period 6 .. P .. u l s a r t i .. mi n g .. a .. n d .. n e .. u t r o n s t a r .. m .. a s s e s .. period .. period .. period .. period .. period .. period .. period .. period .. period .. period .. period .. period .. period .. period .. period .. period .. period .. period .. period .. period .. period .. period .. period .. period .. period .. 46 4 period 7 .. P .. u l s a r .. t i .. m i n g .. a n .. d g .. r a v i t a t i o n .. a l .. w a v e .. d e t e c t i o n .. period .. period .. period .. \ hspace ∗{\4.7f i l l P}4 ulsar . 7 \quad tiP ming\quad u an l s dg a r \ ravitationquad t i \quad alm i wave n g \quad detectiona n \quad .d g \quad r a v i t a t i o n \quad a l \quad w a v e \quad d e t e c t i o n \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad 48 period...... 48 .. period .. period .. period .. period .. period .. period .. period .. period .. period .. period .. period .. period .. period .. period .. period .. period .. 48 \ hspace ∗{\4.7.1f i l l }4 Probing . 7 . 1 \quad theP r gravitation o b i n g \quad alt h waveb e \quad ackgroungravitation d . . .\quad a l \quad w a v e b \quad a c k g r o u n \quad d \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad 48 4 period. . 7 period . . 1 . .. P . r o . b i n . g .. . t h . e .. . g r . a v . i t a. t i . o n 48 .. a l .. w a v e b .. a c k g r o u n .. d .. period .. period .. period .. period .. period .. period .. period .. period .. period .. period .. period .. period .. period .. period .. period .. period .. period .. period .. 48 \ hspace ∗{\4.7.2f i l l }4 Con . 7 . strain 2 \quad C ts o n on\quad ms assive t r a i n black\quad t hole s \quad binaries.o n \quad m .\quad . a s s i v e \quad b l a c k \quad h o l e \quad b i n a r i e s . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad 49 4 period. . 7 period . . 2 . .. C . o n . .. . s tr . a i . n .. . t s . .. o . n .. . m . .. a . s s 49 i v e .. b l a c k .. h o l e .. b i n a r i e s period .. period .. period .. period .. period .. period .. period .. period .. period .. period .. period .. period .. period .. period .. period .. period .. period .. period .. \ hspace ∗{\4.7.3f i l l }4 Am. 7 . illisecon 3 \quad A m dp\quad ulsari l l i tim s e c ing o n array\quad d p .\quad . .u . l . s a . r .\quad t i m \quad i n g \quad a r r a y \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad 49 period. .. 49 ...... 49 4 period 7 period 3 .. A m .. i l l i s e c o n .. d p .. u l s a r .. t i m .. i n g .. a r r a y .. period .. period .. period .. period .. period .. \ hspace ∗{\4.8f i l l Goingfurt}4 . 8 \quad G her o i . n g . f . u r . t .\quad . .h . e r .\quad . .. .\quad . .. .\quad . .. \ .quad . . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad 50 period...... 50 .. period .. period .. period .. period .. period .. period .. period .. period .. period .. period .. period .. period .. period .. period .. period .. period .. period .. period .. 49 \noindent55 Sum\ h f i l l S mary u m \ h f i l l andm a r y F\ h f i l l utura n d \ h e f i l l F Prosp\ h f i l l u t ects u r \ h f i l l 53e \ h f i l l P r o s p \ h f i l l e c t s \ h f i l l 53 4 period6 8 .. G o A i n c g k f u r t .. h e r n .. o period w .. period l .. e period .. period d g e .. m period .. period e n .. t period s .. period 55 .. period .. period .. period .. period .. period .. period .. period .. period .. period .. period .. period .. period .. period .. period .. period .. period .. period .. period .. \noindentA6 T\ h f i ab l l A c lesof k \ h f i l l Bn o inary w \ h f i l l anl e \ dh f i l Ml d g illisecon e m \ h f i l l e n d t Ps \ h uls f i l l 55 perioda .. rperiod s 56 .. period .. period .. period .. period .. period .. period .. period .. period .. period .. period .. period .. 50 5 .... S u m .... m a r y .... a n d .... F .... u t u r .... e .... P r o s p .... e c t sRefer .... 53 en ces 61 \ hspace6 ....List A∗{\ c kf .... i l l ofn}A o wTables\quad .... l eT ....\ dquad g e ma .... b e\ nquad t s ....l 55 e s o f \quad B \quad i n a r y \quad a n \quad d \quad M \quad i l l i s e c o n \quad d \quad P \quad u l s a r s \quad 56 A .. T .. a b .. l e s o f .. B .. i n a r y .. a n .. d .. M .. i l l i s e c o n .. d .. P .. u l s a r s .. 56 \ hspace ∗{\1f K i l l } noR e wn f e r andlikely\quad e n \quad D Nc e S s \ binaries..quad 6 1 ...... R e. f er . ..e . n .. . c e. s .. . 6 1 ...... 322Parametersfor List .. of Tables \noindenttheL 20 i s t \ isolatedmquad o f Tables illisecon d pulsars curren tlyk nown in th 1 ..e K .. G n a o l .. a w c tn i .. c a n d l i k e l y .. D .. N .. S .. b i n a r i e s period period .. period .. period .. period .. period .. period .. period .. period .. perioddisk...... period .. period .. period .. period .. period .. period .. period .. period .. period .. period .. period .. period .. period .. period1 \quad .. periodK \quad .. periodn o ..\ periodquad ..w period n \quad .. perioda n .. d period l i k .. 32e l y \quad D \quad N \quad S \quad b i n a r i e s . . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad 32 2 \quad...... 56P \quad a r a m \quad e t e r s f o r \quad t h e \quad 2 0 \quad i s o l a t e d m \quad i l l i s e c o n \quad d \quad p u l s a r s \quad c u r r e n \quad t l y k \quad n o w n \quad i n \quad t h e \quad G a l a c t i c 3 Para meters2 .. for P .. a r the19 a m .. e t e eccen r s f o r .. tric( t h e ..e 2 0 > .. i s0 o.05) l a t e bin d m .. ary i l l i s ep c o ulsarsc n .. d .. p u l urrently s a r s .. c u r r ekn n .. t own l y k .. nth o w at n .. i aren .. t h e .. G a l a c t i c \ hspace ∗{\notinf i l l }d i glob s k \quad ular. \ clusters.quad . \quad .. \ .quad . .. \ .quad .. .\quad . .. .\quad . .. .\quad . . . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad 56 d i s. k .. . period . . .. period . . .. . period . . .. period . . .. . period . .. . period . . .. period . . .. 57 period .. period .. period .. period .. period .. period .. period 4 P arametersfor64.. period .. period .. low-eccentricity period .. period .. period .. period binary .. period p .. period ulsarscurrently .. period .. period .. period kno .. wn period in .. period the .. period Galactic .. period .. period\ centerline .. period{3 .. period\quad ..P period a r a.. period\quad ..m period e t ..e period r s \quad .. periodf.. o period r \quad .. periodt h .. e period 1 9 \ ..quad periode .. c period c e n ..\ periodquad ..t period r i c .. $ ( e disk...... > 0 . 0 5 ) $ \quad b i n \quad a r y \quad p \quad u l s a r s c \quad u r r e n t l y \quad k n \quad o w n \quad t h \quad a t \quad a r e } period...... 58 .. 56 3 .. P a r a .. m e t e r s .. f o r .. t h e 1 9 .. e c c e n .. t r i c open parenthesis e greater 0 period 0 5 closing parenthesis .. b i n .. a r y .. p\ hspace .. u l s a∗{\ r sf c i .. l l u}n r r o e n t t i l y n ..\ kquad n .. og w ln .. o t b h\ ..quad a t ..u a r l e a r \quad c l u s t e r s . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad 57 n o t i n .. g l o b .. u l a r .. c l u s t e r s period .. period .. period .. period .. period .. period .. period .. period .. period .. period .. period\ centerline .. period{4 .. period\quad ..P period\quad .. periodarametersfor64 .. period .. period .. period .. period\quad ..l period o w − .. periodeccentricity .. period .. period .. period\quad .. periodb i .. n a r y \quad p \quad ulsarscurrently \quad k n o \quad w n \quad i n \quad t h e \quad G a l a c t i c } period .. period .. period .. period .. period .. period .. period .. period .. period .. 57 \ hspace4 .. P∗{\ .. a rf ia l m l } ed t ei r s s f\ oquad r 6 4k .. l . o\ wquad hyphen. e\ cquad c e n t. r\ iquad c i t y. .. b\quad i n a r. y ..\quad p .. u l. s\ aquad r s c u. r r\quad e n t l y. ..\quad k n o ... w\ nquad .. i n. .. t\quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad . \quad 58 h e .. G a l a c t i c d i s .. k period .. period .. period .. period .. period .. period .. period .. period .. period .. period .. period .. period .. period .. period .. period .. period .. period .. period .. period .. period .. period .. period .. period .. period .. period .. period .. period .. period .. period .. period .. period .. period .. period .. period .. period .. period .. period .. period .. period .. period .. period .. period .. period .. period .. period .. 58 BinaryBinary and and Millisecond Millisecond Pulsars Pulsars .... 5 5 \noindenthline Binary and Millisecond Pulsars \ h f i l l 5 1 .. Preamble \ [ Pulsars\ r u l e { endash3em}{ rapidly0.4 pt }\ rotating] highly magnetised neutron stars endash have many applications in physics and1 astronomy Preamble period .. Striking examples include the confirmation of the existence of gravitational ra hyphen diationPulsars open – rapidlysquare bracketrotating 3 highly 6 6 comma magnetised .. 3 6 neutron 7 comma stars .. – 3 have 6 8 manyclosing applications square bracket in physics comma and the astronomy first extra hyphen solar planetary system\noindent. open Striking square1 \quad examples bracketPreamble 4 include 0 4 comma the confirmation 2 9 3 closing of square the existence bracket and of gravitational the first detection ra - diation of [ 3 6 6 , 3 6 7 , gas3 in 6 a 8 globular] , the first cluster extra open - solar square planetary bracket system 1 1 [ 6 4 closing 0 4 , 2 9square 3 ] and bracket the first period detection The ofdiverse zoo of radio pulsars currently known is summarized\noindentgas in in aPulsars globular−− clusterrapidly [ 1 1 6 ] rotating . The diverse highly zoo of radio magnetised pulsars currently neutron known stars is summarized−− have many in Figure applications in physics andFigure astronomy1 . .. 1 period . \quad Striking examples include the confirmation of the existence of gravitational ra − diationFigureFigure 1 :[ Venn 13 : 6 diagram 6Venn , \ diagramquad showing3 showing 6 the 7 numbers ,the\quad numbers and3 locations and 6 8 locations ] of, the of variousthe first various types extra types of radio of− radiosolar pulsars pulsars planetary known known as system of [ 4 0 4 , 2 9 3 ] and the first detection of as ofSeptember September 2008 2008 . The period large The and large small and Magellanic small Magellanic clouds are denoted clouds areby LMC denoted and bySMC LMC . and SMC period \noindentPulsar researchgasPulsar hasin research aproceeded globular has at proceeded a clusterrapid pace at a [ during rapid 1 1 pace the 6 ] first during . Thethree the diverse versions first three of zoo this versions article of radioof open this article square pulsars [ bracket 2 currently 1 8 2 , .. 1 8 comma known is summarized in Figure2 ....2 1 1 9\ 9quad comma , 2 21 .... ] . . Surveys 2 2 1 closing with thesquare Parkes bracket radio period telescope Surveys [ 3 0 with 8 ] , the at Green Parkes Bank radio [ telescope2 7 8 ] , Arecibo open square [ 2 7 4 bracket ] 3 0 8 closing square bracketand comma the at Green Bank open square bracket 2 7 8 closing square bracket comma Arecibo open square bracket 2 7 4 closing square bracket\noindentGiant and the MetreFigure Wave 1 Radio: Venn Telescope diagram [ 2 7showing 7 ] have more the than numbers doubled and the locations number of pulsars of the known various a types of radio pulsars known asGiant ofdecade SeptemberMetre ago Wave . With Radio 2008 new Telescope . instrumentation The large open square and coming bracket small online 2 Magellanic 7 , and7 closing new telescopes square clouds bracket planned are have denoted [ 1more 0 5 than, by 1 doubled 8 LMC 6 , 1 and 5 the 4 ] SMC number . of pulsars known a , these are exciting times for pulsar astronomy . \ hspacedecade∗{\ agof period i l l } Pulsar WithThe new aims research instrumentation of this review has proceeded are coming to introduce online at comma the a rapid reader and tonew pace the telescopes field during and planned to the fo cus first open on some square three of bracketthe versions 1 0 5 comma of this .. 1 article8 6 [ 2 \quad 1 8 , commamany 1 5 4 applications closing square ofpulsar bracket research comma in relativistic astrophysics . We begin in Section 2 with an overview \noindenttheseof are the exciting2 pulsar\ h f phenomenon i times l l 1 for 9 pulsar , ,\ ah reviewf astronomy i l l 2 of 2 the period1 key ] . observed Surveys population with the properties Parkes , the radio origin telescope and evolution [ of 3 0 8 ] , at Green Bank [ 2 7 8 ] , Arecibo [ 2 7 4 ] and the Thepulsars aims of and this the review main are search to introduce strategies the . reader In Section to the 3 , fieldwe review and to present fo cus understanding on some of the in pulsar demography \noindentmany, discussing applicationsGiant selection Metre of pulsar effects Wave research and Radio theirin relativistic Telescope correction astrophysics techniques [ 2 7 7period .] This have .. leads We more begin to empirical than in Section doubled estimates .. 2 .. with the of the number total of pulsars known a an overviewnumber of of normal the pulsar and phenomenon millisecond pulsars comma a ( review see of the key observed population properties comma the \noindentoriginSection anddecade evolution 3 . 3 ago ) of and pulsars . relativistic With and new the binaries main instrumentation search ( see strategies Section 3 periodcoming . 4 ) in .. In the online Section Galaxy , 3 and comma has new we implications telescopesreview present for the planned [ 1 0 5 , \quad 1 8 6 , 1 5 4 ] , theseunderstandingdetection are exciting of in gravitational pulsar times demography radiation for comma pulsar by current discussing astronomy and planned selection . telescopes effects and . Our their review correction of pulsar techniques timing in period Section This4 leads covers to the empirical basic techniques estimates ( of see the Section total number 4 . 2 ) , of timing normal stability and millisecond ( see Section pulsars 4 . 3 .. ) open , binary parenthesis see \ hspaceSectionpulsars∗{\ .. 3f ( iperiod see l l } SectionThe 3 closing aims 4 . 4 parenthesis of ) , and this using reviewand pulsars relativistic are as sensitive to binaries introduce detectors open parenthesis of the long reader - period see Section to gravitational the 3 period field waves 4 closing and to parenthesis fo cus in on the some Galaxy of the and has( implications see Section 4 for . 7 the ) . We conclude with a brief outlook to the future in Section 5 . Up - to - date tables \noindentdetectionof parameters ofmany gravitational applications of binary radiation and millisecond of by current pulsar pulsars and research planned are included telescopes in in relativistic Appendix period Our A review . astrophysics of pulsar timing . \quad We begin in Section \quad 2 \quad with anin overview Section 4 covers of the the basic pulsar techniques phenomenon open parenthesis , a review see Section of the 4 period key 2 observedclosing parenthesis population comma timing properties stability , open the parenthesis seeorigin Section and 4 period evolution 3 closing parenthesis of pulsars comma and binary the main search strategies . \quad In Section 3 , we review present understandingpulsars open parenthesis in pulsar see Section demography 4 period ,4 closing discussing parenthesis selection comma and effects using pulsars and theiras sensitive correction detectors of techniques long hyphen period . This leads to empirical estimates of the total number of normalLiving and Reviews millisecond in Relativity pulsars \quad ( see gravitational waves ht tp : / / w w w . l i vi ngrev i e w s . org / lrr - 2008 - 8 open parenthesis see Section 4 period 7 closing parenthesis period .... We conclude with a brief outlook to the future in Section .... 5 period ....\noindent Up hyphenSec to hyphention \quad date tables3 . 3 ) and relativistic binaries ( see Section 3 . 4 ) in the Galaxy and has implications for the detectionof parameters of of gravitational binary and millisecond radiation pulsars are by included current in andAppendix planned .. A period telescopes . Our review of pulsar timing inhline Section 4 covers the basic techniques ( see Section 4 . 2 ) , timing stability ( see Section 4 . 3 ) , binary Living Reviews in Relativity \noindentht tp : slashpulsars slash w w ( .. see w period Section l i vi 4ngrev . 4 i e ) w , s periodand using org slash pulsars lrr hyphen as 2008 sensitive hyphen 8 detectors of long − period gravitational waves \noindent ( see Section 4 . 7 ) . \ h f i l l We conclude with a brief outlook to the future in Section \ h f i l l 5 . \ h f i l l Up − to − date t a b l e s

\noindent of parameters of binary and millisecond pulsars are included in Appendix \quad A.

\ [ \ r u l e {3em}{0.4 pt }\ ]

\ hspace ∗{\ f i l l } Living Reviews in Relativity

\ hspace ∗{\ f i l l } ht tp : / / w w \quad w. l i vi ngrev i ews . org / lrr − 2008 − 8 6 ....6 Duncan R period Lorimer Duncan R . Lorimer \noindenthline 6 \ h f i l l Duncan R . Lorimer 2 .. Pulsar .. Phenomenology \ [ Most\ r u l of e { the3em basic}{0.4 observational pt }\ ] facts about radio pulsars were est ablished shortly after their dis hyphen covery2 .. open Pulsar square bracket Phenomenology 1 4 1 closing square bracket .. in 1 967 period .. Although there are still many open questions comma .. the basic modelMost has of the long basic observational facts about radio pulsars were est ablished shortly after their dis - covery [ 1 \noindentbeen4 established1 ]2 in\ 1quad 967 beyond .Pulsar Although all reasonable\quad there arePhenomenology doubt still comma many open i period questions e period , pulsars the basic are model rapidly has rotating long been comma established highly magnetised neutronbeyond stars all formed reasonable during doubt the supernova , i . e . pulsars explosions are rapidly of massive rotating st ars , period highly magnetised neutron stars formed \noindent2 periodduring 1Most the.. The supernova of l ighthouse the explosions basic model observational of massive st ars . facts about radio pulsars were est ablished shortly after their dis − coveryFigure2 . 2\ 1quad .. shows The[ an 1animationl 4 ighthouse 1 ] \quad depicting modelin the1 967 rotating . \quad neutronAlthough star comma there also known are as still the quotedblleft many open lighthouse questions quotedblright , \quad the basic model has long beenmodelFigure established period 2 .. shows As the beyond an neutron animation all star depicting spinsreasonable comma the rotating .. doubt charged neutron , particles i . star e are . , also pulsars accelerated known are as along the rapidly magnetic “ lighthouse rotating field ” lines model , highly magnetised neutronforming. As a stars beam the neutron open formed parenthesis star during spins depicted, the charged supernova by particlesthe gold cones are explosions accelerated closing parenthesisof along massive magnetic period st field .. Thears lines accelerating . forming a particles beam emit electromagnetic radiation( depicted comma by most the gold readily cones detected ) . atThe radio accelerating frequencies particles as a sequence emit electromagnetic of observed pulses radiation period , Eachmost pulsereadily \noindentis produceddetected2 as at . the radio 1 \ magneticquad frequenciesThe axis l openas ighthouse a sequence parenthesis of model observed and hence pulses the radiation . Each pulse beam is closing produced parenthesis as the magnetic crosses the axis observer ( quoteright s line of sightand each hence rotation the radiation period .. beam The repetition ) crosses the period observer of the ’ s pulses line of is sight therefore each simplyrotation the . rotation The repetition period period of \noindentof thethe neutron pulsesFigure is star therefore period 2 \quad simply .. Theshows movingthe rotation an quotedblleft animation period of tracker the depicting neutron ball quotedblright star the . rotating The on moving the pulse neutron “ tracker profile star ball in the ” on, animation also the known shows as the the ‘‘ lighthouse ’’ modelrelationshippulse . \ profilequad between inAs the observedthe animation neutron intensity shows star and the rotational spinsrelationship , phase\quad between ofcharged the observed neutron particles intensity star period and are rotational accelerated phase of the along magnetic field lines formingFigureneutron 2 a : .... beam star Still . ( from depicted a movie by showing the The gold rotating cones neutron ) . \ starquad openThe parenthesis accelerating or .... quotedblleft particles lighthouse emit electromagnetic quotedblright closing parenthesisradiationFigure model 2 , : most for pulsar readilyStill from a detected movie showing at The radio rotating frequencies neutron star ( asor a sequence “ lighthouse of ” ) observedmodel for pulsar pulses . Each pulse isemission producedemission period . as .... Animation the Animation magnetic designed designed axis by by Michael (Michael and Kramer hence Kramer . the period ( To radiation watch.... open the parenthesis movie beam , please ) To crosses go watch to the the onlinethe movie observer version comma please ’ s goline to the of online versionsightof this each review rotation article at .h ttp\quad : /The / w wwrepetition . l iv in periodgr e v i ofe ws the . org pulses / lrr is - 20 therefore 8 - 8 .) simply the rotation period 38 2 ofof the thisNeutron review neutron article stars star are at h essentially . ttp\quad : slashThe large slash movingcelestial w ww flywheels period ‘‘ tracker l withiv in moments gr ball e v i ’’ e of ws on inertia period the∼ pulseorg10 slashkg profilem lrr. The hyphen rotating in 20 the 8 hyphen animation 8 period shows closing the parenthesisrelationshipneutron star between model [ 2 9 observed 0 , 1 2 2] intensity predicts a gradual and rotational slowdown and phasehence an of increase the neutron in the pulse star period . as Neutronthe outgoing stars are radiation essentially carries large away celestial rotational flywheels kinetic with energy moments . This of inertia idea gained thicksim strong 1 0 to support the power when of a 38 period kg m to the power of 2 period 1 \noindentTheincrease rotatingFigure of neutron 36 . 2 5 star ns : per\ modelh f day i l l open wasStill measured square from bracket for a the movie 2 pulsar9 0 comma showing B 531 1 + .. The 21 2 2in closing rotating the Crab square nebula neutron bracket [ 3 predicts 2 star 1 ] , which (a gradual or \ h fslowdown i l l ‘‘ lighthouseand hence ’’ ) model for pulsar an increaseimplied in that a rotating neutron star with a large magnetic field \noindentthemust pulse be periodemission the dominant as the . outgoing\ energyh f i l l radiation supplyAnimation for carries the nebula designed away rotational[ 1 2 by3 ] . Michael kinetic energy Kramer period . This\ h f iidea l l gained( To watch the movie , please go to the online version strong2 . support 2 Pulse when a periodsperiod increase and of slowdown 36 period 5 ns rates per day was measured for the pulsar B 53 1 plus 2 1 to the power of 1 \noindentin the Crabof nebula this open review square article bracket 3 2 at 1 closing h ttp square : / bracket /www comma . l whichiv in implied gr e that v i a e rotating ws . neutron org / star lrr with− 20 a large 8 − magnetic8 . )

field −15 19s/s.Asshowninthe Neutron∼ 10 starss/s.Agrowing are essentially large celestial flywheels with moments of00 inertia $ \sim˙ 1pulsars 0 ˆ{ 38 }$ must be the dominant energy supply00 for the nebula open square bracket 1fractionare“millisecondpulsars 2 3 closing square bracket,with1. period4ms.P .30msandP .1 P˙ . “normal withpulseperiodsP ∼0.5swhichincreasesecularly@ratesThepulsarcatalogue[2 48, 12]containsup−to−dateparametersfor1775 − Mostoftheseare kg2 period $ m ˆ{ 2 ..2 Pulse} . periods $ and slowdown rates 0 Thethicksim rotating 1˙ 0 to neutron the power star of minus model 1 5 s[ slash 2 9 s 0 period , 1 \ Aquad growing2 2 from ] predicts 1 9 s slash a s gradual period As slowdown shown in the and to quotedbllefthence an increase normal in the“ pulseP – P perioddiagram ”as thein Figure outgoing 3 , normal radiation and millisecond carries pulsars away are distinct rotational populations kinetic . energy . This idea gained quotedblright with pulseThe periods differences P thicksim in P and 0 periodP˙ imply 5 s fundamentally which increase different secularly magnetic at rates field from strengths fraction andare quotedblleft ages . millisecond pulsars quotedblrightstrong support comma whenwith 1 aperiod period 4 ms increaselesssim P lesssim of 36 30 .ms 5 and ns P-dotaccent per day was lesssim measured 1 to The pulsar for the catalogue pulsar open B square $ 53 bracket 1 2 4 + 8 comma2 1 1 ˆ 2{ closing1 }$ square bracket contains up hyphen to hyphen date parameters for 1 775 sub 0 to the power of minus to the power of pulsars in the Crabthepulsar nebula [ 3 2 1 ] , whichmagnetic implieddipole thatmay a rotating neutron star with a large magnetic field dotaccent-PTreating to the powerB of period(asP a Mostrotating of these are , 1 show [226]thatLinesofthesurface Bmagnetic fieldstrength ∝ P˙ ) /12andthecharacteristicageτc =P/(2P˙ ). constant andτcare quotedblleft P endash P-dotaccent diagram quotedblright .. in Figure 3 comma normal and millisecond pulsars are distinct populations \noindent must be the dominant energy supply for the nebula [ 1 2 3 ] . period drawn on Figure 3 , from which we infer typical values of 1012 G and 107 yr for the normal pulsars The differences in P and P-dotaccent imply fundamentally different magnetic field strengths and ages period \noindentTreating field2 . strength 2 \quad to thePulse power periods of the pulsar and B slowdown varpropto open rates parenthesis as P sub P-dotaccent sub closing parenthesis to the power of a rotating slash 1 2 and the to the power of magnetic sub characteristic to the power of dipole sub age to the power of comma to the power of\ [ 1\ subsim tau sub1 c to 0 theˆ{ −power1 of may 5 } subs = P slash/ ssub open . parenthesis A growingˆ 2 dotaccent-P{ 1 closing 9 s parenthesis / s period . to As the power shown of show in to the } { ‘‘ normal ’’ with pulse periods P \sim 0 . 5 s which increase secularly the power1 ofLike openmost square astronomical bracket sources 2 2 6 , closing pulsars aresquare named bracket after their that position Lines inof the the sky constant . Those to the pulsars power discovered of surface prior Bto magnetic and tau sub c are @drawn r athe t eon mid s Figure ˆ 1{ 990fraction s 3 are comma named from based are which on the ‘‘we Besselian infer millisecond typicalequatorial values coordinate of 1 pulsars 0 system to the ( Bpower 1 950 ’’ of ) and 1 2 , have G and with a B 1 prefix 0 tothe 1 power . of 4 7 yr ms for the\ normall e s s s i m pulsars P \ lesssimhlinefollowed by 30 their right ms ascension and and\ declinationdot{P}\ . Morel e recently s s s i m discovered 1 } pulsars{ The follow pulsar the Julian ( J 2000 catalogue ) epoch . Pulsars [ in 2 4 8 , 1 21 sub ]globular Like contains mostclusters astronomical , where up the positional− sourcesto designation comma− pulsars isdate not unique are parameters named , have additionalafter their characters for position1 to in distinguish the 775 sky} periodˆ them{ p .u .. For l s Those a example r s pulsars{\dot discovered{P}}} { 0 ˆ{ − }}ˆ{ . } MostpriorPSR to of J the1748 mid these− 12446 990 sad are are in the named}\ globular] based cluster on Terzan the Besselian 5 [ 1 4 0 ] equatorial . coordinate system open parenthesis B 1 950 closing parenthesis and have a B prefix followed by their right ascension and declination period More recently discovered pulsars follow the Julian open parenthesis J 2000 closing \noindent ‘ ‘ $ P $ −− $ \dot{P} $ diagram ’ ’ \quad in Figure 3 , normal and millisecond pulsars are distinct populations . parenthesisLiving epoch Reviews period in Relativity Pulsarsht tp in globular: / / w clusters w w . comma l i vi where ngre the v positional i e w s . designation or g / lrr is not - unique 2008 - comma 8 have additional characters to distinguish \ hspacethem period∗{\ f i Forl l }The example differences PSR J 1 748 in minus $ 2446P $ ad and in the $ globular\dot{P cluster} $ imply Terzan 5 fundamentally open square bracket different 1 4 0 closing magnetic square bracket field strengths and ages . period \ [hline Treating { fi eld strength }ˆ{ the p u l s a r } B \ varpropto ( as { P } {\dot{P}}ˆ{ a } { ) } r o tLiving a t i n g Reviews{ / in{ Relativity1 } 2 and the }ˆ{ magnetic } { characteristic }ˆ{ d i p o l e }ˆ{ , } { age }ˆ{ 1 } {\tau { c }}ˆ{ may } { = P/ht tp} :ˆ slash{ show slash} w{ w( w period 2 l\ idot vi ngre{P} v i e). w s period}ˆ{ or[ g slash 2 } lrr hyphen2 6 2008 ] hyphen that 8 { Lines } o f the { constant }ˆ{ s u r f a c e } B magnetic { and \tau { c } are }\ ]

\noindent drawn on Figure 3 , from which we infer typical values of $ 1 0 ˆ{ 1 2 }$ G and $ 1 0 ˆ{ 7 }$ yr for the normal pulsars

\ begin { a l i g n ∗} \ r u l e {3em}{0.4 pt } \end{ a l i g n ∗}

$ 1 { Like }$ most astronomical sources , pulsars are named after their position in the sky . \quad Those pulsars discovered prior to the mid 1 990 s are named based on the Besselian equatorial coordinate system ( B 1 950 ) and have a B prefix

\noindent followed by their right ascension and declination . More recently discovered pulsars follow the Julian ( J 2000 ) epoch . Pulsars in globular clusters , where the positional designation is not unique , have additional characters to distinguish them . For example PSR J $ 1 748 − 2446 $ ad in the globular cluster Terzan 5 [ 1 4 0 ] .

\ [ \ r u l e {3em}{0.4 pt }\ ]

\noindent Living Reviews in Relativity

\noindent http : //www. l i vi ngrev i ews . org/ lrr − 2008 − 8 BinaryBinary and and Millisecond Millisecond Pulsars Pulsars .... 7 7 \noindenthline Binary and Millisecond Pulsars \ h f i l l 7 Figure 3 : The P endash P-dotaccent diagram showing the current sample of radio pulsars period Binary pulsars are highlighted \ [ by\ r open u l e { circles3em}{ period0.4 pt Lines}\ ] of constant magnetic field open parenthesis dashed closing parenthesis comma characteristic age open parenthesis dash hyphenFigure dotted 3 : The closingP – parenthesisP˙ diagram and showing spin hyphenthe current down sample of radio pulsars . Binary pulsars are highlighted by energyopen loss circles rate . open Lines parenthesis of constant magnetic dotted closing field ( dashedparenthesis ) , characteristic are also shown age ( period dash - dotted ) and spin - down \noindenthlineenergy lossFigure rate ( 3 dotted : The ) are also $P$ shown−− . $ \dot{P} $ diagram showing the current sample of radio pulsars . Binary pulsars are highlighted byLiving open Reviews circles in Relativity . Lines of constant magnetic field ( dashed ) , characteristic age ( dash − dotted ) and spin − down ht tp : slash slash w w .. w period l i vi ngrev i e w s period org slash lrr hyphen 2008 hyphen 8 \noindent energy loss rate ( dotted ) are also shown . Living Reviews in Relativity \ [ \ r u l e {3em}{0.4 pt }\ ] ht tp : / / w w w . l i vi ngrev i e w s . org / lrr - 2008 - 8

\ hspace ∗{\ f i l l } Living Reviews in Relativity

\ hspace ∗{\ f i l l } ht tp : / / w w \quad w. l i vi ngrev i ews . org / lrr − 2008 − 8 8 ....8 Duncan R period Lorimer Duncan R . Lorimer \noindenthline 8 \ h f i l l Duncan R . Lorimer and 1 0 to the power of 8 G and 1 0 to the power of 9 yr for the millisecond pulsars period For the rate of loss of kinetic energy comma sometimes\ [ \ r u l e {3em}{0.4 pt }\ ] 8 9 calledand the 10 spinG and hyphen 10 yr down for luminositythe millisecond comma pulsars we have . For E-dotaccent the rate of lossvarpropto of kinetic dotaccent-P energy , sometimes slash P to the power of 3 period .. The lines ˙ ˙ 3 ˙ of constantcalled E-dotaccent the spin - down shown luminosity on Figure , 3 we have E ∝ P /P . The lines of constant E shown on Figure 3 indicate \noindentindicatethat thattheand most the $ most energetic 1 energetic 0 objects ˆ{ 8 objects} are$ the G are and very the very young $ 1 young normal 0 normal ˆ{ pulsars9 pulsars}$ and yr the and for most the the most rapidly millisecond rapidly spinning millisecond pulsars . For the rate of loss of kinetic energy , sometimes spinningpulsars millisecond . pulsars period \noindentThe mostThe rapidlycalled most rapidly rotating the rotatingspin neutron− neutrondown star currently luminosity star currently known comma ,known we have ,.. J J 1 1748 748 $ \ minus−dot2446{E 2446}\ ad , ad withvarpropto comma a spin with rate a ofspin\dot 7 1 rate{ 6P} of / P ˆ{ 3 } . $7 1\ 6Hzquad Hz , resides commaThe in resides lines the globular in of the constant globular cluster Terzan cluster $ \ 5Terzandot [ 1{ 4E 0 5} ] open .$ As shownsquare discussed bracket on Figure by 1 Lattimer 4 0 closing 3 & squarePrakash bracket [ 2 0 period 6 ] , .. As discussed by Lattimer indicate that the most energetic objects are the very young normal pulsars and the most rapidly ampersandthe limiting Prakash ( open non - square rotating bracket ) radius 2 .. of 0 a6 1closing.4M neutron square bracket star with comma this period is 1 4 . 3 km . If a precise spinningthemeasurement limiting millisecond open for parenthesis the pulsar pulsars non mass hyphen can . be rotating made through closing parenthesis future timing radius measurements of a 1 period ( Section 4 M sub 4 odot ) , then neutron this star with this period is 1 4 periodpulsar 3 km could period be If a a very precise useful probe of the equation of state of super dense matter . Themeasurement mostWhile rapidly forthe the hunt rotating pulsar for more mass neutron rapidly can be made rotating star through pulsars currently future and timing even known “ measurements sub , -\ millisecondquad J open $pulsars parenthesis 1 ”748 contin Section− - ues..2446 4 ,closing $ parenthesis ad , with comma a spin rate of 7then 1 6and this Hz most pulsar , resides neutron could star be in a equations very the useful globular of probe stateallow of cluster the higher equation Terzan spin of rates state 5 than [of1 super 7 4 1 0 6 dense Hz ] ., matterit\quad has been periodAs suggested discussed [ 3 8 by ] Lattimer $ \& $ PrakashWhilethat the [ the 2hunt dearth\quad for more of0 pulsars 6 rapidly ], with rotatingP < 1. pulsars5 ms is and caused even by quotedblleft gravitational sub wave hyphen emis millisecond - pulsars quotedblright .. contin hyphen uession comma from and Rossby most -neutron mode instabilities star equations [ 5 of] . state The mostallow rapidly higher spin rotating rates pulsars than 7 [ 1 1 6 Hz 4 0comma ] are predominantly it has been \noindentsuggestedmembers openthe of squarelimitingeclipsing bracket binary ( non 3 systems 8 closing− rotating which square could bracket ) radiushamper that their the ofa dearth detection $1 of pulsars in . radio with4 surveys M P less{\ . 1Indepenodot period} -5$ dent ms neutron is caused by star gravitational with this period is 1 4 . 3 km . If a precise wave emisconstraints hyphen on the limiting spin frequencies of neutron stars come from studies of millisecond X - ray binaries \noindentsion[from 6 6 ] which Rossbymeasurement are hyphen not thought mode forthe toinstabilities be pulsar selection openmass - effect square can limited bracket be [ made 6 7 5 ] closing . Thisthrough analysissquare future bracket does not periodtiming predict The measurementsa significant most rapidly rotating ( Section pulsars\quad open 4 ) , squarethenpopulation bracket this 1pulsar .. of 4 neutron0 closing could stars square be with a bracket very spin rates are useful predominantly in excess probe of 730 of Hz the . equation of state of super dense matter . members2 . 3 of eclipsing Pulse binary profiles systems which could hamper their detection in radio surveys period Indepen hyphen WhiledentPulsars theconstraints hunt are weak on for the radio more limiting sources rapidly spin . frequencies rotating of Measured neutron pulsars intensities stars and come even at from 1 . ‘‘4studies GHz sub vary of− millisecondmillisecond between 5µ Jy and pulsars 1 Jy ’’ \quad contin − −26 −2 −1 uesX hyphen( , 1 and Jy ray≡ most10 binaries neutronW open m Hz square star). As equationsbracket a result 6 6 closing, of even state with square a allow bracketlarge radio higher which telescope are spin not , thoughtrates the coherent than to be addition selection7 1 6 Hz of hyphen , it effect has limited been open squaresuggestedmany bracket hundreds 6 [ 7 3 closing 8 or ] eventhat square thousands the bracket dearth period of pulses of This is pulsars usuallyanalysis required does with not in $ orderP < to produce1 . a detectable 5 $ ms “ integrated is caused by gravitational wave emis − 00 predictprofile a significantRemarkably population , although of neutron the individualstars with spinpulses rates vary in dramatically excess of 730 , Hz the period integrated profile at a given \noindent2 period 3sion ... Pulse from profiles Rossby − mode instabilities [ 5 ] . The most rapidly rotating pulsars [ 1 \quad 4 0 ] are predominantly membersPulsarsobserving are of weak eclipsing frequency radio sources is very binary stableperiod systems and .... Measured can be which thought intensities could of as ata hamper fingerprint 1 period their 4 of GHz the detectionvary neutron between star in’ 5 s mu emission radio Jy and beam surveys 1 Jy . Indepen − dentopen.constraints Profile parenthesis st ability 1 Jy on is equiv of the key 1 0limiting importance to the power inspin pulsar of minus frequencies timing 2 6 measurementsW m to of the neutron power discussed of stars minus in Section 2 come Hz to from the4 . power studies of minus of 1 millisecond closing parenthesis periodX − ray As aThe result binaries selection comma [of even 6 integrated 6 with ] which a large profiles are radio in not telescope Figure thought comma 4 shows to thea be coherentrich selection diversity addition in− morphologyeffect limited including [ two 6 7 ] . This analysis does not predictof manyexamples hundredsa significant of “or interpulses even thousands population ” – of a pulses secondary of is neutron usually pulse required separated stars in with by order about spin to produce 1 80 rates degrees a detectable in from excess the main of pulse730 Hz . . quotedblleftOne interpretation integrated for profileRow this phenomenon 1 quotedblright is that Row the two 2 period pulses profile originate comma from although opposite the magnetic individual poles pulses of the vary dramatically comma the\noindent integratedneutron2 star . 3 ( see\quad howeverPulse [ 2 profiles 4 9 ] ) . Since this is an unlikely viewing angle , we would expect interpulses profileto be at a givenrare phenomenon observing frequency . Indeed is , very the fraction stable and of known can be pulsars thought in of which as a fingerprint interpulses of are the observed in their \noindentneutronpulse star profilesPulsars quoteright is only are s a emission few weak percent radio beam [ 1 period 9 sources 4 ] . Profile Recent . st\ h abilitywork f i l l [ 3isMeasured 9 of 2 key ] on importance the intensities statistics in of pulsar interpulses at timing 1 . among measurements 4 GHz the vary between $ 5 \mudiscussed$known Jy in and population Section 1 Jy .. show 4 period that the interpulse fraction depends inversely on pulse period . The origin of this Theeffect selection could of be integrated due to alignment profiles in between Figure .. the 4 spinshows a rich diversity in morphology including 7 \noindenttwoand examples magnetic( 1 of Jy .. axis quotedblleft $ of\ neutronequiv interpulses stars1 on 0 timescales quotedblright ˆ{ − of2 order .. endash6 10}$yr aW [ secondary 3 9$ 2 m ] . ˆ{ pulse − separated2 If} weHz take by ˆ about{ this − result 1 801 } degrees at ) from . $ the As main a result , even with a large radio telescope , the coherent addition ofpulse manyface period value hundreds .. , One and interpretation or assume even that thousands for all this millisecond phenomenon of pulsespulsars is thatdescend is the usually from two pulses normal required originate pulsars in from( Section order oppositeto 2 . 6 produce ) , then a detectable ‘‘magnetic integratedthe implication poles of the$ is\ l that eneutron f t millisecond. pro star f i open l pulsars e \ parenthesisbegin should{ array besee preferentially}{ howeverc} ’’ open\\ aligned square. \end rotators bracket{ array . 2 However ..}Remarkably 4 9 closing , their square\ appearsright bracket. ,closing $ although parenthesis the individual pulses vary dramatically , the integrated periodprofileto Since be atthis no astrong is given an unlikely evidence observing viewing in favour angle frequency of thiscomma expectation we is very based stable on the and pulse can profile be morphology thought of of millisecond as a fingerprint of the neutronwouldpulsars expect star [ 2 interpulses ’ 0 s3 ] emission . to be a rare beam phenomenon . Profile period st Indeed ability comma is theof fractionkey importance of known pulsars in pulsar in which timing measurements discussedinterpulsesTwo are incontrasting observed Section phenomenological in\ theirquad pulse4 . profiles models is only have a been few proposedpercent open to explain square the bracket observed 1 9 4pulse closing shapes square . bracketThe period .. Recent work open square“ core bracket and cone 3 9 ” 2 closing model square [ 3 1 0 bracket ] depicts on the beam as a core surrounded by a series of Thethe selectionnested statistics cones of ofinterpulses . integrated Alternatively among , the profiles the known “ patchy population in beam Figure ” show model\quad that [ the 24 interpulseshows 4 3 , 1a 2 fraction rich 8 ] has diversity depends the beam populated in morphology including twoinversely examplesby a series on pulse of of randomly period\quad period -‘‘ distributed interpulses.. The origin emitting of this ’’ regions\ effectquad . could Recent−− a be work secondary due suggeststo alignment that pulse between the separated observational the spin by data about can 1 80 degrees from the main pulseandbe magnetic .better\quad explained axisOne of neutron interpretation by a hybrid stars onempirical timescales for model this of depictedorder phenomenon 1 0 in to Figure the power 5is thatwhich of 7 yr employs the open two square patchy pulses bracket beams originate 3 in 9 a 2 core closing from square opposite bracket period ....magnetic If weand take conepoles this structure result of at the [ 1 7 9neutron ] . star ( see however [ 2 \quad 4 9 ] ) . Since this is an unlikely viewing angle , we wouldface value expectA key comma feature interpulses .. of and this assume new tomodel that be all is a that millisecond rare the phenomenonemission pulsars height descend . of Indeed young from pulsars normal , the is pulsars radically fraction open different parenthesis of known from that Section pulsars .. 2 in period which 6 closing parenthesisinterpulsesof the comma older are population observed . Monte in their Carlo simulationspulse profiles [ 1 7 9 is ] using only this a phenomenological few percent [ model 1 9 appear 4 ] . to\quad Recent work [ 3 9 2 ] on thethenbe statistics the very implication successful of is at interpulses that explaining millisecond the among rich pulsars diversity the should known of be pulse preferentially population shapes . aligned Further show rotators work that in period this the area interpulse However is necessary comma fraction to depends inverselytheirunderstand appears on to the pulse be origin no strong period of this evidence model . \quad in , and favourThe improve of origin this our expectation understanding of this based effect of on the could pulse profile be due to alignment between the spin morphology of millisecond pulsars open square bracket 2 .. 0 3 closing square bracket period \noindentTwo contrastingand magnetic phenomenological axis ofmodels neutron have been stars proposed on timescales to explain the of observed order pulse $ 1 0 ˆ{ 7 }$ yr [ 3 9 2 ] . \ h f i l l If we take this result at shapes period .. The .. quotedblleft core and cone quotedblright .. model open square bracket 3 1 0 closing square bracket depicts the beam \noindentLivingf Reviews a c e value in Relativity , \quad and assume that all millisecond pulsars descend from normal pulsars ( Section \quad 2 . 6 ) , as a coreht surrounded tp : / / by w a w series w . of l i vi ngre v i e w s . or g / lrr - 2008 - 8 thennested the cones implication period .. Alternatively is that comma millisecond the .. quotedblleft pulsars patchy should beam be quotedblright preferentially .. model aligned open square rotators bracket 2 . .. However4 3 comma , .. 1their 2 .. 8 closing appears square to bracket be no has strong the beam evidence populated in by a favour of this expectation based on the pulse profile morphologyseries of randomly of millisecond hyphen distributed pulsars emitting [ 2 regions\quad period0 3 Recent ] . work suggests that the observational data can be better explained by a hybrid empirical model depicted in Figure 5 .. which employs patchy Twobeams contrasting in a core and phenomenological cone structure open square models bracket have 1 been7 9 closing proposed square bracket to explain period the observed pulse shapesA key feature . \quad of thisThe new\quad model‘‘ is that core the and emission cone height ’’ \ ofquad youngmodel pulsars [ is 3 radically 1 0 ] different depicts the beam as a core surrounded by a series of from that of the older population period .. Monte Carlo simulations .. open square bracket 1 7 9 closing square bracket using this phenomenological\noindent nested cones . \quad Alternatively , the \quad ‘‘ patchy beam ’’ \quad model [ 2 \quad 4 3 , \quad 1 2 \quad 8 ] has the beam populated by a seriesmodel appear of randomly to be very− successfuldistributed at explaining emitting the rich regions diversity . of Recent pulse shapes work period suggests .. Further that work the observational data canin this be area better is necessary explained to understand by a hybrid the origin empirical of this model model comma depicted and improve in our Figure understanding 5 \quad of which employs patchy beamshline in a core and cone structure [ 1 7 9 ] . Living Reviews in Relativity A keyht tp feature : slash slash of w this w w period new model l i vi ngre is v that i e w s the period emission or g slash height lrr hyphen of 2008 young hyphen pulsars 8 is radically different from that of the older population . \quad Monte Carlo simulations \quad [ 1 7 9 ] using this phenomenological model appear to be very successful at explaining the rich diversity of pulse shapes . \quad Further work in this area is necessary to understand the origin of this model , and improve our understanding of

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\noindent Living Reviews in Relativity

\noindent http : //www. l i vi ngrev i ews . org/ lrr − 2008 − 8 BinaryBinary and and Millisecond Millisecond Pulsars Pulsars .... 9 9 \noindenthline Binary and Millisecond Pulsars \ h f i l l 9 Figure 4 : A variety of integrated pulse profiles taken from the available literature period References : Panels a comma \ [ b\ commar u l e {3em d comma}{0.4 f pt open}\ square] bracket 1 2 4 closing square bracket comma Panel c open square bracket 2 3 closing square bracket comma PanelsFigure e comma 4 : g commaA variety i openof integrated square pulse bracket profiles 2 0 3taken closing from square the available bracket literature comma . Panel References h open : Panels square a , bracket b , d , f3 1 closing square bracket period[ Each 1 2 4 profile ] , Panel represents c [ 2 3 ] 360, Panels degrees e , g of , i rotational [ 2 0 3 ] , Panel h [ 3 1 ] . Each profile represents 360 degrees of rotational \noindentphasephase period .Figure These These profiles 4profiles : are A arefreely variety freely available available of from integrated froman online an online database pulse database [ 3profiles 7 8 ]open . square taken bracket from 3 the 7 8 closing available square bracketliterature period . References : Panels a , bhline , d , f [ 1 2 4 ] , Panel c [ 2 3 ] , Panels e , g , i [ 2 0 3 ] , Panel h [ 3 1 ] . Each profile represents 360 degrees of rotational phaseLiving . Reviews These in profiles Relativity are freely available from an online database [ 3 7 8 ] . ht tp : slash slash w w .. w period l i vi ngrev i e w s period org slash lrr hyphen 2008 hyphen 8 \ [ \ r u l e {3em}{0.4 pt }\ ] Living Reviews in Relativity ht tp : / / w w w . l i vi ngrev i e w s . org / lrr - 2008 - 8

\ hspace ∗{\ f i l l } Living Reviews in Relativity

\ hspace ∗{\ f i l l } ht tp : / / w w \quad w. l i vi ngrev i ews . org / lrr − 2008 − 8 1 01 .... 0 Duncan R period Lorimer Duncan R . Lorimer \noindenthline 1 0 \ h f i l l Duncan R . Lorimer Figure 5 : A recent phenomenological model for pulse shape morphology period The neutron star is depicted by \ [ the\ r u grey l e { sphere3em}{ and0.4 pt only}\ a] single magnetic pole is shown for clarity period .. Left : .. a young pulsar with emission fromFigure a patchy 5 : conalA recent ring phenomenological at high altitudes model from for the pulse surface shape of morphology the neutron . star The periodneutron .. star Right is depicted : .. an by older the pulsar grey in whichsphere emission and only emanates a single magnetic from a pole series is ofshown patchy for clarity rings over . a Left range : of a altitudes young pulsar period with .. emission Centre : from .. schematic a patchy \noindentrepresentationconal ringFigure at of high the 5 altitudes change : A recent in from emission the phenomenological surface height of with the neutron pulsar age star model period .for Right Figure pulse : designed an shape older by pulsar Aris morphology Karastergiou in which emission . Theand neutron star is depicted by theS imon greyemanates Johnston sphere from open a andseries square only of patchy bracket a singlerings 1 7 over 9 closing magnetic a range square of altitudes pole bracket is . period shown Centre for : clarity schematic . representation\quad Left of the : \quad a young pulsar with emission fromhlinechange a patchy in emission conal height ring with at pulsar high age . altitudes Figure designed from by Aris the Karastergiou surface and of theS imon neutron Johnston [ star 1 7 9 ] . . \quad Right : \quad an older pulsar inLiving which Reviews emission in Relativity emanates from a series of patchy rings over a range of altitudes . \quad Centre : \quad schematic representationht tp : slash slash wof w the w period change l i vi in ngre emission v i e w s period height or g with slash lrr pulsar hyphen age 2008 . hyphen Figure 8 designed by Aris Karastergiou and S imon Johnston [ 1 7 9 ] . Living Reviews in Relativity \ [ \ r uht l e tp{3em :}{ /0.4 / w pt w}\ w .] l i vi ngre v i e w s . or g / lrr - 2008 - 8

\noindent Living Reviews in Relativity

\noindent http : //www. l i vi ngrev i ews . org/ lrr − 2008 − 8 BinaryBinary and and Millisecond Millisecond Pulsars Pulsars .... 1 1 1 1 \noindenthline Binary and Millisecond Pulsars \ h f i l l 1 1 the shape and evolution of pulsar beams and fraction of sky they cover period This is of key importance \ [ to\ r the u l e results{3em}{ of0.4 population pt }\ ] studies reviewed in Section 3 period 2 period 2 periodthe shape 4 .. The and pulsar evolution distance of pulsar scale beams and fraction of sky they cover . This is of key importance to the Quantitativeresults of estimatespopulation of studies the distance reviewed to each in Section pulsar 3 can . 2 be . made from the measurement of pulse \noindentdispersion2 . 4the endash The shape the pulsar delay and in evolution distance pulse arrival scale of times pulsar across abeams finite bandwidth and fraction period Dispersionof sky they occurs cover because . This is of key importance tothe theQuantitative group results velo city estimates of of the population pulsed of the radiation distance studies to through each reviewed pulsar the ionised can inbe component made Section from of the 3 the . measurement interstellar 2 . medium of pulse dispersion is frequency– the delay dependent in pulse period arrival .. times As shown across in a finiteFigure bandwidth 6 comma pulses. Dispersion emitted occurs at lower because radio the frequencies group velo travel city of \noindentslowerthe through pulsed2 . radiation the 4 \ interstellarquad throughThe medium pulsar the ionised comma distance component arriving scale laterof the than interstellar those emitted medium at is higher frequency frequencies dependent period . As Figureshown 6 : inPulse Figure dispersion 6 , pulses shown emitted in this at Parkes lower radio observation frequencies of the travel 1 28 slower ms pulsar through B 1 356 the endash interstellar 60 period medium The , dispersion \noindentmeasurearriving isQuantitative 295 later cm than to the those power estimates emitted of endash at higher 3 of pc the period frequencies distance .. The . quadratic to each frequency pulsar dependence can be of made the dispersion from the delay measurement is clearly visible of period pulse d iFigure s pFigure e r s provided i o n 6−− : Pulse bythe Andrew dispersion delay Lyne in shown period pulse in this arrival Parkes observation times acrossof the 1 28 a ms finite pulsar B bandwidth 1 356 – 60 . The . Dispersion dispersion occurs because −−3 theQuantitatively groupmeasure isvelo295cm comma city thepc of delay . the Capital The pulsed quadratic Delta radiation frequency t in arrival dependence through times between of the the adispersion ionised high frequency delay component is nuclearly sub visible h of i and the . a Figure low interstellar frequency medium ishline frequencyprovided by Andrew dependent Lyne . . \quad As shown in Figure 6 , pulses emitted at lower radio frequencies travel slower through the interstellar medium , arriving later than those emitted at higher frequencies . Living Reviews inQuantitatively Relativity , the delay ∆t in arrival times between a high frequency νhi and a low frequency ht tp : slash slash w w .. w period l i vi ngrev i e w s period org slash lrr hyphen 2008 hyphen 8 \noindent Figure 6 : Pulse dispersion shown in this Parkes observation of the 1 28 ms pulsar B 1 356 −− 60 . The dispersion

\noindent measure is $ 295 cm ˆ{ −− 3 }$ pc . \quad The quadraticLiving Reviews frequency in Relativity dependence of the dispersion delay is clearly visible . Figure provided by Andrewht tp Lyne : / . / w w w . l i vi ngrev i e w s . org / lrr - 2008 - 8

\ hspace ∗{\ f i l l } Quantitatively , the delay $ \Delta t $ in arrival times between a high frequency $ \nu { h i }$ and a low frequency

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\ hspace ∗{\ f i l l } Living Reviews in Relativity

\ hspace ∗{\ f i l l } ht tp : / / w w \quad w. l i vi ngrev i ews . org / lrr − 2008 − 8 1 21 .... 2 Duncan R period Lorimer Duncan R . Lorimer \noindenthline 1 2 \ h f i l l Duncan R . Lorimer nu sub lo pulse can be shown open square bracket 2 2 6 closing square bracket to be \ [ Equation:\ r u l e {3em open}{ parenthesis0.4 pt }\ ] 1 closing parenthesis .. Capital Delta t = 4 period 1 5 ms times bracketleftbigg to the power of open parenthesis to the powerνlo pulse of hline can be sub shown GHz [ to 2 2the 6] power to be of nu sub lo closing parenthesis minus 2 minus open parenthesis nu sub hi divided by GHz to the power of closing parenthesis minus 2 bracketrightbigg times parenleftbigg DM divided by cm to the power of minus 3 pc parenrightbigg comma \noindentwhere the dispersion$ \nu { measurel o }$ pulse can be shown [ 2 2 6 ] to be ν ) νhi ) DM Equation: open parenthesis∆t = 2 closing4.15ms parenthesis× [( ..lo DM =− 2 n− sub( e from− 02] to× integral( to the), power of d dl comma(1) GHz GHz cm−3pc \ beginis the{ integrateda l i g n ∗} column density of electrons comma n sub e comma out to the pulsar at a distance d period This equation \Delta t = 4 . 1 5 ms \times [ ˆ{ ( ˆ{\ r u l e {3em}{0.4 pt }}}ˆ{\nu { l o } ) } { GHz } maywhere be solved the dispersion for d given measure a measurement of DM and a model of the free electron distribution − calibrated2 − from( the\ f r.. a 1 c {\ 0 ornu so pulsars{ hi with}}{ independentGHz }ˆ{ ) ..} distance − estimates2 ] and\times measurements( \ f r a c { DM }{ cm ˆ{ − 3 } pc } ),of scattering\ tag ∗{$ for ( lines 1 of sight ) $ towards} various Galactic and extragalactic sources open square bracket 3 6 4 comma 3 9 0 closing square \end{ a l i g n ∗} 0 bracket period .. A DM = ne R d dl, (2) recent model of this kind comma known as NE 200 1 open square bracket 8 4 comma .. 8 5 closing square bracket comma provides distance \noindent where the dispersion measure estimatesis the with integrated an average column density of electrons , ne, out to the pulsar at a distance d. This equation uncertaintymay be solved of thicksim for d 30given percent a measurement period of DM and a model of the free electron distribution \ beginBecausecalibrated{ a l thei g n electron∗} from the density 1 0 modelsor so pulsars are only with as independent good as the scope distance of their estimates input data and measurements allow comma one of scattering DMshouldfor = linesbe nmindful of{ sighte of} towardsˆ systematic{ 0 } various{\ uncertaintiesint Galacticˆ{ d and period}} extragalacticdl For example , \ sourcestag comma∗{$ [ 3 ( studies 6 4 ,2 3 of 9 0 the) ]$ . Parkes} A multibeam pulsar \enddistribution{ recenta l i g n ∗} model open of square this kind bracket , known 1 9 9 commaas NE 200 2 .. 1 2 [ 4 8 closing 4 , 8 square 5 ] , provides bracket suggest distance that estimates the NE with 2001 an model average underestimates the distances of pulsarsuncertainty close of ∼ 30%. \noindentto the Galacticis the planeBecause integrated period the electron .. This column suspicion density densitymodels has been are dramaticallyof only electrons as good confirmed as the $ scope , recently ofn their{ bye input an} extensive data, $ allow out , to one the pulsar at a distance $ danalysisshould . $ open be This squaremindful equation bracket of systematic 1 2 0 closing uncertainties square bracket . For example of pulsar , studies DMs and of themeasurements Parkes multibeam of Galactic pulsar H alpha distri- emission period This work shows thatbution the [ 1 9 9 , 2 2 4 ] suggest that the NE 2001 model underestimates the distances of pulsars close to the \noindentdistributionGalacticmay of plane Galactic be . solved This free suspicion electrons for $ hasto d be $been exponential given dramatically a in measurement form confirmed with a recentlyscale of DMheight by and an of extensive1 a 830 model sub analysis minus of the 2 [ 5 1 0 free 2 to 0 ]the electron power of plus distribution 1 2 0 pc period of pulsar DMs and measurements of Galactic H α emission . This work shows that the \noindent calibrated from the \quad 1 0 or so pulsars with independent +120\quad distance estimates and measurements Thisdistribution value is a factor of Galactic of two free higher electrons than previouslyto be exponential thought in period form with .. A a revised scale height version of of 1830 the− NE250 pc 200 . 1This value ofmodel scatteringis a which factor t of akes twofor into higher lines account than of these previously sight and towards other thought developments . various A revised is Galactic currently version ofin and thepreparation NEextragalactic 200 1open model square which sources bracket t akes 7 [ 9 3 closing 6 4 square , 3 9 bracket 0 ] . \quad A period into account these and other developments is currently in preparation [ 7 9 ] . \noindent2 period2 . 5 5recent .. Pulsars Pulsars model in binary in of binary systems this systemskind , known as NE 200 1 [ 8 4 , \quad 8 5 ] , provides distance estimates with an average uncertaintyAs canAs can be inferred be inferred of from $ from\sim Figure Figure ..30 1 comma 1\ ,%. only only a few$ a few percent percent of all of known all known pulsars pulsars in the in theGalactic Galactic disk disk are membersare membersof binary of binary systems systems . Timing period measurements .. Timing measurements ( see Section open 4 parenthesis ) place useful see constraintsSection .. 4 on closing the masses parenthesis of the place useful constraints on the\ hspacecompanions∗{\ f i l l } whichBecause , often the supplemented electron by density observations models at other are wavelengths only as , good tell as the scope of their input data allow , one massesus a of great the companions deal about their which nature comma . often supplemented The present by observations sample of orbiting at other companions wavelengths are comma either tell white \noindentus adwarfs greatshould deal , main about sequence be their mindful naturestars or period of other systematic neutron.... The presentstars uncertainties . sample Two of notable orbiting .hybrid For companions example systems are are ,either thestudies white “ ofplanet the Parkes multibeam pulsar distributiondwarfspulsars comma ” B main 1257 [ 1 + sequence 9 12 9 and , 2B stars 1620\quad or− other262. 4 neutronPSR ] suggest B 1257 stars + period 12 that is a .... 6 the . Two 2 -NE ms notable 2001 pulsar hybrid model accompanied systems underestimates by are at the least .... three quotedblleft the distances planet of pulsars close topulsars theterrestrial quotedblrightGalactic - mass plane bodies B 1 257 .[ 4 plus\ 0quad 4 1 , 2 and9This 3 , B 4 1 0 suspicion 620 3 ] while minus B 26 1620 has period− been26 .., PSRan dramatically 1 1B - 1 ms 257 pulsar plus 1 in confirmed 2 the is a globular 6 period recently cluster 2 hyphen ms by pulsar an extensive accompanied analysis [ 1 2 0 ] of pulsar DMs and measurements of Galactic H $ \alpha $ emission . This work shows that the by at leastM 4 , is part of a triple system with a 1 – 2MJupiter planet [ 3 7 0 , 1 6 , 3 6 9 , 3 3 8 ] orbiting a neutron threestar terrestrial – white hyphendwarf stellar mass binary bodies system open square . The bracket current 4 0 limits 4 comma from 2 pulsar 9 3 comma t iming 4 0 favour 3 closing a roughly square 45 bracket - yr while B 1 620 minus 26 comma\noindentmildly an 1 1distribution - hyphen eccentric ms (e pulsar∼ 0. of16) in Galactictheorbit globular with semi free cluster - major electrons axis ∼ 25 to AU be . Despite exponential several tentative in form claims with over a the scale height of $ 1 830M ˆ 4{years comma+ , no 1 is other part 2 of convincing a 0 triple} { system − cases2 for with planetary 5 a 1 endash 0 } companions$ 2 pc M sub . Jupiter to pulsars planet exist open . Orbiting square bracket companions 3 7 0 are comma much .. 1 6 comma 3 6 9 comma ..This 3 3 8more closing value common square is a around bracket factor millisecond orbiting of two a neutron pulsars higher (∼ than80% of previously the observed sample thought ) . \quad A revised version of the NE 200 1 model which t akes into account these and other developments is currently in preparation [ 7 9 ] . starthan endash around white the dwarf normal stellar pulsars binary (. system1 %). period .. TheIn general current , limits binary from systems pulsar with t iming low - favour mass companions a roughly −5 45 hyphen(. 0.7M yr – mildly predominantly hyphen eccentric white dwarfs open ) parenthesis have essentially e thicksim circular 0 orbits period : 1 6 10 closing. e . parenthesis0.01. Binary orbit pulsars with semi hyphen major axis \noindent 2 . 5 \quad Pulsars in binary systems thicksimwith 25 AUhigh period - mass Despite companions several (& tentative1M – massive white dwarfs , other neutron stars or main sequence stars ) claimstend over to have the years more comma eccentric no orbits other, convincing0.15 . e . cases0.9. for planetary companions to pulsars exist period Orbiting \noindentcompanions2 . 6As are can Evolution much be more inferred of common normal from around and Figure millisecond millisecond\quad pulsars1 , pulsars only open parenthesisa few percent thicksim of 80 all percent known of the pulsars observed in sample the Galactic closing disk are parenthesismembersA simplified of binary version systems of the presently . \quad favouredTiming model measurements [ 3 9 , 1 1 0 ( , 3 see 3 9 , Section 2 ] to explain\quad the4 formation ) place of useful constraints on the massesthanthe around various of the the types companionsnormal of systems pulsars observedwhich open parenthesis , is often shown lesssimin supplemented Figure 1 percent7 . Starting closing by observations with parenthesis a binary period st at ar system other.... In , general a wavelengths neutron comma binary , tell systems with low hyphenstar is mass formed companions during the supernova explosion of the initially more massive star . From \noindentopenthe parenthesis virialus theorem a greatlesssim , in 0 deal periodthe absence about 7 M sub of their any odot other endashnature factors predominantly . ,\ theh f i binary l l The white will present dwarfsbe disrupted closing sample if parenthesis more of than orbiting have half theessentially companions circular are orbits either : 1 white 0 to thetotal power pre of - minussupernova 5 lesssim mass eis lesssim ejected 0 from period the 0 system 1 period during Binary the ( assumed symmetric ) explosion [ 1 4 2 \noindentpulsars, 3 with 6dwarfs ] . high In practice hyphen , main ,mass the sequence fraction companions of survivingstars open parenthesis or binaries other is gtrsimneutron also affected 1 M sub stars by odot the . endash magnitude\ h f i massive l l Two white notable dwarfs hybrid comma other systems neutron are stars the \ h f i l l ‘ ‘ planet or main \noindentsequence starspulsars closing ’’B parenthesis $1 tend 257 to have + more 1 eccentric 2$ orbits andB comma $1 0 period 620 1 5− lesssim26 e lesssim . $ 0 period\quad 9PSR period B $ 1 257 +2 period 1 2 6 $ .. Evolution i s a 6 of . normal 2 − ms and pulsar millisecond accompanied pulsars by at least threeLiving terrestrial Reviews in Relativity− mass bodies [ 404 , 293 , 403 ] whileB $1 620 − 26 , $ an 1 1 − ms pulsar in the globular cluster A simplifiedht tp : version / / w of w the w . presently l i vi favoured ngre v imodel e w open s . square or g / bracket lrr - 3 2008 9 comma - 8 .. 1 1 .. 0 comma 3 3 9 comma .. 2 closing square bracket to explain the formation of \noindentthe variousM4 types , of is systems part observed of a triple is shown system in Figure with 7 period a 1 ..−− Starting$ 2 with M a binary{ J u pst i tar e r system}$ comma planet [ 370 , \quad 1 6 , 3 6 9 , \quad 3 3 8 ] orbiting a neutron s ta a neutron r −− white star is formeddwarf during stellar the supernova binary system explosion . of\ thequad initiallyThe more current massive limits star period from .. pulsar From t iming favour a roughly 45the− virialyr mildly theorem− commaeccentric in the absence $ ( of any e other\sim factors0 comma . the 1 binary 6 will )$ be disrupted orbitwithsemi if more than− major a x i s $ \sim 25half $ theAU total . Despite pre hyphen several supernova tentative mass is ejected from the system during the .. open parenthesis assumed symmetric closing parenthesis claimsexplosion over open the square years bracket , no1 .. other 4 2 comma convincing .. 3 6 closing cases square for bracket planetary period In companions practice comma to the pulsars fraction of exist surviving . Orbiting binaries is alsocompanions affected by the are magnitude much more common around millisecond pulsars $ ( \sim 80 \% $ of the observed sample ) hline \noindentLiving Reviewsthan in around Relativity the normal pulsars $ ( \ l e s s s i m 1 \%). $ \ hfill In general , binary systems with low − mass companions ht tp : slash slash w w w period l i vi ngre v i e w s period or g slash lrr hyphen 2008 hyphen 8 \noindent $ ( \ lesssim 0 . 7 M {\odot }$ −− predominantly white dwarfs ) have essentially circular orbits $ : 1 0 ˆ{ − 5 }\ l e s s s i m e \ lesssim 0 . 0 1 .$ Binary pulsars with high − mass companions $ ( \ gtrsim 1 M {\odot }$ −− massive white dwarfs , other neutron stars or main sequence stars ) tend to have more eccentric orbits $ , 0 . 1 5 \ l e s s s i m e \ l e s s s i m 0 . 9 . $

\noindent 2 . 6 \quad Evolution of normal and millisecond pulsars

\noindent A simplified version of the presently favoured model [ 3 9 , \quad 1 1 \quad 0 , 3 3 9 , \quad 2 ] to explain the formation of the various types of systems observed is shown in Figure 7 . \quad Starting with a binary st ar system , a neutron star is formed during the supernova explosion of the initially more massive star . \quad From

\noindent the virial theorem , in the absence of any other factors , the binary will be disrupted if more than half the total pre − supernova mass is ejected from the system during the \quad ( assumed symmetric ) explosion [ 1 \quad 4 2 , \quad 3 6 ] . In practice , the fraction of surviving binaries is also affected by the magnitude

\ [ \ r u l e {3em}{0.4 pt }\ ]

\noindent Living Reviews in Relativity

\noindent http : //www. l i vi ngrev i ews . org/ lrr − 2008 − 8 BinaryBinary and and Millisecond Millisecond Pulsars Pulsars .... 1 3 1 3 \noindenthline Binary and Millisecond Pulsars \ h f i l l 1 3 and direction of any impulsive .. quotedblleft kick quotedblright .. velo city the neutron star receives at birth from a slightly \ [ asymmetric\ r u l e {3em explosion}{0.4 pt open}\ ] square bracket 1 4 2 comma .. 1 9 closing square bracket period Binaries that disrupt produce a high hyphen velocityand isolated direction neutron of any star impulsive “ kick ” velo city the neutron star receives at birth from a slightly asymmetric andexplosion an OB runaway [ 1 4 2 , star 1 open 9 ] . Binaries square bracket that disrupt 4 0 closing produce square a high bracket - velocity period isolated The high neutron probability star of disruption explains qualitatively why\noindent soand few anand OB runaway direction star [ of 4 0 any ] . The impulsive high probability\quad of disruption‘ ‘ kick explains ’ ’ \quad qualitativelyvelo city why the so few neutron normal star receives at birth from a slightly asymmetricnormalpulsars pulsars have explosion have companions companions [ 1. Those 4 period 2 , that Those\quad survive that1 9 willsurvive ] likely . willBinaries have likely high have that orbital high disrupt orbital eccentricities eccentricities produce due to a due the high violent− velocity isolated neutron star to theconditions violent conditions in the supernova in the supernova explosion explosion . There are period currently There four are currently known normal four known radio normal pulsars radio with massive \noindentpulsarsmain with sequenceand massive an companions OB main runaway sequence in eccentric star companions [ orbits 4 0 in which ] eccentric . The are examples orbitshigh which probability of binary are examples of of disruption binary explains qualitatively why so few normalsystemssystems pulsars which which survived havesurvived the companions thesupernova supernova explosion . explosion Those open that [ 1 square 6 9 survive , bracket 1 8 2 will1, 6 39 4comma likely 8 , 3 .. 4 1have 9 8 , 2 2 comma high 3 6 ] .. orbital . 3 4 Over 8 comma the eccentricities .. 3 4 9 comma due 2 .. 3 6 7−8 closingto thenext square violent 10 bracketyr after conditions period the .. explosion Over in the , the thenext neutron 1supernova 0 to the star power may explosion be of observable 7 hyphen . 8 There as yr a normal are radio currently pulsar spinning four knowndown normal radio pulsarsafterto the a period withexplosion& massiveseveral comma seconds main the neutron sequence. After star this may companionstime be , observable the energy in as output eccentric a normal of the radio star orbits pulsar diminishes spinningwhich to aare down point examples where it of binary to ano period longer gtrsim produces several significant seconds amounts period After of radio this emission time comma . the energy output of the star diminishes to a point \noindentwhere it nosystems longerFigure produces which 7 : significant survivedCartoon amountsshowing the varioussupernova of radio evolutionary emission explosion period scenarios [ involving 1 6 9 binary , \quad pulsars1 . 8 2 , \quad 3 4 8 , \quad 3 4 9 , 2 \quad 3 6 ] . \quad Over the next $ 1Figure 0 7 ˆ{ : ..7 Cartoon−For showing8 those}$ few various yr binaries evolutionary that remain scenarios bound , involving and in which binary the pulsars companion period is sufficiently massive afterFor those the few explosion binaries that , remain the neutron bound comma star and may in be which observable the companion as is a sufficiently normal radio massive pulsar spinning down tohline a period $ \ gtrsim $ several seconds . After this time , the energy output of the star diminishes to a point where it no longer produces significant amounts of radio emission . Living Reviews in Relativity Living Reviews in Relativity ht tp : slash slash w w .. w period l i vi ngrev i e w s period org slash lrr hyphen 2008 hyphen 8 \ centerline { Figure 7 : \quadht tpCartoon : / / w showingw w . various l i vi ngrev evolutionary i e w s . scenarios org / lrr - involving 2008 - 8 binary pulsars . }

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\ hspace ∗{\ f i l l } Living Reviews in Relativity

\ hspace ∗{\ f i l l } ht tp : / / w w \quad w. l i vi ngrev i ews . org / lrr − 2008 − 8 1 41 .... 4 Duncan R period Lorimer Duncan R . Lorimer \noindenthline 1 4 \ h f i l l Duncan R . Lorimer to evolve into a giant and overflow its Roche lobe comma the old spun hyphen down neutron star can gain a new \ [ lease\ r u l of e { life3em as}{ a0.4 pulsar pt }\ by accreting] matter and angular momentum at the expense of the orbital angularto evolve momentum into a giant of the and binary overflow system its Roche open lobe square , the bracket old spun 2 closing - down square neutron bracket star can period gain a The new term lease quotedblleft of recycled pulsar quotedblrightlife as a is pulsar oftenused by accreting to describe matter and angular momentum at the expense of the orbital angular momentum \noindentsuchof objects the binaryto period evolve system .. During into [ 2 ] . this Thea giant accretion term “ and recycled phase overflow comma pulsar ”the itsis oftenX hyphen Roche used rays to lobe describe produced , the such by old objects the spun fri .ct− ional Duringdown heating this neutron of the star can gain a new leaseinfallingaccretion of matter life phase onto as , the athe pulsar X neutron - rays produced by star accreting mean by that the such fri matter ct a ional system andheating is expected angular of the infalling to momentum be visible matter as at anonto the X the hyphen expense neutron ray star of the orbital angularbinarymean period momentum that .. such Two a ofclasses system the of is binary X expected hyphen system toray be binaries visible [ 2 relevant as ] an . 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At at the face end value of the comma spin these- up phase parameters , the secondary suggest that sheds the its companion outer layers is \noindentalsoto a becomeneutronof thea star white comma pulsar dwarf and in and orbitthe its system around companion appears a rapidly to tobe spinning a be younger $millisecond 1 version . of 25 the double M {\ pulsarodot period}$ Despite and $ 1 . 37 M {\odot }$ respectivelyintensive searches [ 1 comma 8 0 ]no . pulsations We note from , howeverthe companion , st ar open parenthesis expected to be a recycled radio pulsar closing parenthesis have so far been observed open square bracket 2 3 2 closing square bracket period This could be due to unfavourable beaming and slash or intrinsic\noindent radiothat the pulsar exhibits significant amounts of timing noise ( see Section \quad 4 . 3 ) , making the analysis of theLiving system Reviews far in Relativity from trivial . Taken at face value , these parameters suggest that the companion is faintnessht tp period : / Continued / w w w . searches l i vi for ngre radio v pulsations i e w s .from or these g / companions lrr - 2008 are - 8strongly encouraged comma alsohowever a neutron comma as star geodetic , andprecession the maysystem make appears their radio to beams be a visible younger in future version years period of the double pulsar . Despite intensive2 period 6 period searches 2 .. Low , no hyphen pulsations mass systems from the companion st ar ( expected to be a recycled radio pulsar ) The companion in a low hyphen mass X hyphen ray binary evolves and transfers matter onto the neutron star on \noindenta much longerhave timescale so far comma been spinning observed it up [ to 2 periods 3 2 ] as . short This as acould few ms be open due square to bracketunfavourable 2 closing square beaming bracket and period / or .. intrinsic Tidal radio forcesfaintness during . Continued searches for radio pulsations from these companions are strongly encouraged , howeverthe accretion , as process geodetic serve to precession circularize the may orbit make period their At the radio end of thebeams spin visiblehyphen up in phase future comma years the secondary . sheds its outer layers to become a white dwarf in orbit around a rapidly spinning millisecond \noindenthline 2 . 6 . 2 \quad Low − mass systems Living Reviews in Relativity \noindentht tp : slashThe slash companion w w w period in l a i vi low ngre− vmass i e w sX period− ray or gbinary slash lrr evolves hyphen 2008 and hyphen transfers 8 matter onto the neutron star on a much longer timescale , spinning it up to periods as short as a few ms [ 2 ] . \quad Tidal forces during the accretion process serve to circularize the orbit . At the end of the spin − up phase , the secondary sheds its outer layers to become a white dwarf in orbit around a rapidly spinning millisecond

\ [ \ r u l e {3em}{0.4 pt }\ ]

\noindent Living Reviews in Relativity

\noindent http : //www. l i vi ngrev i ews . org/ lrr − 2008 − 8 BinaryBinary and and Millisecond Millisecond Pulsars Pulsars .... 1 5 1 5 \noindenthline Binary and Millisecond Pulsars \ h f i l l 1 5 pulsar period This model has gained strong support in recent years from the discoveries of quasi hyphen periodic \ [ kHz\ r u oscillations l e {3em}{0.4 in a pt number}\ ] of low hyphen mass X hyphen ray binaries .. open square bracket 3 9 6 closing square bracket comma .. as well aspulsar Doppler . hyphenThis model shifted has 2 gained period strong 49 hyphen support in recent years from the discoveries of quasi - periodic kHz ms Xoscillations hyphen ray in apulsations number of from low the - mass transient X - ray X binaries hyphen ray [ 3burster 9 6 ] , SAX as Jwell 1 808 as Doppler period 4 - minus shifted 3658 2 . 49 open - square bracket 3 9 8 comma 6\noindent 5 closingms X square -pulsar ray bracketpulsations . 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Figure open provided square bracket by Ingrid 3 4 7 closing square bracket periodspin Stairs ..− Theup [ solid3 phase 4 line 7 ] wasusing anwell adaptation below of the the orbital Eddington period - eccentricity limit [ relationship1 3 2 ] .tabulated by Fernando Camilo . shows theFurther median support of the for predicted the above relationship evolutionary between scenarios orbital comes period from two and correlations eccentricity in open the obsquare - served bracket sample 2 9 8 closing square bracket period\noindentof Dashed low -Figure linesmass binary 8 : pulsars\quad .Eccentricity Firstly , as seen in versus Figure 8 orbital , there is aperiod strong correlation for a sample of 2 1 low − mass binary pulsars which are not inshow globular 95 percent clusters the confidence , with limit the about triangles this relationship denoting period three The dotted recently line shows discovered P sub b varpropto systems e to [ the 3 4 power 7 ] of . 2\quad period The solid line Figureshows provided the median by of the predicted relationship between orbital period and eccentricity [ 2 9 8 ] . Dashed lines Ingrid Stairs open square bracket 3 .. 4 7 closing square bracket using an adaptation of the orbital period hyphen eccentricity relationship \noindent show $ 95 \% $ the confidence limit about this relationshipLiving Reviews . in The Relativity dotted line shows $ P { b } tabulated by Fernando ht tp : / / w w w . l i vi ngrev i e w s . org / lrr - 2008 - 8 \ varproptoCamilo period e ˆ{ 2 } . $ Figure provided by IngridFurther Stairs support for [ 3 the\quad above evolutionary4 7 ] using scenarios an adaptation comes from two of correlations the orbital in the period ob hyphen− eccentricity relationship tabulated by Fernando Camiloserved sample . of low hyphen mass binary pulsars period Firstly comma as seen in Figure 8 comma there is a strong correlation hline FurtherLiving Reviews support in Relativity for the above evolutionary scenarios comes from two correlations in the ob − servedht tp : slash sample slash of w w low .. w− periodmass l binaryi vi ngrev pulsars i e w s period . 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\ hspace ∗{\ f i l l } Living Reviews in Relativity

\ hspace ∗{\ f i l l } ht tp : / / w w \quad w. l i vi ngrev i ews . org / lrr − 2008 − 8 1 61 .... 6 Duncan R period Lorimer Duncan R . Lorimer \noindenthline 1 6 \ h f i l l Duncan R . Lorimer between orbital period and eccentricity period .. The data are in very good agreement with a theoretical \ [ relationship\ r u l e {3em which}{0.4 predicts pt }\ ] a relic orbital eccentricity due to convective eddy currents in the ac hyphen cretionbetween process orbital open period square and bracket eccentricity 2 9 8 closing . The square data are bracket in very period good .. agreement Secondly with comma a theoretical as shown relationship in Panel b of Figure 9 comma where companionwhich masses predicts have a relic orbital eccentricity due to convective eddy currents in the ac - cretion process [ 2 9 8 ] . \noindentbeenSecondly measuredbetween , as accurately shown orbital in comma Panel period b through of Figure and radio 9 , eccentricity wheretiming companion open parenthesis . masses\quad see haveThe Section data .... 4 are period in 4 very closing good parenthesis agreement and slash with or through a theoretical opticalrelationshipbeen observa measured hyphen which accurately predicts , through a relic radio timing orbital ( see eccentricitySection 4 . 4 due ) and to / or convective through optical eddy observa currents - in the ac − cretiontionstions open process[ 3 square 8 4 ] , bracket they [ 2 are 9 3 in8 8 good4 ] closing . agreement\quad squareSecondly with bracket a relation comma , as between shownthey are companion in in good Panel agreement mass b of and Figure with orbital a relation period9 , where between companion companion masses mass and have orbitalpredicted period by binary evolution theory [ 3 6 1 ] . A word of caution is required in using these models to make \noindentpredictedpredictions bybeen binary , however measured evolution . When accurately theory confronted open square , with through bracket a larger 3 radio 6ensemble 1 closing timing of square binary ( bracket pulsars see Section period using statistical .. A\ h word f i l l arguments of4 caution . 4 ) is andrequired / or in using through these optical observa − modelsto constrain the companion masses ( see Panel a of Figure 9 ) , current models \noindentto makehave predictionsproblemstions in[ comma 3explaining 8 4 however ] the , they full period range are .. Whenof in orbital good confronted periods agreement withon this a larger diagramwith ensemble a [ relation 3 4 7 of ] . binary between pulsars companion using mass and orbital period statisticalFigure arguments 9 : Orbital to constrain period the versus companion companion masses mass openfor binary parenthesis pulsars seeshowing Panel the a of whole Figure sample 9 closing where parenthesis , in the comma current models \noindenthaveabsence problemspredicted of mass in explaining determinations by binary the full , statistical range evolution of arguments orbital theory periods based on [ 3athis random 6 diagram 1 ] distribution . open\quad square ofA orbital word bracket inclination of 3 caution 4 7 closing angles is square ( required bracket period in using these models toFigure makesee Section9 :predictions .. Orbital 4 . 4 ) periodhave ,been versushowever used companion to constrain . \quad mass theWhen masses for binary confronted as shown pulsars ( Panel showing with a ) , aand the larger onlywhole sample ensemble where ofcomma binary pulsars using statisticalin thethose absence with well arguments of mass determined determinations to companion constrain comma masses the statistical ( Panel companion b ) arguments . masses based The dashed on ( seea random lines Panel show distribution the a ofuncertainties Figure of orbital in 9 the ) , current models inclinationpredicted angles relation open [ 3 6 parenthesis 1 ] . This relationship see Section indicates 4 period that 4 as closing these systems parenthesis finished have a period been of used stable to mass constrain transfer the masses as shown open parenthesis\noindentdue to Panelhave Roche a closing -problems lobe overflow parenthesis in , the explaining comma size and and hence only the period full of range the orbit of was orbital determined periods by the mass on of this the evolved diagram [ 3 4 7 ] . thosesecondary with well star determined . Figure provided companion by Marten masses van open Kerkwijk parenthesis [ 3 8 Panel 4 ] . b closing parenthesis period .... The dashed lines show the uncertainties in\noindent the 2 . 7Figure Intermediate 9 : \quad massOrbital binary period pulsars versus companion mass for binary pulsars showing the whole sample where , inpredicted theThe absence range relation of white open of mass squaredwarf determinations masses bracket observed 3 6 1 closing is becoming , square statistical bracket broader period . arguments Since This this relationship article based originallyindicates on a random ap that - peared as distributionthese [ systems finished of orbital a period ofinclination stable2 1mass 8 ] , the angles number ( of see“ intermediate Section - 4 mass . 4 binary ) have pulsars been ” used [ 5 3 ] to has constraingrown significantly the masses [ 5 7 ] . These as shown ( Panel a ) , and only transfersystems due are to Roche distinct hyphen to the lobe millisecond overflow pulsar comma – white the size dwarf and binaries hence period in several of the ways orbit : was determined by the mass of \noindentthe evolvedthose secondary with1 . star Thewell period spin determined Figure period provided of the companion radio by Marten pulsar masses is van generally Kerkwijk ( longerPanel open ( b square9 – ) 200 . bracket\ msh f) i . ll 3 8The 4 closing dashed square lines bracket show period the uncertainties in the 2 period 7 .. Intermediate2 mass . The binary mass pulsars of the white dwarf is larger ( typically & 0.5M ). −3 \noindentThe range3predicted of . white The dwarf orbit relation masses, while stillobserved [ essentially 3 6 is 1 becoming ] circular . This broader , is relationship often period significantly .. Since indicates thismore article eccentric originally that (e & as10 ap these hyphen). systems finished a period of stable mass transferpeared4 open . due square The to binary Roche bracket parameters− 2lobe 1 8 closing overflow do not square necessarily , bracket the follow size comma the and the mass hence number – period period of quotedblleft or eccentricity of the intermediate orbit – period was re hyphen determined - mass binary by the pulsars mass of quotedblrightthelationships evolved .. open secondary . square bracket star 5 . 3 closing Figure square provided bracket by has Marten grown significantly van Kerkwijk open square [ 3 bracket8 4 ] 5 . 7 closing square bracket period TheseIt is systems not presently are distinct clear to whether the millisecond these systems pulsar originated endash white from dwarf low - binaries or high -in mass several X - ways ray binaries : . It was \noindent1 periodsuggested ..2 The . by 7spin van\quad period den HeuvelIntermediate of the [radio 3 8 2 pulsar] that mass they is generally binary have more longer pulsars in common open parenthesis with high 9 - endash mass systems 200 ms . closing parenthesis period 2 period .. The mass of the white dwarf is larger open parenthesis typically gtrsim 0 period 5 M sub odot closing parenthesis period \noindent3 period ..The The orbitrange comma of white while still dwarf essentially masses circular observed comma is often becoming significantly broader more eccentric . \quad openSince parenthesis this e article gtrsim 1 0 originally to the ap − powerpeared of minus [ 2 3 1 closing 8 ] ,parenthesis the number period of ‘‘ intermediate − mass binary pulsars ’’ \quad [ 5 3 ] has grown significantly [ 5 7 ] . TheseLiving systems Reviews are in Relativity distinct to the millisecond pulsar −− white dwarf binaries in several ways : 4 periodht tp .. : The / binary / w w parameters w . l i vido not ngre necessarily v i e w follow s . orthe g mass / lrr endash - 2008 period - 8 or eccentricity endash period re hyphen lationships period \ centerlineIt is not presently{1 . \ clearquad whetherThe spin these systems period originated of the from radio low pulsar hyphen or is high generally hyphen mass longer X hyphen ( 9 ray−− binaries200 ms period ) . } It was suggested by van den Heuvel open square bracket 3 8 2 closing square bracket that they have more in common with high hyphen mass\ centerline systems period{2 . \quad The mass of the white dwarf is larger ( typically $ \ gtrsim 0 . 5 M {\odot } )hline . $ } Living Reviews in Relativity \ centerlineht tp : slash{ slash3 . \ wquad w w periodThe orbit l i vi ngre , whilev i e w s still period or essentially g slash lrr hyphen circular 2008 hyphen , is 8 often significantly more eccentric $ ( e \ gtrsim 1 0 ˆ{ − 3 } ) . $ }

4 . \quad The binary parameters do not necessarily follow the mass −− period or eccentricity −− period re − lationships .

\noindent It is not presently clear whether these systems originated from low − or high − mass X − ray binaries . It was suggested by van den Heuvel [ 3 8 2 ] that they have more in common with high − mass systems .

\ [ \ r u l e {3em}{0.4 pt }\ ]

\noindent Living Reviews in Relativity

\noindent http : //www. l i vi ngrev i ews . org/ lrr − 2008 − 8 BinaryBinary and and Millisecond Millisecond Pulsars Pulsars .... 1 7 1 7 \noindenthline Binary and Millisecond Pulsars \ h f i l l 1 7 Subsequently comma Li proposed open square bracket 2 1 0 closing square bracket that a thermal hyphen viscous inst ability in the accretion disk\ [ \ ofr u a l low e {3em hyphen}{0.4 pt }\ ] massSubsequently X hyphen ray , Li binary proposed could [ 2 truncate 1 0 ] that the a accretion thermal - phase viscous and inst produce ability a in more the slowlyaccretion spinning disk of neutron a low - mass starX period - ray binary could truncate the accretion phase and produce a more slowly spinning neutron \noindent2 periodstar . 8Subsequently .. Isolated recycled , pulsars Li proposed [ 2 1 0 ] that a thermal − viscous inst ability in the accretion disk of a low − massThe2 Xscenarios .− 8ray outlined Isolated binary qualitatively could recycled truncate above pulsars represent the accretion a reasonable phase understanding and produce of binary a evolu more hyphen slowly spinning neutron t ionThe period scenarios There outlined are comma qualitatively however commaabove represent a number a reasonableof pulsars with understanding spin properties of binary that evolu suggest - t iona phase . There of recycling \noindenttookare place , howevers but t a r have ., a no number orbiting of pulsars companions withspin period properties While the that existence suggest of a suchphase systems of recycling in globular took place clus but hyphen have tersno are orbiting more readily companions explained . While by the the high existence probability of such of systems stellar interactionsin globular clus compared - ters are to more the readily explained \noindentdiskby open the2 square high . probability8 bracket\quad 3Isolated of 3 7stellar closing interactions squarerecycled bracket compared pulsars comma to the it is disk somewhat [ 3 3 7 ]surprising , it is somewhat to find surprising them in the to Galacticfind disk period Out of a total ofthem 72 Galactic in the Galactic disk . Out of a total of 72 Galactic \noindentmillisecondmillisecondThe pulsars pulsars scenarios comma , 1 6 1 are 6outlined are isolated isolated ( qualitativelysee open Table parenthesis 2 ) . above see Table Although represent .... 2 it closing has been a parenthesis reasonable proposed period that understanding these .... Although mil - it hasof beenbinary proposed evolu − thatt ion theselisecond . mil There hyphen pulsars are have , ablatedhowever their , companion a number via of their pulsars strong withrelativistic spin winds properties [ 1 9 2 ] as that may be suggest a phase of recycling tooklisecondhappening place pulsars but in have the have PSRablated no B 1957 their orbiting + companion 20 system companions via [ 1 their1 9 ] strong, it . is While not relativistic clear the whether windsexistence the open energetics square of such bracket or timescales systems 1 9 2 closing inglobular square bracket clus as may− be tershappeningfor are this more in process the PSRreadily are B feasible 1 957 explained plus [ 2 0 20 8 ]system . by openthe squarehigh probabilitybracket 1 1 9 closing of stellar square bracket interactions comma it is not compared clear whether to the the energetics ordisk timescales [ 3 3 7There ] , it are isfour somewhat further “ anomalous surprising ” isolated to find pulsars them with periods in the in Galactic the range 28 disk – 60 ms . Out [ 5 8 of , a total of 72 Galactic for this2 process2 9 ] . When are feasible placed open on the squareP – bracketP˙ diagram 2 0 8 , closingthese objects square populate bracket period the region o ccupied by the double \noindentThereneutron are fourmillisecond star further binaries quotedblleft . pulsars The most anomalous , natural 1 6 arequotedblright explanation isolated for isolated their ( see existence pulsars Table with , therefore\ periodsh f i l l , in is2 thethat ) .range they\ h f 28are i l endashl “ failedAlthough 60 ms open it hassquare been bracket proposed that these mil − 5 8 commadouble neutron star binaries ” which disrupted during the supernova explosion of the secondary [ 5 8 ] . A \noindent2 ..simple 2 9 closinglisecond calculation square bracket [ pulsars 2 2 9period ] , have suggested When ablated placed that for on their every the P doubleendash companion neutron P-dotaccent via star theirdiagram we should strong comma these relativistic objects populate winds the region [ 1 9 o 2ccupied ] as may be by thesee double of order ten such isolated objects . Recent work [ 2 9 ] has investigated why so few are observed . \noindentneutronUsing star thehappening binaries most recent period in population the .. The PSRB most synthesis natural $ 1 models explanation 957 to + follow for their20 the $ existence evolution system comma of [ binary 1 therefore 1 systems9 ] , comma it[ 2 is is 8 notthat ] , it they clear whether the energetics or timescales areappears quotedblleft that failed the discrepancy double neutron may star not bebinaries as significant quotedblright as previously which disrupted supposed during . In the particular supernova , the explosion space of the \noindentsecondaryvelocityfor open distribution thissquare process bracket of surviving 5 8 are closing binary feasible square systems bracket [ is 2 narrower 0 period 8 ] than . A simple for the calculation isolated objects open thatsquare were bracket during 2 the .. 2 9 closing square bracket commasecond suggested supernova that for explosion every double . The neutron isolated star systems we should o ccupy a larger volume of the Galaxy than the surviving \ hspaceseebinaries of∗{\ orderf iand ten l l } such areThere harder isolated are to objects detect four .further period When Recent this ‘‘ anomalouswork selection open effect square ’’ is isolatedaccounted bracket 2 9for pulsars closing [ 2 9 ] square , thewith relative bracket periods sample has investigated in the range why so 28 few−− are60 ms [ 5 8 , observedsizes period appear to be consistent with the disruption hypothesis . \noindentUsing2 . the 92 most\quad A recent new2 population 9 class ] . ofWhen synthesismillisecond placed models on pulsars theto follow $ P the? $ evolution−− $ of\dot binary{P} systems$ diagram open square , these bracket objects 2 .. 8 closing populate square the region o ccupied by the double bracketneutronOne comma of star the most binaries remarkable . \quad recentThe discoveries most is natural the binary explanation pulsar J 1903 + for 327[70] their. existenceFound , therefore in , is that they areit appearsan ‘‘ on failed - that going the double multibeam discrepancy neutron survey may with not star be the as binaries Arecibo significant telescope ’’ as previously which [ 2 7 5 disrupted , supposed 8 2 ] , this period during 2 . 1 .. 5 In - msthe particular pulsar supernova is comma distinct explosion of the secondarythefrom space all velocity[ other 5 8 millisecond distribution ] . A simple pulsars of surviving in calculation that binary its 95 systems - day [ 2orbit is\quad narrower has an2 eccentricity 9 than ] for , suggested the of isolated 0 . 43 ! objects Inthat addition for , every t iming double neutron star we should thatmeasurements were during the of the second relativistic supernova periastron explosion advance period and .. The Shapiro isolated delay systems in this o system ccupy a ( larger see volume \noindent see of order ten such isolated objects . Recent work [ 2 9 ] has investigated why so few are observed . of theSection Galaxy 4 than . 4 ) the , show surviving the mass binaries of the andpulsar are to harder be 1.74 to± detect0.4M periodand the .. companion When this star selection to be effect1.51± is0.015M . accountedOptical for observations open square show bracket a possible 2 9 closing counterpart square which bracket is commaconsistent the with relative a sample sizes appear to be consistent with the disruption \noindent Using the most recent population synthesis models to follow the evolution of binary systems [ 2 \quad 8 ] , hypothesis1M periodst ar . While similar systems have been observed in globular clusters ( e . g . PSR J 514 − 4002 A it2 period appearsin NGC 9 .. 1 Athat 85 new 1 [ the class 1 1 7 discrepancyof ]millisecond ) , presumably pulsars may a result not ? of be exchange as significant interactions ,as the previously standard recycling supposed hypothesis . \quad In particular , theOneoutlined space of the most velocity in Section remarkable 2 distribution . 6 cannotrecent discoveries account of for surviving is pulsars the binary like binaryJ pulsar 1903 + J 3271systems 903 in plus the Galactic 327is narroweropen disk square . than bracket for 7 0 the closing isolated square bracket objects period ....that Found wereHow in during could such the an eccentricsecondbinary supernova millisecond explosion pulsar system . \quad formThe ? One isolated possibility systems is that the o ccupybinary a larger volume ofan the onsystem hyphen Galaxy was going produced than multibeam the in an surviving exchange survey with interaction binaries the Arecibo in a and globulartelescope are cluster open harder square and to subsequently bracket detect 2 7 .ej 5 ected\commaquad , or 8When 2the closing cluster this square selection bracket comma effect this is 2accounted periodhas 1 5 since hyphen for disrupted ms[ 2 pulsar 9 . Statistical ] is , distinct the estimates relative [ 7 sample 0 ] of the sizes likelihood appear of both to these be channels consistent are in withthe range the 1 –disruption hypothesis . from10% all, otherimplying millisecond that a globular pulsars in cluster that itsorigin 95 hyphen cannot be day ruled orbit out has . an eccentricity of 0 period 43 ! In addition comma \noindentt imingAnother measurements2 . 9 possibility\quad of theA is relativisticthatnew the class pulsar periastron of is millisecond a member advance of and an pulsars Shapirohierarchical delay $ triple in? this$ system system with open a one parenthesis solar mass see Sectionwhite .. dwarf 4 period in the 4 closing 95 - day parenthesis orbit , and comma a main show sequence the mass star of in the a much pulsar wider to be and 1 periodhighly inclined74 plusminux orbit which0 period 4 M sub odot and the companion\noindenthas so starOne far to not be of been the revealed most remarkable by timing . Therecent origin discoveries of the high eccentricity is the is binary through pulsar perturbations J $ from 1 903 + 327 [ 71 period 0the outer ] 5 1 plusminux. star $ , the\ h sof 0 i periodl - l calledFound 0 Kozai 1 5 in M mechanism sub odot period [ 1 9 7 .. ] Optical . Formation observations show a possible counterpart which is consistent with a 1 Mestimates sub odot based st ar periodon observational While similar data systems on stellar have multiplicity been observed [ 3 0 4 in ] globularfind that clusters around open4% of parenthesis all binary e period g period PSR J 5 1 4 minus\noindent 4002millisecond Aan on pulsars− going are expected multibeam to be triple survey systems with [ 7 the 0 ] . Arecibo The existence telescope of a single [ 2triple 7 5 system , 8 2among ] , this 2 . 1 5 − ms pulsar is distinct fromin NGCthe all current 1 other 85 1 sample open millisecond square of millisecond bracket pulsars 1 pulsars 1 7 closing appears in that square to be its bracket consistent 95 closing− day with parenthesis orbit this hypothesis has comma an . eccentricity presumably a result of of0 exchange . 43 ! Ininteractions addition , commat iming the standard measurements recycling of hypothesis the relativistic periastron advance and Shapiro delay in this system ( see outlined in Section 2 period 6 cannot account for pulsars like J 1 903 plus 327 in the Galactic disk period \noindentHow couldSec such tion an eccentric\quad binary4 . 4 millisecond ) , show pulsar the system mass formof the ? .. pulsarOne possibility to be is that $1 . 74 \pm 0 . 4 M {\odot }$ and the companion star to be Living Reviews in Relativity the binary system was producedht intp an : exchange / / w w interaction w . l in i a vi globular ngrev cluster i e w and s . subsequently org / lrr - 2008 - 8 $ej 1ected . comma 5 or the1 cluster\pm has0 since . disrupted 01 period 5 Statistical M {\ estimatesodot } open. $ square\quad bracketOptical 7 0 closing observations square bracket ofshow the likelihood a possible counterpart which is consistent with a of both these \noindentchannels are$ in 1 the Mrange{\ 1 endashodot } 1$ 0 percent st ar comma . While implying similar that a systems globular cluster have origin been cannot observed be ruled in out globular period clusters ( e . g . PSR J $ 5Another 1 possibility 4 − is4002 that the $ pulsar A is a member of an hierarchical triple system with a one solar mass white dwarf in the 95 hyphen day orbit comma and a main sequence star in a much wider and highly \noindentinclined orbitin whichNGC 1 has 85 so 1 far [ not 1 been1 7 revealed ] ) , presumably by timing period a result.. The origin of ofexchange the high eccentricity interactions , the standard recycling hypothesis outlinedis throughin perturbations Section from 2 . the 6 cannot outer star account comma the for so hyphen pulsars called like Kozai J mechanism $ 1 903 open square + bracket327 $ 1 9in 7 closing the Galactic square bracket disk . period .. Formation Howestimates could based such on an observational eccentric data binary on stellar millisecond multiplicity open pulsar square system bracket form 3 0 4 closing $ ? $ square\quad bracketOne find possibility that around 4 ispercent that of allthe binary binary system was produced in an exchange interaction in a globular cluster and subsequently ejmillisecond ected , pulsars or the are clusterexpected to has be triple since systems disrupted open square . Statistical bracket 7 0 closing estimates square bracket [ 7 period 0 ] of .. The the existence likelihood of a single of triple both these systemchannels are in the range 1 −− $ 1 0 \%, $ implying that a globular cluster origin cannot be ruled out . among the current sample of millisecond pulsars appears to be consistent with this hypothesis period Anotherhline possibility is that the pulsar is a member of an hierarchical triple system with a one solarLiving mass Reviews white in Relativity dwarf in the 95 − day orbit , and a main sequence star in a much wider and highly inclinedht tp : slash orbit slash wwhich w .. w has period so l fari vi ngrev not i been e w s period revealed org slash by timinglrr hyphen . 2008\quad hyphenThe 8 origin of the high eccentricity is through perturbations from the outer star , the so − called Kozai mechanism [ 1 9 7 ] . \quad Formation

\noindent estimates based on observational data on stellar multiplicity [ 3 0 4 ] find that around $ 4 \% $ of all binary

\noindent millisecond pulsars are expected to be triple systems [ 7 0 ] . \quad The existence of a single triple system among the current sample of millisecond pulsars appears to be consistent with this hypothesis .

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\ hspace ∗{\ f i l l } Living Reviews in Relativity

\ hspace ∗{\ f i l l } ht tp : / / w w \quad w. l i vi ngrev i ews . org / lrr − 2008 − 8 1 81 .... 8 Duncan R period Lorimer Duncan R . Lorimer \noindenthline 1 8 \ h f i l l Duncan R . Lorimer If future observations of the proposed optical counterpart confirm it as the binary companion \ [ through\ r u l e { spectral3em}{0.4 line pt measurements}\ ] of orbital Doppler shifts comma the above triple hyphen system scenario will be ruledIf out future period observations Such an observation of the proposed would optical favour counterpart a hybrid scenario confirm suggested it as the by binary van den companion Heuvel open through square bracket 3 8 3 closing squarespectral bracket line measurements of orbital Doppler shifts , the above triple - system scenario will Ifin future whichbe ruled the observations out white . Such dwarf an and observation of pulsar the merge proposed would due favour to optical gravitational a hybrid counterpart scenario radiation suggested losses confirm period by van Tidal it den as disruption Heuvel the [ binary 3 8 3 ] in companion throughof thewhich white spectral the dwarf white in dwarf linethe inspiral and measurements pulsar would merge produce due of an to orbital gravitationalaccretion Doppler disk radiation and induce shifts losses an eccentricity. , Tidal the disruptionabove in triple of the− whitesystem scenario will thedwarf orbit of in the the outer inspiral star would leaving produce behind an an accretion eccentric disk binary and system induce periodan eccentricity .. This idea in the could orbit naturally of the outer star \noindentaccountleaving forbe behind the ruled high an pulsar eccentricout mass . Such binary observed an system observation in this . system Thiswhich idea would could could favour naturally arise from a hybridaccount accretion for scenario of the a high pulsarsuggested mass by van den Heuvel [ 3 8 3 ] inwhite whichobserved hyphen the in dwarf this white system debris dwarf which disk and following could pulsar arise coalescence from merge accretionperiod due of to Alternatively a gravitational comma radiation as suggested losses by Champion . Tidal et al disruptionperiod open square bracketof thewhite 7 0 white closing - dwarf squaredwarf debris bracket indisk the following comma inspiral coalescence would . Alternatively produce an , as accretion suggested by disk Champion and et induce al . [ 7 an0 ] , eccentricity the in thethemillisecond orbitmillisecond of pulsar pulsar the outer might might have have star ablated ablated leaving the the white white behind dwarf dwarf an companion companion eccentric in in a atriple binary triple system system system leaving leaving .only\quad the unevolvedThis idea could naturally accountonlycompanion the unevolved for the in an companion high elliptical pulsar orbit in an . mass elliptical observed orbit period in this system which could arise from accretion of a 2 period2 . 1 1 0 .. Pulsar Pulsar velocities velocities \noindentPulsarsPulsars havewhite have long long− beendwarf been known known debris to have to have space disk space velocities following velocities at least at coalescence least an order an order of magnitude of . magnitude Alternatively larger larger than than , as suggested by Champion et al . [ 7 0 ] , −−1 thethosethose millisecond of their of their main main sequence pulsar sequence progenitors might progenitors have comma ablated , which which have havethe typical typical white values values dwarf between between companion 1 1 0 and in 50 50 kma km triple s s to the. Proper power system of endash leaving 1 period onlyPropermotions the motions unevolved for over for over 250 companion 250 pulsars pulsars have have nowin nowan been ellipticalbeen measured measured largely orbit largely by radio .by radio timing timing and and interfero interfero - hyphen metricmetric techniques techniques open [ 2 square 3 7 , 2 bracket 4 , 1 1 2 1 3 , 7 1 comma 3 3 , 1 2 4 .... 4 , 4 4 comma 0 6 ] . 1 These 1 .... data 1 comma imply 1 a 3 broad 3 comma velo .... city 1 spectrum4 4 comma .... 4 0 6 closing square bracket\noindentranging period2 These . 1 data 0 \quad implyPulsar a broad velo velocities city spectrum ranging from a proper 0 to sub motion over 1 0 sub and km s to the power of endash 1 open square bracket 2 4 parallax 2 closing square bracket \noindent Pulsars have long been known to have space velocities at least an order of magnitude larger than comma with the current measurement record−−1 implying a holder transverse to the power of being PSR velocity B subbeing of 1 plus 1 0 3 from minus −90 s . fromaproper0tomotionover10andkms [2 4parallax2], withthecurrentmeasurementrecordimplyingaholder PSRvelocityBof 1+103 7km2], −1 9 0 to 508 sub 1 83 plus 55 open square bracket 7 sub km 2 closing square bracket comma minus 1 from s periodtransverse to with 508183+55[ with \noindentAs Figurethose 1 0 .. i llustrates of their comma main high sequence hyphen velo progenitors city pulsars born , which close to have the Galactic typical plane values quickly between migrate to 1 0 and 50 km $ s ˆ{ −− As Figure 1 0 i llustrates , high - velo city pulsars born close to the Galactic plane quickly migrate to higher 1 }higher. $ Galactic latitudes period Given such a broad velocity spectrum comma as many as half of all pulsars will Galactic latitudes . Given such a broad velocity spectrum , as many as half of all pulsars will eventually escape Propereventually motions escape the for Galactic over 250gravitational pulsars potential have nowopen squarebeenmeasured bracket 2 4 2 largely comma .. by 8 1 radio closing square timing bracket and periodinterfero − the Galactic gravitational potential [ 2 4 2 , 8 1 ] . Figure 10 : .. Still from a movie showing A simulation following the motion of 1 0 pulsars in a model \noindentgravitationalFiguremetric 10 potential : techniquesStill of from our Galaxy a movie [ forshowing 2 3200 7 Myr A , simulation 2 period\ h f i The l following l 4 view , is1 the edge 1 motion\ h hyphen f i of l l 1 01 on pulsars comma, 1 3 in ia3 period model , \ h e gravitational f period i l l 1 the 4 4 horizontal , \ h f i axis l l 4 represents 0 6 ] . These data imply a broad velo city spectrum ranging thepotential Galactic of plane our Galaxy open parenthesis for 200 Myr 30 . The kpc view across is edge closing - on parenthesis , i . e . the while horizontal the vertical axis represents axis represents the Galactic plusminux plane 1 0 kpc from the plane ( 30 kpc across ) while the vertical axis represents ±10 kpc from the plane . This snapshot period\ [ from This{ snapshota proper } 0 to { motion } over 1 0 { and } km s ˆ{ −− 1 } [ 2 4 { p a r a l l a x } 2shows ]shows the , the initial withinitial configuration configuration the ofcurrent of young young neutron neutron{ measurement stars . period ( To watch} openrecord the parenthesis movie{ implying , please To watch go to} thea online movie holder version comma please{ t r a go n s to v e the r s e online}ˆ{ versionbeing } PSR{ v e l o c i t y } B of{ thisofo f this review} review1 article article+ at 1 at httphttp 0 : :slash 3 / ˆ/ slash{ w − w w w .w9 w l period i 0 v} in{ l g i508 rv evin g i{ r e ev1 w is e . 83 w o s} rperiod g+ / o 55 r l g r slash r [ -} ..2 0 l7 r 0 r 8 hyphen{ -km 8 .} 2 02 0 8 hyphen ] , 8 period− closing1 ˆ{ s) parenthesis . } { with }\ ] Such large velocities are perhaps not surprising , given the violent conditions under which neu - tron stars Such large velocities are perhaps not surprising comma given the violent conditions under which neu hyphen are formed . If the explosion is only slightly asymmetric , an impulsive “ kick ” velo city of tron stars are formed period If the explosion is only slightly asymmetric comma an impulsive quotedblleft kick quotedblright velo city of up to 1 0 km s−−1 can be imparted to the neutron st ar [ 3 3 6 ] . In addition , if the neutron star pro - \noindentup to 1 0 kmAs s Figure to the power 1 0 of\quad endashi 1 llustrates can be imparted , high to the− neutronvelo st city ar open pulsars square bracketborn close 3 3 6 closing to the square Galactic bracket period plane In quickly migrate to genitor was a member of a binary system prior to the explosion , the pre - supernova orbital velocity will also additionhigher comma Galactic if the neutron latitudes star pro . Givenhyphen such a broad velocity spectrum , as many as half of all pulsars will contribute to the resulting speed of the newly - formed pulsar . The relative contributions of these two factors eventuallygenitor was a escape member ofthe a binary Galactic system gravitational prior to the explosion potential comma the [ pre2 4 hyphen 2 , \ supernovaquad 8 1 orbital ] . velocity to the overall pulsar birth velo city distribution is currently not well understood . will also contribute to the resulting speed of the newly hyphen formed pulsar period The relative contributions of \noindentthese two factorsFigure to 10 the overall: \quad pulsarStill birth from velo city a movie distribution showing is currently A simulation not well understood following period the motion of 1 0 pulsars in a model gravitationalhline potential of our Galaxy for 200 Myr . The view is edge − on , i . e . the horizontal axis represents the Galactic plane ( 30 kpc across ) while the vertical axis represents $ \pm 1 0 $ kpc from the plane . This snapshot LivingLiving Reviews Reviews in Relativity in Relativity ht tpht : tpslash : slash / / w w w w w w period . l i l i vi vi ngre v v i ei w e s w period s . or or g g slash / lrr lrr -hyphen 2008 2008 - 8 hyphen 8 \noindent shows the initial configuration of young neutron stars . ( To watch the movie , please go to the online version

\noindent of this review article at http : //www. l i v in g r ev i ews . o r g/ \quad l r r − 2 0 0 8 − 8 . )

Such large velocities are perhaps not surprising , given the violent conditions under which neu − tron stars are formed . If the explosion is only slightly asymmetric , an impulsive ‘‘ kick ’’ velo city of

\noindent upto10km $sˆ{ −− 1 }$ can be imparted to the neutron st ar [ 3 3 6 ] . In addition , if the neutron star pro − genitor was a member of a binary system prior to the explosion , the pre − supernova orbital velocity will also contribute to the resulting speed of the newly − formed pulsar . The relative contributions of these two factors to the overall pulsar birth velo city distribution is currently not well understood .

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\noindent Living Reviews in Relativity

\noindent http : //www. l i vi ngrev i ews . org/ lrr − 2008 − 8 BinaryBinary and and Millisecond Millisecond Pulsars Pulsars .... 1 9 1 9 \noindenthline Binary and Millisecond Pulsars \ h f i l l 1 9 The distribution of pulsar velo cities has a high velo city component due to the normal pulsars \ [ open\ r u l square e {3em bracket}{0.4 pt 2}\ .. 4 2] comma .. 1 4 4 comma 1 0 6 closing square bracket comma and a lower velo city component from binary and millisecondThe pulsars distribution open square of pulsar bracket velo 2 cities 1 7 comma has a high8 0 comma velo city .. 2component 4 4 comma due to the normal pulsars [ 2 4 2 , 1 41 4 4closing 4 , 1 0 square 6 ] , and bracket a lower period velo One city reason component for this from dichotomy binary and appears millisecond to be that pulsars comma [ 2 1 in 7 , order 8 0 , to 2survive 4 4 , and subsequently form Therecycled distribution1 pulsars 4 4 ] . through One of reason pulsar the foraccretion this velo dichotomy process cities outlined appears has aabove to high be comma that velo , thein city order binary componentto systems survive contain and due subsequently only to the normal form pulsars [those 2 \recycledquad neutron4 pulsars st2 ars , \ through withquad lower1 the 4 birth accretion 4 , velocities 1 0 process 6 period] outlined , and In addition a above lower , comma the velo binary the city systems surviving component contain neutron only starfrom those has binary neutronto pull and millisecond pulsars [ 2 1 7 , 8 0 , \quad 2 4 4 , thest companion ars with loweralong birthwith it velocities comma thus . 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Inof pulsar addition the spin hyphen axis , wind and the nebulae the surviving velo open city vector square neutron at bracket star 2 8 1 has closing to square pull bracketthe companionbirth comma . These where alongdata have with recently it been , thus combined slowing with modeling the system of pulsar down - wind . nebulae [ 2 8 1 ] , where strong strongevidence evidence is found is found for for a model a model in which in which the the natal natal impulse impulse is provided is provided by byan ananisotropic anisotropic flux flux of neutrinos from \ hspaceof neutrinosthe∗{\ protof i from l - l neutron} Further the proto star hyphen oninsights timescales neutron into of star a few pulsar on seconds timescales kicks . of from a few seconds analyses period of proper motion and polarization data [ 1 6 5 , 2 period2 . 1 1 1 .. Pulsar Pulsar searches searches \noindentTheThe radio radio1 sky 6 sky is 6 being is , being\ h repeatedly f i repeatedly l l 3 1 searched 1 searched ] find for newfor strong new pulsars pulsars evidence in a in variety a variety for of ways of an ways period alignment . In In the the following following between , we comma the outline spin axis and the velo city vector at we outlinethe major the search major strategies search strategies that are that optimized are optimized for binary for andbinary millisecond and millisecond pulsars pulsars . period \noindent2 period2 . 1 1 1birth 1 . period 1 . All 1 These .. - All sky hyphen data searches sky have searches recently been combined with modeling of pulsar − wind nebulae [ 2 8 1 ] , where strongTheThe oldest evidence oldest radio radio pulsars is pulsars found form form a relaxed for a relaxed a population model population in of which stars of stars oscillating the oscillating natal in the inimpulse Galactic the Galactic isgravitational provided gravitational by potential an anisotropic flux ofpotential neutrinos[ 1 3 1 open ] . square from The scale bracket the height proto 1 3 for 1− closing suchneutron a populationsquare star bracket is on at period least timescales 500 .. The pc [ scale 2 of 2 height a 1 ] few , about for seconds such 1 0 a times population . that of is the at least 500 pc open square bracketmassive 2 .. 2 1 stars closing which square populate bracket the comma Galactic about plane 1 0 . times Since the typical ages of millisecond pulsars are several \noindentthatGyr of the or2 more massive . 1 , we 1 stars expect\quad which , fromPulsar populate our vantage searches the Galactic point in plane the Galaxy period , .. to Since be in the the typical middle ages of an of essentially millisecond isotropic pulsarspopulation are several of nearby Gyr or sources more comma . All we- sky expect searches comma for millisecond from our vantage pulsars point at high in Galacticthe Galaxy latitudes comma have to be been in the \noindentmiddlevery of effective anThe essentially radio in probing skyisotropic this is population population being repeatedly . of nearby sources searched period for .. All new hyphen pulsars sky searches in a for variety millisecond of ways . In the following , wepulsars outlineMotivated at high the Galactic by major the latitudes discovery search have of strategies two been recycled very effective pulsars that atarein probinghigh optimized latitudes this population with for the binary Arecibo period and tele - millisecond scope [ 4 0 1 , pulsars . Motivated4 0 4 ] ,by surveys the discovery carried outof two at Areciborecycled , pulsars Parkes at , Jodrell high latitudes Bank and with Green the Arecibo Bank by tele others hyphen \noindentscopeinopen the 12 square 990 .1 s [ 1bracket 5 8 . , 51 9 4\ ,quad 0 6 1 0 comma , 2All 5 1 , ..− 2 4 4sky 0 4 4 ] discovered closing searches square around bracket 30 further comma objects surveys . Althoughcarried out further at Arecibo searching comma Parkes comma Jodrell Bank andof this Green kind Bank has bybeen others carried out at Arecibo in the past decade [ 2 3 3 ] , much of the recent efforts have been \noindentin theconcentrated 1 990The s open oldest along square the radio plane bracket of pulsars 5 our 8 comma Galaxy form 5 and 9 comma a in relaxedglobular 6 0 comma clusters population .... discussed 2 5 1 commaof below stars . 2 Very .... oscillating 4 recently 4 closing , however square in bracket the Galactic discovered gravitational around 30potential further, 1 2objects , 0 [ square 1 period 3 degrees1 Although ] . of\quad sky further wasThe surveyed searching scale using height a new for 350 such - MHz a receiver population on the Green is at Bank least Telescope 500 pc [ [ 2 \quad 2 1 ] , about 1 0 times thatof this3 of 9 kind 3 the , has 4 massive 3 been ] . carried Processing stars out at which of Arecibo these populate data in the is currentlypast the decade Galactic underway open square , plane with bracket two . millisecond\ 2quad 3 3 closingSince pulsars square the found bracket typical with comma ages much of of millisecond the recent effortspulsarsaround are 10% several of the dataset Gyr analysedor more . , we expect , from our vantage point in the Galaxy , to be in the middlehave2 been . 1of 1 concentrated an . 2 essentially Searches along close the isotropic plane to the of our plane population Galaxy of our and Galaxy in of globular nearby clusters sources discussed . \ belowquad periodAll − sky searches for millisecond pulsarsVeryYoung recently at pulsars high comma are Galactic however most likely comma latitudes to be 1 found 2 comma have near 0 to square been their degrees veryplaces of effective of birth sky was close surveyed into the probing Galactic using a thisnew plane 350 population. This hyphen was MHz . receiver on thethe Green target Bank region Telescope of the main open Parkes square multibeam bracket 3 survey 9 3 comma and has .. 4 so 3closing far resulted square in bracket the discovery period of .. 783 Processing pulsars of these data is currently underwayMotivated[ 2 comma 5 by 0 , thewith 2 6 two4discovery , 1 9 9 , 1 of 4 two 5 , 1 0recycled 8 , 2 2 4 pulsars , 1 8 7 , 4at 9 ] high , almost latitudes half the number with currently the Arecibo known tele − scopemillisecond! [ Such 4 0pulsars a 1 large , found\ haulquad with inevitably4 0 around 4 ] results 1 , 0 surveys percent in a number of carried thedataset of interesting out analysed at individual Arecibo period objects , Parkes such as , the Jodrell relativistic Bank and Green Bank by others 2 periodbinary 1 pulsar1 period J 1141 2 .. Searches− 6545[183 close, 288 to, the25 plane, 148 of, our35] Galaxy, a young pulsar orbiting an \noindent in the1990s [58 ,59 ,60 , \ h f i l l 2 5 1 , 2 \ h f i l l 4 4 ] discovered around 30 further objects . Although further searching Young∼ 11 pulsarsM star are ( most probably likely a to main be foundsequence near B to - star their [ 3 places 4 8 , of birth3 4 9 close] ) , a to young the Galactic pulsar in plane a ∼ 5 period yr - eccentric Thisorbit was ( thee = target 0.955; region the most of the eccentric main Parkes found so multibeam far ) around survey a 1 and 0 – 20hasM so companion far resulted [ in 2 the 3 6 , 2 2 4 ] , several \noindentdiscoveryintermediate ofof 783 thispulsars - mass kind binary open has square pulsars been bracket [ 5 carried 7 ] , 2 and .. 5 two 0 out comma double at ..Arecibo neutron 2 6 4 comma star in binaries the .. 1 9 past [9 2 comma 4 decade 0 , 1 .. 14 0[5 7 ]comma 2 . 3 Further 3 1 ] 0 8, comma much of.. 2 the 2 4 comma recent 1 efforts 8have 7 commaanalyses been .. 4 concentrated 9of closing this rich square data bracket set along are now comma the in plane progress almost of half and our the will number Galaxy ensure yetcurrently and more in discoveries globular in the clusters near future discussed . below . Veryknown recentlyMotivated ! .. Such a , by large however the haul successes inevitably , 1 at 2 Parkes , results 0 ,square a in multibeam a number degrees survey of interesting of is now sky in individual was progress surveyed objects with the such using Arecibo a telescope new 350 [ − MHz receiver onas the the2 7 relativistic 5Green ] and the Bank binary Effelsberg Telescope pulsar radio J 1 telescope 1 [ 4 3 1 9minus 3 . , 6545 The\quad Areciboopen4 square 3 survey ] .bracket\ hasquad so 1 far 8Processing 3 discovered comma 2 8 46 8of comma these 2 5 data comma is 1 currently4 8 comma 3 underway 5 closing , with two squaremillisecondpulsars bracket [ comma 2 pulsars7 5 , a young found 8 pulsar 2 ] with with orbiting notable around an finds including $ 1 0 a highly\% $ relativisticof the binary dataset [ 2 3 2 analysed ] and an eccentric . thicksimmillisecond 1 1 M pulsar sub odot binary star [ open 7 0 ] parenthesis . Hundreds probably more pulsars a main could sequence be found B hyphenin this survey star open over square the next bracket five years 3 4 8 comma .... 3 4 9 closing square\noindent. bracket A significant2 closing . 1 1fraction parenthesis . 2 \ ofquad this comma yieldSearches a are young expected closepulsar to in tobe a distant thicksim the plane millisecond 5 yr hyphen of our pulsars eccentric Galaxy in the orbit open parenthesis e = 0 period 955 semicolon the most eccentric found so far closing parenthesis around a 1 0 endash 20 M sub odot companion\noindent openYoung square pulsars bracket 2 are .... 3 most 6 comma likely 2 .... 2to 4 closing be found square near bracket to comma their several places of birth close to the Galactic plane . Thisintermediate was the hyphen target mass region binary pulsars of the open main square Parkes bracket multibeam 5 7 closing square survey bracket and comma has so and far two doubleresulted neutron in star the binaries open discovery of 783 pulsars [ 2 \quad 5 0 , \quad 2 6 4 , \quad 1Living 9 9 , Reviews 1 \quad in Relativity4 5 , 1 0 8 , \quad 2 2 4 , 1 8 7 , \quad 4 9 ] , almost half the number currently square bracket 2 .. 4 0 comma ..ht 1 0 tp 7 closing : / / square w w bracket w . period l i vi .. ngrev Further i e w s . org / lrr - 2008 - 8 knownanalyses ! of\quad this richSuch data a set large are now haul in progress inevitably and will results ensure yet in more a numberdiscoveries of in interestingthe near individual objects such asfuture the period relativistic binary pulsar J $ 1 1 4 1 − 6545 [ 1 8 3 , 2 8 8 , 2 5Motivated , 1 by 4 the successes 8 , at 3 Parkes 5 comma ] a ,$ multibeam ayoungpulsarorbitingan survey is now in progress with the Arecibo telescope open square bracket 2 7 5 closing square bracket and the Effelsberg radio telescope period .. The Arecibo survey has so far discovered\noindent 46 $ \sim 1 1 M {\odot }$ star ( probably a main sequence B − s t a r [ 3 4 8 , \ h f i l l 3 4 9 ] ) , a young pulsar in a $ \pulsarssim open5 $ square yr − brackete c c e 2n t7 r 5 i ccomma .... 8 2 closing square bracket with notable finds including a highly relativistic binary open square bracket 2 3 2 closing square bracket and an eccentric \noindentmillisecondorbit pulsar binary $ ( open e square = bracket 0 . 7 0 955 closing square ; $ thebracket most period eccentric Hundreds more found pulsars so far could ) be arounda10 found in this survey−− over$ 20 Mthe next{\odot }$ companion [ 2 \ h f i l l 3 6 , 2 \ h f i l l 2 4 ] , several five years period A significant fraction of this yield are expected to be distant millisecond pulsars in the \noindenthline intermediate − mass binary pulsars [ 5 7 ] , and two double neutron star binaries [ 2 \quad 4 0 , \quad 1 0 7 ] . \quad Further analysesLiving Reviews of this in Relativity rich data set are now in progress and will ensure yet more discoveries in the near f uht t u tp r e : slash . slash w w .. w period l i vi ngrev i e w s period org slash lrr hyphen 2008 hyphen 8 Motivated by the successes at Parkes , a multibeam survey is now in progress with the Arecibo telescope [ 2 7 5 ] and the Effelsberg radio telescope . \quad The Arecibo survey has so far discovered 46

\noindent pulsars [ 2 7 5 , \ h f i l l 8 2 ] with notable finds including a highly relativistic binary [ 2 3 2 ] and an eccentric

\noindent millisecond pulsar binary [ 7 0 ] . Hundreds more pulsars could be found in this survey over the next five years . A significant fraction of this yield are expected to be distant millisecond pulsars in the

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\ hspace ∗{\ f i l l } Living Reviews in Relativity

\ hspace ∗{\ f i l l } ht tp : / / w w \quad w. l i vi ngrev i ews . org / lrr − 2008 − 8 20 ....20 Duncan R period Lorimer Duncan R . Lorimer \noindenthline 20 \ h f i l l Duncan R . Lorimer disk of our Galaxy period With the advent of sensitive low hyphen noise receivers at lower observing frequencies comma \ [ surveys\ r u l e { of3em the}{ Galactic0.4 pt }\ plane] are being carried out with the GMRT open square bracket 1 7 1 closing square bracket comma Green Bank open squaredisk of bracket our Galaxy 1 3 8 . closing With the square advent bracket of sensitive and low - noise receivers at lower observing frequencies , surveys Westerborkof the Galactic open square plane bracket are being 3 2 carried 6 closing out square with the bracket GMRT period [ 1 7 .. 1 At ] , Greenthe time Bank of writing [ 1 3 8 comma] and no new millisecond pulsars have been found\noindent inWesterbork thesedisk [ 3of 2 6 our ] . Galaxy At the time . With of writing the , advent no new millisecond of sensitive pulsars low have− beennoise found receivers in these searches at lower observing frequencies , surveyssearches, though comma of significant the though Galactic amounts significant plane ofamounts data are remain of being data to be remain carried fully processed to be out fully with . processed the GMRTperiod [ 1 7 1 ] , Green Bank [ 1 3 8 ] and 2 period2 . 1 1 1 1 . period 3 Searches 3 .. Searches at intermediateat intermediate and and high high Galactic Galactic latitudes latitudes \noindentTo probeTo probe moreWesterbork more deeply deeply into [ into the 3 2 populationthe 6 population ] . \ ofquad millisecond of millisecondAt the and time andrecycled recycled of pulsars writing pulsars than , than possible no possible new at millisecond at high Galactic pulsars have been found in these searcheshighlatitudes Galactic , ,though latitudes the Parkes significant comma multibeam the Parkes system amounts multibeam was also of system data used to remain was survey also intermediateused to be to survey fully lati intermediate processed - tudes [ 1 lati0 .2 hyphen, 1 0 0 ] . tudesAmong open thesquare 69new bracket pulsars 1 0 2 found comma in the 1 0 survey0 closing , 8 square are relatively bracket distant period ..recycled Among the 69 new pulsars found in the survey comma 8 are relatively\noindentobjects distant2 . . recycled Two1 1 of . the 3 \ newquad recycledSearches pulsars at from intermediate this survey [ 1 and 0 0 ] high are Galacticmildly relativistic latitudes neutron star objects- white period dwarf .. Two binaries of the . new An recycled analysis pulsars of the from full this results survey from open this square survey bracket should 1 0 significantly 0 closing square im - bracket prove .. are mildly relativistic neutron\noindentour knowledgeTo probe on the more Galaxy deeply - wide into population the population and birth - rate of of millisecond millisecond pulsars and . recycled Arecibo surveys pulsars at than possible at highstarintermediate hyphen Galactic white latitudes latitudes dwarf binaries also continue , periodthe Parkes to .. find An analysis new multibeam pulsars of the , such full system results as the was long from -also this period survey used binaries should to J survey 2016 significantly + 1948 intermediate and im hyphen lati − tudesproveJ 407 our [ 102 + knowledge 1607[279 ,100, on2 the 33], Galaxy]and . the\quad hyphen likelyAmong double wide population the neutron 69 starnew and system pulsarsbirth hyphen J 1829 found + rate 2456[68] of in millisecond the. survey pulsars , period8 are Arecibo relatively distant recycled surveysAlthough at intermediate the density latitudes of pulsars also continue decreases to find with new increasing pulsars Galacticcomma such latitude as the , discoverieslong hyphen away period from binaries the \noindentJ 20plane 1 6 plus provideo b 1 j e 948 c t strong s and . J\ constraints 407quad plusTwo 1 607 on of the open the scale square new height bracket recycled of the 2 millisecond 7 9 pulsars comma 2pulsar 3 from 3 closing population this square survey . bracketTwo recent [ comma 1 0 surveys 0 and ] \ thequad likelyare double mildly neutron relativistic neutron stars t a system r with− white Jthe 1 829 Parkes dwarf plus multibeam 2456 binaries open system square . \ bracketquad [ 4 9 ,An 6 8 1 closing analysis 5 6 ] square have of resulted bracket the full inperiod a number results of interesting from this discoveries survey . should significantly im − proveAlthoughPulsars our the atknowledge density high latitudes of pulsars on are the decreases especially Galaxy with important− increasingwide for population the Galactic millisecond latitude and pulsar birth comma timing− discoveriesrate array of ( away Section millisecond 4 . 7 . 3 ) pulsars . Arecibo surveysfromwhich the at plane benefits intermediate provide from strong widely constraints latitudesseparated pulsars on also the scaleon continue the height sky to of search to the findmillisecond for correlations new pulsar pulsars in population the , cosmic such period gravitational as the long − period binaries J$20Twowave recent background 1surveys 6 with on + a the variety 1 Parkes 948$andJ$407 of multibeam angular scales system . .. open square + 1 bracket 607 4 9 comma [ 2 .. 1 7.. 5 6 9 closing , square 2 bracket 3 3 have ] resulted ,$ in aandthe number2 . of 1likely 1 . 4 double Targeted neutron searches star of globular systemJ clusters $1 829 + 2456 [ 6 8 ] . $ interestingGlobular discoveries clusters have period long Pulsars been known at high to latitudes be breeding are especially grounds for important millisecond for the and millisecond binary pul pulsar - sars [ 6 3 ] . 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Twocorrelationstimes recent more in surveys the abundant cosmic with in gravitational clusters the than Parkes wave in the background multibeam Galactic disk on system a . variety In ad\ ofquad - ditionangular[ , 4 scalesexchange 9 , period\quad interactions1 \quad between5 6 ] have resulted in a number of interesting2 periodbinary 1 and1 period discoveries multiple 4 .. systemsTargeted . insearches Pulsars the cluster of at globular can high result clusters latitudes in the formation are of especially exotic binarysystems important [ 3 3 7 for ] . the To millisecond pulsar timingGlobulardate array , clusters searches ( have Sectionhave long revealed been 4 . 140 known 7 pulsars . 3to )be in which breeding 26 benefits grounds for from millisecond widely and separated binary pul hyphen pulsars on the sky to search for correlationssarsglobular open square clusters in bracket the [ 2 7 6cosmic 6 3 ] .closing gravitationalEarly square highlights bracket include period wave The the background double main reason neutron on for star a this variety binary is the inhigh Mof stellar 1 angular 5 [ 3 density 0 5 ] andscales and consequently . high rate of stellara low - mass binary system with a 95 - min orbital period in 47 Tucanae [ 5 6 ] , one of 23 millisecond \noindentinteractionpulsars2 currentlyin . globular 1 1 known . clusters 4 \quad inthis relativeTargeted cluster to most alone searches of [ 5the 6 , rest 2 2 of 3 of] the . globular Galaxy period clusters .. As a result comma low hyphen mass X hyphen rayOn binaries - going are surveys almost of 1 clusters 0 times continue more abundant to yield in new clusters surprises than [ in 3 1 the 6 , Galactic 8 9 ] , disk with period no less .. than In ad 70 hyphen \noindentditiondiscoveries commaGlobular .. in exchange the past clusters fiveinteractions years have between long [ 3 1 binary 4 been ] . and known multiple Among to thesebe systems breeding is the in the most cluster grounds eccentric can resultbinary for millisecond in pulsar in a and binary pul − sarstheglobular formation [ 6 3 cluster ] of . exotic The so far binarymain – J 514 reason systems− 4002 open for is a square 4 this . 99 ms bracket is pulsar the 3 high in3 7 a closing highly stellar eccentricsquare density bracket (e = 0 period.89) and binary consequently .. To date comma high searches rate have of revealed stellar 140interaction pulsarssystem in 26in the in globular globular cluster clusters NGC 1 851 relative [ 1 to1 4] most . The of cluster the with rest the of most the pulsars Galaxy is now . Terzan\quad 5As a result , low − mass X globular− raywhich clusters binaries boasts open33 [ are 3 square 1 7 almost , 2 bracket 7 6 ] , 1 30 2 0 7 of 6times which closing were more square found abundant bracket with periodthe in Green clusters.... EarlyBank Telescopehighlights than in [ include 2 the 7 8 ] the Galactic. The double spin neutron disk . star\quad binaryIn in adM − 1d 5 i open t i operiods n square , \ andquad bracket orbitalexchange 3 0parameters 5 closing interactions square of the new bracket pulsars between and reveal binarythat , as a and population multiple , they systems are significantly in the different cluster can result in thea lowto formation hyphen the pulsars mass of of binary 47 exotic Tucanae system binary which with a have systems95 hyphen periods min[ in 3 the orbital 3 range 7 ] period .2 –\quad 8 in ms 47 [ TucanaeTo 2 2 3 date ] . open The , searches square spin bracket have 5 6 closingrevealed square 140 bracket pulsars comma in 26 one of 23periods millisecond of the new pulsars span a much broader range ( 1 . 4 – 80 ms ) including the first , third and fourth \noindentpulsarsshortest currentlyglobular spin periodsknown clusters in of this all pulsars cluster [ 2 alonecurrently 7 6 open ] . known square\ h f i . l bracket l TheEarly binary 5 6 highlights comma pulsars 2 include 2 3 closing include six systems square the bracket with double eccentric period neutron star binary in M 1 5 [ 3 0 5 ] and Onorbits hyphen and going likely surveys white of dwarf clusters companions continue . to No yield such new systems surprises are known open square in 47 Tucanae bracket . 3 The 1 6 differencecomma .. between8 9 closing square bracket comma with\noindent nothe less two thana pulsar low 70 − populationsmass binary may reflect system the with different a 95 evolutionary− min orbital states and period physical in conditions 47 Tucanae of the [two 5 6 ] , one of 23 millisecond discoveriesclusters in . In the particular past five ,years the central .... open stellar square density bracket of Terzan3 1 4 closing 5 is about square twice bracket that period of 47 Tucanae .... Among , suggesting these is the most eccentric binary pulsar\noindent inthat a thepulsars increased currently rate of stellar known interactions in this might cluster disrupt the alone recycling [ 5process 6 , for2 2 the 3 neutron ] . stars in some globularbinary cluster systems so farand endash induce J larger 5 1 4 eccentricities minus 4002 is in a others 4 period . 99 ms pulsar in a highly eccentric open parenthesis e = 0 period 89 closing parenthesis\ hspace ∗{\ binaryf i l l }On − going surveys of clusters continue to yield new surprises [ 3 1 6 , \quad 8 9 ] , with no less than 70 system in the globular cluster NGC 1 851 open square bracket 1 .... 1 4 closing square bracket period The cluster with the most pulsars is \noindent discoveries in the past five years \ h f i l l [ 3 1 4 ] . \ h f i l l Among these is the most eccentric binary pulsar in a now TerzanLiving 5 Reviews in Relativity whichht boasts tp : 33 / open / w squarew w . bracket l i vi 3 1ngre 7 comma v i e 2 7 w 6 s closing . or square g / lrr bracket - 2008 comma - 8 30 of which were found with the Green Bank Telescope open\noindent square bracketglobular 2 7 8 clusterclosing square so bracket far −− periodJ $ The 5 spin 1 4 − 4002 $ is a 4 . 99 ms pulsar in a highly eccentric $(periods e and = orbital 0 parameters . 89 of )$ the new binary pulsars reveal that comma as a population comma they are significantly different to the pulsars of 47 Tucanae which have periods in the range 2 endash 8 ms open square bracket 2 2 3 closing square bracket period ..\noindent The spin system in the globular cluster NGC 1 851 [ 1 \ h f i l l 1 4 ] . The cluster with the most pulsars is now Terzan 5 periods of the new pulsars span a much broader range open parenthesis 1 period 4 endash 80 ms closing parenthesis including the first comma\noindent third andwhich boasts 33 [ 3 1 7 , 2 7 6 ] , 30 of which were found with the Green Bank Telescope [ 2 7 8 ] . The spin periodsfourth shortest and orbital spin periods parameters of all pulsars of currently the new known pulsars period The reveal binary that pulsars , includeas a population six systems , they are significantly differentwith eccentric to orbits the and pulsars likely white of 47 dwarf Tucanae companions which period have No periods such systems in are the known range in 47 2 −− Tucanae8 ms period [ 2 2 3 ] . \quad The spin The difference between the two pulsar populations may reflect the different evolutionary states and \noindentphysical conditionsperiods of of the the two clusters new pulsars period In span particular a much comma broader the central range stellar ( density1 . 4 of−− Terzan80 ms 5 is ) about including the first , third and fourthtwice that shortest of 47 Tucanae spin comma periods suggesting of all that pulsars the increased currently rate of stellar known interactions . The binary might disrupt pulsars include six systems withthe recycling eccentric process orbits for the and neutron likely stars in white some binary dwarf systems companions and induce . No larger such eccentricities systems are known in 47 Tucanae . Thein others difference period between the two pulsar populations may reflect the different evolutionary states and physicalhline conditions of the two clusters . In particular , the central stellar density of Terzan 5 is about twiceLiving that Reviews of in 47 Relativity Tucanae , suggesting that the increased rate of stellar interactions might disrupt theht tp recycling : slash slash process w w w period for l the i vi ngre neutron v i e w stars s period in or someg slash binary lrr hyphen systems 2008 hyphen and 8 induce larger eccentricities in o t h e r s .

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\noindent Living Reviews in Relativity

\noindent http : //www. l i vi ngrev i ews . org/ lrr − 2008 − 8 BinaryBinary and and Millisecond Millisecond Pulsars Pulsars .... 2 1 2 1 \noindenthline Binary and Millisecond Pulsars \ h f i l l 2 1 2 period 1 1 period 5 .. Targeted searches of other regions \ [ While\ r u l e globular{3em}{ clusters0.4 pt }\ are] the richest targets for finding millisecond pulsars comma .... other regions of interest2 . 1 have 1 . been 5 searched Targeted period searches .. Recently of other comma regions .. a search of error boxes from unidentified sources from theWhile Energetic globular Gamma clusters hyphen are Ray the Experimentrichest targets Telescope for finding .. open millisecond parenthesis pulsars EGRET , closing parenthesis other regions revealed of three new binary pulsars \noindentJ 1interest 6 1 4 minus2 have . 1 23 been 1 1 . 8 searched comma5 \quad J . 1Targeted 6 1 Recently 4 minus searches , 2230 a and search J of 1 of 744 other error minus boxes regions 3922 from open unidentified square bracket sources 1 3 from9 comma the 8 8 comma 3 1 3 closing squareEnergetic bracket period Gamma None - Ray of these Experiment pulsars Telescope is likely to be ( EGRET en hyphen ) revealed three new binary pulsars J 1614 − 2318, \noindentergeticJ 1614 enoughWhile− 2230 to be and globular associated J 1744 − clusters with3922[139 their, target are88, theEGRET313]. richestNone sources of these targets open pulsars square for is bracket likely finding to 1 3be 9 en closing millisecond - square bracket pulsars period , While\ h f i convincing l l other regions of EGRETergetic enough to be associated with their target EGRET sources [ 1 3 9 ] . While convincing EGRET \noindentassociationsassociationsinterest with with several several have young young been pulsars pulsars searched are are now now . known known\quad open [Recently 1 9 square 9 ] , it bracketis not, \quad clear 1 9 whether 9a closing search millisecond square of bracketerror pulsars commaboxes are itfrom is not unidentified clear whether sources from millisecondtherelevant Energetic to the Gamma energetics− Ray of these Experiment enigmatic sourcesTelescope [ 6 9 ]\ .quad Despite( EGRET this lack ) of revealed success , it threeis quite new possible binary pulsars Jpulsars $that 1 are the 6 relevant recent 1 launches to 4 the− energetics of the23 AGILE of 1 these 8 [enigmatic 1 5 ,$J$1 2 ] sources and GLAST open 6 square [ 2 1 7 bracket 1 4] gamma− 6 9 closing -2230$ ray observatories square andJ bracket will $1 period Despite 744 this− lack3922 of success[ 1provide comma 3 further 9 , opportunities 8 8 for , follow 3 - up 1 . 3 ] .$ Noneofthesepulsarsislikelytobeen − it is quiteOther possible targets that of theinterest recent are launches X - ray ofpoint the sources AGILE found .. open with square the Chandrabracket 1 [ 5 2 2 7 closing 0 ] and square XMM bracket - Newton .. and GLAST .. open square bracket\noindent[ 2 1 7 0 1 3 closingergetic ] observatories square enough bracket and to gamma TeV be sources associated hyphen found ray with with HESS their [ 2target 5 5 ] . EGRET The X sources - ray sources [ 1 have 3 9 been ] . While convincing EGRET associationsobservatoriesparticularly will withfruitful provide several targets further for youngopportunities young pulsars pulsars for , follow arewith hyphen anow number known up of period discoveries [ 1 9 9 of ] extremely , it is faint not objects clear [ 5 whether 4 millisecond pulsarsOther] . targets Althoughare of relevant interest not directly are to X the relevant hyphen energetics ray to the point topic sources of of this these found review enigmaticwith , these the Chandra searches sources areopen revolutionizing square [ 6 9 bracket ] . our Despite 2 7 picture 0 closing this square lack bracket of success .. and , XMMit is hyphenofthe quite young possible neutron star that population the recent and should launches provide ofvaluable the AGILE \quad [ 1 5 2 ] \quad and GLAST \quad [ 2 7 1 ] gamma − ray observatoriesNewtoninsights .. open into square the will beaming bracket provide fraction 1 0 3further closing and birthrate square opportunities bracket of these .. pulsars observatories for . follow and− TeVup sources . found with HESS .. open square bracket 2 5 5 closing2 square . 1 1 bracket . 6 Extragalacticperiod .. The X searches hyphen ray sources have OtherbeenThe targets particularly only radio of fruitful pulsars interest targets known are for outside young X − of pulsarsray the Galactic point comma field sources .. andwith its a found numberglobular with of cluster discoveries the systems Chandra of are extremely the [ 1 92 currently 7 0 ] \quad and XMM − Newtonfaintknown objects\quad in open the[ Large square 1 0 and 3 bracket ] Small\quad 5 Magellanic 4 closingobservatories square Clouds bracket [ and2 5 period 6 TeV , 8 7 .. , sources Although 2 4 7 ] . notfound The directly lack with relevant of HESS millisecond to\quad the pulsars topic[ of2 this 5 5 review ] . \ commaquad theseThe X − ray sources have searchesbeenin particularly are the sample so far fruitful is most likely targets due to the for limited young sensitivity pulsars of the , searches\quad andwith large anumber distance to of the discoveries clouds of extremely faintrevolutionizing. Further objects surveys our [ picture 5 in 4 the ] of Magellanic . the\quad youngAlthough clouds neutron are star warranted not population directly . Surveys and relevantshould provide to valuable the topic of this review , these searches are revolutionizinginsightsof more into distant the beaming galaxies our picture fraction have so and far of been birthrate the fruitless young of these . neutron Current pulsars instrumentation period star population is only and sensitive should to giant provide isolated valuable 2 periodpulsars 1 1 of period the kind 6 .. observed Extragalactic from searchesthe Crab [ 1 3 0 ] and the millisecond pulsars [ 1 9 3 ] . While surveys for \noindentThesuch only events radioinsights pulsars are on into- known going theoutside [ 1 9 beaming 5 ] of , thedetections Galactic fraction of field weaker and and periodic its birthrate globular sources cluster of are these systemslikely to pulsars are require the . enhanced thesensitivity 1 9 currently of the known next in generation the Large radio and Small telescopes Magellanic . Clouds .. open square bracket 2 5 6 comma 8 7 comma .. 2 4 7 closing square bracket\noindent2 period . 1 12 .. . . The7 1 1lack Surveys . of 6 \quad with newExtragalactic telescopes searches millisecondAll surveys pulsars that in have the so sample far been so far conducted is most likely , or will due be to carried the limited out in sensitivity the next offew the years searches , will ultimately be \noindentandsurpassed large distanceThe by only the to next the radio clouds generation pulsars period of Further radio known telescopes surveys outside in . the Theof Magellanic the Allen Galactic Telescope clouds are Array field warranted in and California period its globular[ Surveys 3 3 4 ] is cluster systems are theof more 1now 9 distantbeginning currently galaxies operations known have soand in far could the been allowLarge fruitless large and period - area Small .. coverage Current Magellanic of instrumentation the 1 – Clouds 1 0 is only\quad sensitive[ 2 5 to 6 , 8 7 , \quad 2 4 7 ] . \quad The l a c k o f millisecondgiantGHz isolated sky for pulsars pulsars pulsars of and the in kindtransients the observed sample . In from Europe so the far , Crab the is low open most - frequency square likely bracket array due [ 1 2 3 to1 0 closing the2 , 1limited square 0 4 ] is bracket set sensitivity to discover and the millisecond of the pulsars searches open squareandhundreds bracketlarge 1distance of9 3 faint closing nearby to square the pulsars bracket clouds [ 3 period8 7 . ] in Further the next surveys five years . in While the the Magellanic Square Kilometre clouds Array are [ 1 warranted 5 4 ] . Surveys Whileis not surveys expected for such to be events completed are on until hyphen 2020 going , a number open square of pathfinder bracket instruments1 9 5 closing are square now bracket under development comma detections of weaker periodic sources\noindent. are In Chinalikelyof more , the Five distant hundred galaxies meter Aperture have Spherical so far Telescope been fruitless [ 1 0 5 ] is scheduled . \quad forCurrent completion instrumentation in 20 1 is only sensitive to giantto require3 and isolated will the provideenhanced pulsars significant sensitivity of advances the of the kind next for observed pulsar generation research radio from [ 2 telescopes the6 6 ] .Crab The period Australian [ 1 3 0 ] and the millisecond pulsars [ 1 9 3 ] . While2 periodSquare surveys 1 1Kilometre period for 7 Array.. such Surveys Pathfinder events with new ,are will telescopes haveon − somegoing applications [ 1 9 as5 a ] pulsar , detections instrument [ of 1 6 4weaker ] . Very excitingperiodic sources are likely toAll requirewide surveys - field that the search have enhanced so capabilities far been sensitivity conducted will be offered comma of by the or the willSouth next be carried African generation out MeerKAT in the radio next array few telescopes of years 80 dishes comma set . will to begin ultimatelyoperations be surpassed in 20 1 2 [by 1 the8 6 ]next . generation of radio telescopes period .. The Allen Telescope Array \noindentin California2 . 12 2 .open 1 Going 1 square . 7 bracket further\quad 3Surveys 3 4 closing with square new bracket telescopes is now beginning operations and could allow large hyphen area coverage of the 1 endashTwo books 1 0 , Pulsar Astronomy [ 2 4 1 ] and Handbook of Pulsar Astronomy [ 2 2 6 ] , cover the lit \noindentGHzerature sky forAll and pulsars techniquessurveys and transients andthat provide have period excellent so In far Europe further been comma reading conducted the . low The hyphen , morphological or willfrequency be properties array carried open of out square pulsars in bracket have the next 2 1 .. 2few comma years .. 1 ,0 4 will closingultimatelyrecently square bracket been be comprehensivelysurpassed is set to discover by discussed the next in recent generation reviews [ 3 of 4 0 radio , 3 3 3 telescopes ] . Those seeking . \quad a moreThe theoretical Allen Telescope Array inhundreds Californiaviewpoint of faint are [nearby advised 3 3 pulsars 4 to ] read is openThe now square Theory beginning bracket ofNeutron 3 operations 8 7Star closing Magnetospheres square and bracket could[ 2 in allow 6 the 1 ] next and largeThe five years Physics− area period of coverage the While the Square of the Kilometre 1 −− 1 0 Array openPulsar square Magnetosphere bracket 1 5[ 4 3 closing 4 ] . square Our summary bracket of evolutionary aspects serves merely as \noindentis not expectedGHz tosky befor completed pulsars until and 2020 commatransients a number . In of pathfinder Europe instruments, the low are− frequency now under array [ 2 1 \quad 2 , \quad 1 0 4 ] is set to discover hundredsdevelopment of period faint In nearbyChina comma pulsars the Five [ 3hundred 8 7 ] meter in theAperture next Spherical five years Telescope . open While square the bracket Square 1 0 Kilometre 5 closing square Array bracket [ 1 5 4 ] isis scheduled not expected for to be completed until 2020 , a number of pathfinder instruments are now under development . In China , the Five hundred meter Aperture SphericalLiving Telescope Reviews in Relativity [ 1 0 5 ] is scheduled for completion in 20 1 3 and willht provide tp : significant / / w w advances w . forl i pulsar vi ngrev research i e open w s square . org bracket / lrr 2 - 6 2008 6 closing - 8 square bracket period The Australiancompletion in 20 1 3 and will provide significant advances for pulsar research [ 2 6 6 ] . The Australian Square Kilometre Array Pathfinder comma will have some applications as a pulsar instrument open square bracket 1 6 4 closing square bracket\noindent periodSquare Very Kilometre Array Pathfinder , will have some applications as a pulsar instrument [ 1 6 4 ] . Very excitingexciting wide wide hyphen− field field search search capabilities capabilities will be offered will by be the offered South African by the MeerKAT South array African of 80 MeerKAT array of 80 dishesdishes set set to beginto begin operations operations in 20 1 2 open in 20 square 1 2 bracket [ 1 8 1 68 6 ] closing . square bracket period 2 period 1 2 .. Going further \noindentTwo books2 comma . 1 2 Pulsar\quad AstronomyGoing further open square bracket 2 4 1 closing square bracket and Handbook of Pulsar Astronomy open square bracket 2 2 .. 6 closing square bracket comma cover the lit erature \noindentand techniquesTwo and books provide , Pulsar excellent Astronomy further reading [ 2 period 4 1 .. ] The and morphological Handbook of properties Pulsar of Astronomypulsars [ 2 2 \quad 6 ] , cover the lit erature andhave techniques recently been and comprehensively provide excellent discussed in further recent reviews reading open square . \quad bracketThe 3 4morphological 0 comma .. 3 3 3 properties closing square of bracket pulsars period .. Thosehave seeking recently a more been comprehensively discussed in recent reviews [ 3 4 0 , \quad 3 3 3 ] . \quad Those seeking a more theoreticaltheoretical viewpoint viewpoint are advised are to advised read The to Theory read ofNeutron The Theory Star Magnetospheres ofNeutron Star open Magnetospheres square bracket 2 6 1 [ closing 2 6 square 1 ] and bracket The and ThePhysics of the Pulsar Magnetosphere [ 3 4 ] . \quad Our summary of evolutionary aspects serves merely as Physics of the Pulsar Magnetosphere open square bracket 3 4 closing square bracket period .. Our summary of evolutionary aspects serves merely\ [ \ r u as l e {3em}{0.4 pt }\ ] hline Living Reviews in Relativity \ hspaceht tp :∗{\ slashf i slash l l } Living w w .. w Reviews period l i invi ngrev Relativity i e w s period org slash lrr hyphen 2008 hyphen 8 \ hspace ∗{\ f i l l } ht tp : / / w w \quad w. l i vi ngrev i ews . org / lrr − 2008 − 8 22 ....22 Duncan R period Lorimer Duncan R . Lorimer \noindenthline 22 \ h f i l l Duncan R . Lorimer a primer to the vast body of literature available period Further insights can be found from more detailed \ [ reviews\ r u l e { open3em}{ square0.4 pt bracket}\ ] 3 6 comma .. 3 0 0 comma .. 3 4 5 closing square bracket period Pulsara primer resources to the available vast body on the of literature Internet are available continually . Further becoming insights more can extensive be found and from useful more period detailed reviews [ A good36, starting 300, point 345]. for pulsar hyphen surfers is the Handbook of Pulsar Astronomy website open square bracket 2 2 7 closing square bracket\noindent commaPulsara as primer resources well to available the vast on the bodyInternet of literatureare continually available becoming more . Further extensive and insights useful . can A good be found from more detailed reviewsas thestarting Pulsar [ 3 point Astronomy 6 , for\quad pulsar wiki -3 surfers open 0 0 square ,is the\quadHandbook bracket3 4 3 50 of 7 Pulsar] closing . Astronomy square bracketwebsite and [ the 2 2 Cool 7 ] , as Pulsars well as site the openPulsar square bracket 3 7 5 closing squareAstronomy bracket periodwiki [ 3 0 7 ] and the Cool Pulsars site [ 3 7 5 ] . Pulsarhline resources available on the Internet are continually becoming more extensive and useful . ALiving good Reviews starting in Relativity point for pulsar − surfers is the Handbook of Pulsar Astronomy website [ 2 2 7 ] , as well as the Pulsar Astronomy wiki [ 3 0 7 ] and the Cool Pulsars site [ 3 7 5 ] . ht tpLiving : slash Reviews slash w in w Relativity w period l i vi ngre v i e w s period or g slash lrr hyphen 2008 hyphen 8 \ [ \ r uht l e tp{3em :}{ /0.4 / w pt w}\ w .] l i vi ngre v i e w s . or g / lrr - 2008 - 8

\noindent Living Reviews in Relativity

\noindent http : //www. l i vi ngrev i ews . org/ lrr − 2008 − 8 BinaryBinary and and Millisecond Millisecond Pulsars Pulsars .... 23 23 \noindenthline Binary and Millisecond Pulsars \ h f i l l 23 3 .. Pulsar .. Statistics .. and .. Demography \ [ The\ r u observed l e {3em}{ pulsar0.4 pt sample}\ ] is heavily biased towards the brighter objects that are the easiest to detect3 period Pulsar .. What we Statistics observe represents and only the tip Demography of the i ceberg of a much larger underlying populationThe observed open square pulsar bracket sample 1 is .. heavily 2 7 closing biased square towards bracket the period brighter .. The objects bias isthat well are demonstrated the easiest toby detectthe projection . of pulsars onto the Galactic\noindentWhat we3 \ observequad Pulsar represents\quad only theS t tip a t iof s t the i c s i ceberg\quad ofand a much\quad largerDemography underlying population [ 1 2 7 ] . planeThe shown bias in is Figurewell demonstrated 1 .. 1 period by The the clustering projection of of sources pulsars around onto the GalacticSun seen plane in the shown left panel in Figure is clearly 1 1 . \noindentat varianceThe clusteringThe with observed the of distribution sources pulsar around of other the sample Sun stellar seen is populations in heavily the left which panel biased showis clearly towards a radial at variance distribution the brighter with the distribution objects of that are the easiest tosymmetric dother e t e c t stellar about . \quad populations the GalacticWhat which we centre observe show period a radial Also represents distribution shown in Figure only symmetric 1the .. 1 about tip is the of the cumulative the Galactic i ceberg number centre . of Also of pulsars a shown much in larger underlying populationas aFigure function 1 [ of 1 1 theis the\quad projected cumulative2 7 distance ] number . \quad from of pulsarstheThe Sun bias as compared a function is well to of the the demonstrated expected projected distribution distance by from the for the projection Sun compared of pulsars onto the Galactic planea simpleto shownthe model expected in population Figure distribution with 1 \quad forno selectiona simple1 . Themodel effects clustering population period .. The with of observed no sources selection number aroundeffects distribution . the The Sun observedbecomes seen number in the left panel is clearly atstrongly variancedistribution deficient with becomes beyond the strongly a distribution few kp deficient c period beyond of other a few kpstellar c . populations which show a radial distribution symmetricFigureFigure 1 1 : 1 about Left 1 : panelLeft the panel : The Galactic : Thecurrent current samplecentre sample of . all of Also all known known shown radio radio pulsars in pulsars Figure projected projected 1 \ onto ontoquad the1 Galactic Galactic is the plane plane cumulative . period number of pulsars asThe aThe Galactic function Galactic centre centre of is the is at at the projected the origin origin and and thedistance the Sun is is at at from ( open 0 , 8 theparenthesis. 5 ) kpc Sun . Note compared 0 comma the spiral 8 to period - arm the structure5 closingexpected seen parenthesis in distribution kpc period for Note the spiral hyphena simplethe arm distribution structure model populationwhich seen in is now required with by no the selection most recent Galactic effects electron . \quad densityThe model observed [ 8 4 , 8 5number ] . Right distributionpanel becomes stronglythe: distribution Cumulative deficient which number is beyond now of required pulsars a few as by a the kp function most c . ofrecent projected Galactic distance electron from density the Sun model . openThe solid square line bracket shows 8 the 4 comma 8 5 closing square bracketobserved period Right sample while the dotted line shows a model population free from selection effects . \noindentpanel3 :. .. 1 CumulativeFigure Selection 1 number 1 : effects Left of pulsars panel in aspulsar :a function The searches current of projected sample distance of from all knownthe Sun radioperiod .. pulsars The solid projected line onto the Galactic plane . shows3 . the 1 . observed 1 The sample inverse while square the dotted law and line shows survey a model thresholds population free from selection effects period \noindent The Galactic centre is at the origin and the Sun is at ( 0 , 8 . 5 ) kpc2 . Note the spiral − arm structure seen in 3 periodThe most 1 .. Selection prominent effects selection in pulsar effect searches is the inverse square law , i . e . for a given intrinsic luminosity the 3 period 1 period 1 .. The inverse square law and survey thresholds , \noindentTheobserved most prominentthe flux distribution density selection varies effect inversely which is the with is inverse now the distancesquare required law squared comma by . the i period This most results e period recent in the for Galactic aobserved given intrinsic sample electron Case being 12 density Case 2 comma model [ 8 4 , 8 5 ] . Right panelthedominated observed : \quad flux byCumulative density nearby varies and / inverselynumber or high luminosity with of pulsars the distance objects as squared . a Beyond function period distances .. of This ofprojected results a few kpc in the from distance observed the Sun from , the the Sun . \quad The solid line shows the observed sample while the dotted line shows a model population free from selection effects . sampleapparent being flux dominated density by falls nearby below and the slash detection or high thresholds luminositySmin objectsof most period surveys Beyond . distances of a few kpc from the Sun comma the apparent flux density falls below the detection thresholds S sub minimum of most surveys period \noindenthline 3 . 1 \quad Selection effects in pulsar searches 2 sub Pulsar astronomers usually define the luminosity L equiv Sd to the power of 2 comma where S is the mean flux density at 400 MHz \noindent 3 . 1 . 1 \quad The inverse square law and survey thresholds open parenthesis a 2 standard2Pulsar observingastronomers frequency usually closing define parenthesisthe luminosity andL ≡ d isSd the, where distanceS is derived the mean from flux the density DM at open 400 MHz parenthesis ( a standard see Section 2 period 4 closing parenthesis\noindentobserving periodThe frequency Since most )this prominentand ignoresd is the any distance selection derived from effect the DM is ( see the Section inverse 2 . 4 ) .square Since this law ignores , any i . assumptions e . for a given intrinsic $\ lassumptions e f tabout.luminosity beaming about or beaminggeometrical\ begin { ora factors geometricall i g n ,e itd } is sometimes& factors 2 \\ commareferred to it as is asometimes “ pseudoluminosity referred ” to [ 6 as ] . a quotedblleft pseudoluminosity quotedblright open square&, bracket\end 6{ closinga l i g n esquare d }\ right bracket. $ period thehline observed flux density varies inversely with the distance squared . \quad This results in the observed sample being dominated by nearby and / or high luminosity objects . Beyond distances of a few kpc Living Reviews in Relativity Living Reviews in Relativity from the Sun , the apparent flux density falls below the detection thresholds $ S {\min }$ of most surveys . ht tp : slash slash w w .. w periodht tp l i: vi / ngrev / w i w e w s w period . l orgi vi slash ngrev lrr hyphen i e w s 2008 . hyphen org / lrr 8 - 2008 - 8 \ begin { a l i g n ∗} \ r u l e {3em}{0.4 pt } \end{ a l i g n ∗}

$ 2 { Pulsar }$ astronomers usually define the luminosity $ L \equiv Sd ˆ{ 2 } , $ where $ S $ is the mean flux density at 400 MHz ( a standard observing frequency ) and $ d $ is the distance derived from the DM ( see Section 2 . 4 ) . Since this ignores any assumptions about beaming or geometrical factors , it is sometimes referred to as a ‘‘ pseudoluminosity ’’ [ 6 ] .

\ [ \ r u l e {3em}{0.4 pt }\ ]

\ hspace ∗{\ f i l l } Living Reviews in Relativity

\ hspace ∗{\ f i l l } ht tp : / / w w \quad w. l i vi ngrev i ews . org / lrr − 2008 − 8 24 ....24 Duncan R period Lorimer Duncan R . Lorimer \noindenthline 24 \ h f i l l Duncan R . Lorimer Following open square bracket 9 8 closing square bracket comma we express this threshold as follows : \ [ Equation:\ r u l e {3em open}{0.4 parenthesis pt }\ ] 3 closing parenthesis .. S sub minimum = S slash N sub minimum divided by eta square root of n sub pol Row 1 T underbarFollowing rec [ plus 9 8 ] T , we sub express sky Row this 2 thresholdK . parenleftbigg as follows G : divided by K Jy to the power of minus 1 to the power of parenrightbigg minus 1 parenleftbigg Capital Delta nu divided by MHz parenrightbigg minus 1 slash 2 parenleftbigg t sub int divided by s parenrightbigg minus 1 slash\noindent 2 parenleftbiggFollowing W divided [ 9 by 8 P ] minus , we W express parenrightbigg this 1 threshold slash 2 mJy as comma follows : S/N  T rec + T  G ) ∆ν t W where S slashS N= sub minimummin is the thresholdsky ( signal hyphen− 1( to hyphen) − 1/2( noiseint ) ratio− 1/2( comma eta)1/ is2 a mJy generic, fudge(3) factor open parenthesis min √ K −1 lesssim\ begin 1{ closinga l i g n ∗} parenthesisη npol which ac hyphen KJy MHz s P − W S counts{\min for losses} = in sensitivity\ f r a c { S/N open parenthesis{\ emin period}}{\ g periodeta comma\ sqrt due{ n to sampling{ pol }}}\ and digitizationl e f t (\ begin noise{ closingarray parenthesis}{ c} T {\ commaunderline {\}} where S /N is the threshold signal - to - noise ratio , η is a generic fudge factor ( 1) which ac - nr e sub c pol + is the T number{minsky of}\\ K \end{ array }\ right )( \ f r a c { G }{ K Jy. ˆ{ − 1 }}ˆ{ ) } − 1 ( \ f r a c {\Delta counts for losses in sensitivity ( e . g . , due to sampling and digitization noise ), n is the number of \nupolarizations}{ MHz } recorded) − open1 parenthesis / 2 either ( 1\ f or r a 2 c { closingt { parenthesisi n t }}{ commas } ) T subpol− rec1 and T / sub 2 sky are ( the\ f r receiver a c { W and}{ P sky noise− polarizations recorded ( either 1 or 2),T and T are the receiver and sky noise temperatures , Wtemperatures} ) 1 comma / 2 mJy , \ tag ∗{rec$ (sky 3 ) $} G is the gain of the antenna , ∆ν is the observing bandwidth , t is the integration time ,W is the detected \endG{ isa the l i g gainn ∗} of the antenna comma Capital Delta nu is the observingint bandwidth comma t sub i nt is the integration time comma W is the pulse width and P is the pulse period . detected pulse width and P is the pulse period period 3 . 1 . 2 Interstellar pulse dispersion and multipath scattering \noindent3 period 1where period 2 S .. Interstellar $ / N pulse{\min dispersion}$ isand the multipath threshold scattering signal − to − noise ratio $ , \eta $ is a generic fudge factor It follows from Equation ( 3 ) that the minimum flux density increases as W/(P − W ) and hence W $ (It follows\ lesssim from Equation 1 ) open $ parenthesis which ac 3− closing parenthesis that the minimum flux density increases as W slash open parenthesis P increases . Also note that if W P, the pulsed signal is smeared into the background emission and is no longer minus W closing parenthesis and hence& W detectable , regardless of how luminous the source may be . The detected pulse width W may be broader \noindentincreases periodcounts Also for note losses that if W in gtrsim sensitivity P comma the ( pulsede . g signal . , isdue smeared to sampling into the background and digitization emission and noise $ ) , than the intrinsic value largely as a result of pulse dispersion and multipath n is{ nopol longer}$ detectable is the comma number regardless of of how luminous the source may be period .. The detected pulse width scattering by free electrons in the interstellar medium . The dispersive smearing scales as ∆ν/ν3, where W may be broader than the intrinsic value largely as a result of pulse dispersion and multipath ν is the observing frequency . This can largely be removed by dividing the pass - band into a number of \noindentscattering bypolarizations free electrons in recorded the interstellar ( either medium period1 or .. $ The 2 dispersive ) , smearing T { scalesr e c } as$ Capital and Delta $ T nu{ slashsky nu}$ to the are power the of receiver and sky noise temperatures , channels and applying successively longer time delays to higher frequency channels before summing over all 3 comma channels to produce a sharp profile . This process is known as incoherent dedispersion . \noindentwhere nu is$G$ the observing is the frequency gain period of the .. This antenna can largely $ ,be removed\Delta by dividing\nu $ the is pass the hyphen observing band into bandwidth $ , t { i The smearing across the individual frequency channels , however , st ill remains and becomes significant nt a} number$ is of the channels integration and applying time successively $ , W$longer time is the delays to higher frequency channels at high dispersions when searching for short - period pulsars . Multipath scattering from electron density detectedbefore summing pulse over width all channels and $to P produce $ is a sharpthe pulse profile period period .. This . process is known as incoherent irregularities results in a one - sided broadening of the pulse profile due to the delay in arrival times . A simple dedispersion period scattering model is shown in Figure 1 2 in which the scattering electrons are assumed to lie in a thin screen \noindentThe smearing3 . across 1 . the 2 \ individualquad Interstellar frequency channels pulse comma dispersion however comma and multipath st ill remains scattering and becomes between the pulsar and the observer [ 3 3 1 ] . The timescale of significant at high dispersions when searching for short hyphen period pulsars period Multipath scattering from this effect varies roughly as ν−4, which can not currently be removed by instrumental means . \noindentelectron densityIt follows irregularities from results Equation in a one ( hyphen 3 ) that sided broadeningthe minimum of the flux pulse density profile due increases to the delay as $W / ( P − Figure 1 2 : Left panel : Pulse scattering caused by irregularities in the interstellar medium . The different path Win )$ arrival andhence times period A $W$ simple scattering model is shown in Figure 1 2 .. in which the scattering electrons lengths and travel times of the scattered rays result in a “ scattering tail ” in the observed pulse profile which lowers are assumed to lie in a thin screen between the pulsar and the observer open square bracket 3 3 1 closing square bracket period .. The its signal - to - noise ratio . Right panel : A simulation showing the percentage of Galactic pulsars that are likely to be timescale\noindent of increases . Also note that if $W \ gtrsim P , $ the pulsed signal is smeared into the background emission and undetectable due to scattering as a function of observing frequency . Low - frequency ( 1 GHz ) surveys clearly isthis no effect longer varies detectable roughly as nu to, regardlessthe power of minus of how 4 comma luminous which can the not source currently may be. beremoved . \quad by instrumentalThe detected means period pulse width miss a large percentage of the population due to this effect . $W$Figure 1 may 2 : Left be panel broader : Pulse than scattering the caused intrinsic by irregularities value largely in the interstellar as a result medium of period pulse The dispersion different and multipath Dispersion and scattering are most severe for distant pulsars in the inner Galaxy where the number of free path lengths and travel times of the scattered rays result in a quotedblleft scattering tail quotedblright in the observed pulse profile electrons along the line of sight becomes large . The strong frequency dependence of both effects means that \noindentwhich lowersscattering its signal hyphen by free to hyphen electrons noise ratio in period the interstellarRight panel : A simulation medium . showing\quad theThe percentage dispersive of Galactic smearing pulsars scales as they are considerably less of a problem for surveys at observing frequencies $ \thatDelta are likely\nu to be/ undetectable\nu ˆ{ due3 } to scattering, $ as a function of observing frequency period .. Low hyphen frequency whereopen parenthesis $ \nu $ lesssim is the 1 GHz observing closing parenthesis frequency surveys . \ clearlyquad missThis a large can percentage largely ofbe the removed population by due dividing to this effect the period pass − band i n t o aDispersion number of and channels scattering are and most applying severe for successively distant pulsars in longer the inner time Galaxy delays where the to higher frequency channels beforenumberLiving summing of Reviewsfree electrons over in Relativity along all thechannels line of sight to becomesproduce large a sharp period The profile strong . frequency\quad dependenceThis process of is known as incoherent dedispersionbothht effects tp : means / . / wthat w wthey . are l i considerably vi ngre v less i e of w a s problem . or g for / surveys lrr - at2008 observing - 8 frequencies hline TheLiving smearing Reviews across in Relativity the individual frequency channels , however , st ill remains and becomes significantht tp : slash slash at whigh w w dispersionsperiod l i vi ngre when v i e w searching s period or gfor slash short lrr hyphen− period 2008 hyphen pulsars 8 . Multipath scattering from electron density irregularities results in a one − sided broadening of the pulse profile due to the delay in arrival times . A simple scattering model is shown in Figure 1 2 \quad in which the scattering electrons are assumed to lie in a thin screen between the pulsar and the observer [ 3 3 1 ] . \quad The timescale of

\noindent this effect varies roughly as $ \nu ˆ{ − 4 } , $ which can not currently be removed by instrumental means .

\noindent Figure 1 2 : Left panel : Pulse scattering caused by irregularities in the interstellar medium . The different path lengths and travel times of the scattered rays result in a ‘‘ scattering tail ’’ in the observed pulse profile which lowers its signal − to − noise ratio . Right panel : A simulation showing the percentage of Galactic pulsars that are likely to be undetectable due to scattering as a function of observing frequency . \quad Low − frequency $ ( \ lesssim 1 $ GHz ) surveys clearly miss a large percentage of the population due to this effect .

Dispersion and scattering are most severe for distant pulsars in the inner Galaxy where the number of free electrons along the line of sight becomes large . The strong frequency dependence of both effects means that they are considerably less of a problem for surveys at observing frequencies

\ [ \ r u l e {3em}{0.4 pt }\ ]

\noindent Living Reviews in Relativity

\noindent http : //www. l i vi ngrev i ews . org/ lrr − 2008 − 8 BinaryBinary and and Millisecond Millisecond Pulsars Pulsars .... 25 25 \noindenthline Binary and Millisecond Pulsars \ h f i l l 25 gtrsim 1 period 4 GHz open square bracket 7 6 comma .. 1 6 8 closing square bracket compared to the 400 hyphen MHz search frequency used\ [ \ inr u early l e {3em surveys}{0.4 period pt }\ ..] An added bonus& 1 for.4 GHz such [observations 7 6 , 1 6 8is ] the compared reduction to inthe T 400 sub - sky MHz which search scales frequency with frequency used in early as approximately surveys . An added nu tobonus the power for such of minusobservations 2 period is 8the open reduction square inbracketTsky which 2 0 7 closing scales with square frequency bracket periodas approximately Pulsar intensities also have an inverse frequency −2.8 dependence\noindentν comma[207]$ . \Pulsargtrsim with theintensities average 1 also .scaling have 4$ an GHz[76,inverse frequency\quad dependence1 6 ,8 with ] compared the average to scaling the 400 − MHz search frequency used in early surveys . \quad An added −1.6 bonusbeingbeing nu for toν such the power[2 observations 34] of, minusso that 1 period flux is densities the 6 open reduction aresquare roughly bracket in an order 2 $ 3 4T of closing magnitude{ sky square}$ lower bracket which at comma 1 scales . 4 GHz .. so compared with that flux frequency densities areas roughly approximately an order ofto magnitude 400 MHz lower . Fortunately at .. 1 period , this 4 GHz can be at least partially compensated for by the use of larger receiver \noindentcomparedbandwidths to$ 400\nu at MHz higherˆ{ period − radio2 .. Fortunately frequencies . 8 } .comma For[ example this 2 can 0 , be the 7 at 1 least.four ] partially− .hyphen $ compensatedPulsar GHz system intensities for at by Parkes the use has also of a have an inverse frequency dependence , with the average scaling largerbandwidth receiver bandwidthsof 288 MHz at [ 2 higher 4 0 ]radio compared frequencies to the period 430 - MHz For example system , comma where nominally the 1 period 32 four-hyphen MHz is GHz system at Parkes \noindenthasavailable a bandwidthbeing [ 2 5 of 1 $]288 . \nu MHzˆ{ open − square1 bracket . 6 2} .. 4[ 0 closing 2 3square 4 bracket ] compared , $ \quad to theso 430 that hyphen flux MHz densities system comma are where roughly an order of magnitude lower at \quad 1 . 4 GHz nominallycompared3 . 32 1 . MHz to 3 400 is Orbital MHz . acceleration\quad Fortunately , this can be at least partially compensated for by the use of largeravailableStandard receiver open pulsar square bandwidths searches bracket use 2 5 Fourier1 at closing higher techniques square radio bracket [2 frequencies period 2 6 ] to search . For for examplea priori ,unknown the $ periodic1 . four−hyphen $ GHz system at Parkes has3 period asignals bandwidth 1 period and usually 3 .. of Orbital assume 288 MHz acceleration that [ the 2 \ apparentquad 4 pulse 0 ] period compared remains to constant the 430 throughout− MHz system the ob - servation, where . nominally 32 MHz is StandardFor searches pulsar with searches integration use Fourier times techniques much greater .. open than square a few minutes bracket ,2 this .. 2 assumption 6 closing square is only bracket valid for .. solitaryto search for .. a priori unknown periodic\noindentpulsarsavailable or binary systems [ 2 5with 1 orbital ] . periods longer than about a day . For shorter - period binary systems , signalsthe and Doppler usually - shifting assume of that the periodthe apparent results pulse in a spreading period remains of the constant signal power throughout over a number the ob hyphen of frequency bins \noindentservationin the period Fourier3 . 1 .. domain . For 3 searches\quad , leading withOrbital to integration a reduction acceleration times in S / much N [ 1 greater 6 2 ] . than An a observer few minutes will perceive comma this the frequency assumption of is onlya pulsar valid to for shift solitary by an pulsars amount oraT/ binary(P c systems), with orbital periods longer than about a day period \noindentForwhere shorteraStandard hyphenis the ( period assumed pulsar binary constant searches systems ) line comma - use of - sightFourier the Doppler acceleration techniques hyphen during shifting the\quad ofobservation the[ period 2 \quad of results length2 in 6T,P a ] spreading\quad to of the search for \quad a priori unknown periodic signalssignalis the power and ( constant over usually a number ) pulsar assume of period frequency that in its bins the rest in frame apparent the Fourier and c is pulse domain the speed period comma of light leading remains . to a constant reduction Given that in throughout the width the ob − s eS r vslash aof t ia o Nfrequency n open . \quad square bin inFor bracket the searches Fourier 1 6 2 domain closing with is square 1 integration/T, we bracket see that period times the signal.. An much will observer greaterdrift intowill perceivemore than than a the few frequency minutes of a , pulsar this to assumption shift by an 2 amountis onlyone aT spectral slash valid open bin for parenthesis if solitaryaT /(P cPc) > closing pulsars1. parenthesisSurvey or sensitivitiesbinary comma systems to rapidly with - spinning orbital pulsars periods in t ight longer orbits than are about a day . Forwheretherefore s h oa r is t e the r significantly− openperiod parenthesis compromised binary assumed systems when constant the , integration the closing Doppler parenthesis times− areshifting largeline hyphen . of of the hyphen period sight acceleration results in during a spreading the observation of theof lengthsignal TFigure comma power 13 P : overLeftpanel a number : A 22 of. 5 - frequency min Arecibo observation bins in theof the Fourier binary pulsar domain B 1913 , + leading 16. The assumption to a reduction in Sis / the Nthat open[ the 1 6pulsar parenthesis 2 ] has . a\ constantquad constantAn period closing observer during parenthesis this will time pulsar is perceive clearly period inappropriate the in its frequency rest given frame the and quadratic of c a is pulsar the drifting speed to in of phase shift light of period by an .... amount Given that $ the aT width/ (the pulse Pc during ) the , $ observation ( linear grey scale plot ) . Right panel : The same observation after applying an of aacceleration frequency bin search in the . This Fourier shows domain the effective is 1 slash recovery T comma of the pulse we see shape that and the a signal significant will drift improvement into more in than the signal \noindentone- spectral to - noisewhere bin ratio if .aT $ a to $ the is power the of ( 2 slashassumed open constantparenthesis Pc) line closing− parenthesiso f − sight greater acceleration 1 period .. Survey during sensitivities the observation to rapidly of length hyphen$ T spinning , P $ pulsars in t ight orbits are therefore significantly compromised when the integration times are large period \noindent is the ( constant ) pulsar period in its rest frame and $ c $ is the speed of light . \ h f i l l Given that the width Figure 13 : Left panel : A 22 period 5 hyphen min Arecibo observation of the binaryLiving pulsar Reviews B 1 9 1 in 3 Relativity plus 1 6 period The assumption that the pulsar has a constantht period tp : during / / wthis w time w is . clearly l i vi inappropriate ngrev i e given w s . the org quadratic / lrr drifting - 2008 - 8 \noindentin phase ofof the a pulse frequency during the bin observation in the open Fourier parenthesis domain linear is grey $ scale1 plot/ closing T , parenthesis $ we see period that .. Right the signal panel : The will same drift into more than observation \noindentafter applyingone an spectral acceleration bin search if period $ aT This ˆ{ shows2 } the/ effective ( Pc recovery ) of> the pulse1 shape . $ and\quad a significantSurvey sensitivities to rapidly − spinning pulsars in t ight orbits areimprovement therefore in the significantly signal hyphen to compromised hyphen noise ratio when period the integration times are large . hline \noindentLiving ReviewsFigure in Relativity 13 : Left panel : A 22 . 5 − min Arecibo observation of the binary pulsar B $ 1 9 1ht 3 tp : +slash slash1 6w w .. .$ w period Theassumption l i vi ngrev i e w s period org slash lrr hyphen 2008 hyphen 8 that the pulsar has a constant period during this time is clearly inappropriate given the quadratic drifting in phase of the pulse during the observation ( linear grey scale plot ) . \quad Right panel : The same observation after applying an acceleration search . This shows the effective recovery of the pulse shape and a significant improvement in the signal − to − noise ratio .

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\ hspace ∗{\ f i l l } Living Reviews in Relativity

\ hspace ∗{\ f i l l } ht tp : / / w w \quad w. l i vi ngrev i ews . org / lrr − 2008 − 8 26 ....26 Duncan R period Lorimer Duncan R . Lorimer \noindenthline 26 \ h f i l l Duncan R . Lorimer As an example of this effect comma as seen in the time domain comma Figure .. 1 3 .. shows a 22 period 5 hyphen min search \ [ mode\ r u l observatione {3em}{0.4 of pt the}\ binary] pulsar B 1 9 1 3 plus 1 6 open square bracket 1 5 0 comma 3 6 6 comma 3 6 7 closing square bracket period Although thisAs an observation example of covers this effect , as seen in the time domain , Figure 1 3 shows a 22 . 5 - min search mode onlyobservation about 5 percent of the of binary the orbit pulsar open B 1913 parenthesis + 16[150 7, period366, 367] 75 hr. Although closing parenthesis this observation comma covers the severe effects of the Doppler smearing on theAs pulse anonly example signal about 5% of of this the orbit effect ( 7 . 75 , ashr ) seen , the severe in the effects time of the domain Doppler , smearing Figure on\quad the pulse1 3 signal\quad shows a 22 . 5 − min search modeobservationofthebinarypulsarBareare very very apparent apparent period . .. While While the the standard standard search search code $1 code nominally nominally 9 1 detects detects 3 the the+ pulsar pulsar 1 with with 6 S S / [ slash N = 1 9N.5 = for 5 9 periodthis 0 5 , 3 6 6 ,for 3 thisobservation 6 observation 7 , it ] is comma clear . $ that it is Although this clear value that is this this significantly value observation is significantly reduced due covers reduced to the due Doppler to the shifting Doppler of shiftingthe pulse period of theseen pulse in the period individual seen in sub the - individual integrations sub . hyphen integrations period \noindentIt is clearlyIt isonly desirableclearly about desirable to employ $ to 5 aemploy technique\% $ a techniqueof to recover the to orbit the recover loss ( in the7 sensitivity . loss 75 in hr sensitivity due ) , to the Doppler due severe to Doppler effects smearing of . the Doppler smearing on the pulse signal smearingOne such period technique .. One such , the technique so - called comma “ acceleration the so hyphen search called ” [ quotedblleft 2 6 2 ] , assumes acceleration the pulsar search has quotedblright a constant .. open square bracket 2 6\noindent 2 closingacceleration squareare bracket very during apparent comma the observation assumes . \quad the. pulsar EachWhile time has the a series standard can then be search re - sampled code to nominally refer it to the detects frame of the pulsar with S / N $ =constantan 9 inertial acceleration . observer 5 $ during using the the observation Doppler formula period to .. relateEach time a time series interval can thenτ in be the re pulsar hyphen frame sampled to that to refer in the it forto theobserved this frame observation frameof an inertial at t ime observer ,t, itas τ is(t using) ∝ clear(1 the + @ Doppler that/c). Searching this formula value over to relate a isrange a significantly time of accelerations interval tau is reducedin desirable the dueto find to the the Doppler shifting ofpulsar thetime frame pulse series to for period that which in the seenthe observed trial in acceleration the frame individual at t most ime closelyt comma sub matches− asintegrations tau the open true parenthesis value . . In t closing the ideal parenthesis case , a time varpropto open parenthesis 1 plus atseries slash cis closing produced parenthesis with a signal period of Searching constant periodover a range for which full sensitivity is recovered ( see right panel of Itof is accelerationsFigure clearly 1 3 ) isdesirable . desirable This technique to to find employ the was time first a series used technique for which to the recover trial acceleration the loss most in closely sensitivity due to Doppler smearingmatchesto find the . PSR true\quad B value 2127One period + 11 such C In [ 4 the technique ] ,ideal a double case neutron comma, the stara so time− binary seriescalled in is M produced ‘‘1 5 accelerationwhich with has a parameters signal search of constant similar ’’ toperiod\quad [ 2 6 2 ] , assumes the pulsar has a constantfor whichB 1913 full acceleration + 16 sensitivity. Its application is recovered during to 47 openthe Tucanae observationparenthesis [ 5 6 ] resulted see right . in\quad panel the discoveryEach of Figure time of 1 nine 3 series closing binary parenthesis millisecond can then period be re ..− Thissampled technique to was refer first it to the frame of an inertial observer using the Doppler formula to relate a time interval $ \tau $ in the used pulsars , including one in a 96 - min orbit around a low - mass (0.15M ) companion . This is currently the pulsarto findshortest PSRframe binary B 2 to 1 27period that plus forin 1 1 any the C open known observed square radio bracket pulsar frame . 4 Theat closing t majority ime square $ of bracket t binary , comma millisecond $ as a double $ pulsars\tau neutron with( orbital star t binary ) in\ varpropto M 1 5 which has ( parameters1 +periods @ similar less / tothan c a day ) found .$ in Searchingoverarangerecent globular cluster searches would not have been discovered without the ofB accelerations1use 9 1 of 3 acceleration plus 1 6 period is searches desirable Its application . to to find 47 Tucanae the time open series square bracket for which 5 6 closing the square trial bracket acceleration resulted in most the discovery closely of nine binarymatches millisecondFor the intermediate true value orbital . periods In the , in ideal the range case 30 , min a – time several series hours , is another produced promising with tech a - signalnique is of constant period forpulsars whichthe dynamic comma full including power sensitivity spectrum one in search a is 96 hyphenrecovered shown in min Figure orbit ( see 1 4around . rightHere a the low panel time hyphen series of mass isFigure split open into 1 parenthesis a 3 number ) . \ ofquad 0 smaller periodThis 1 5 technique M sub odot was closing first used parenthesiscontiguous companion segments period which This are is currently Fourier - transformed separately . The individual spectra are displayed as a \noindentthetwo shortest - dimensionalto binary find period PSRB ( frequency for any $ 2versus known 1 time radio 27 ) image pulsar + . period 1 Orbitally The 1 $ majority modulated C [ 4 of ] binary pulsar , a millisecondsignals double appear neutron pulsars as sinusoidal star binary inM1 5 which has parameters similar to withsignals orbital in periods this plane less as than shown a day in found Figure in 1 recent 4 . globular cluster searches would not have been \noindentdiscoveredFigureB without 14 $: 1 theDynamic 9 use of 1 power acceleration 3 spectra + searches showing 1 6 two period recent . $ pulsar Its discoveries application in the globularto 47 clusterTucanae M 62 [ showing 5 6 ] resulted in the discovery of nine binary millisecond Forfluctuation intermediate frequency orbital as periods a function comma of time in the . Figure range provided 30 min by endash Adam several Chandler hours . comma another promising tech hyphen \noindentnique isThis thepulsars techniquedynamic power, has including been spectrum used by one search various in shown a groups 96 in− Figurewheremin spectra 1 orbit 4 period are around Hereinspected the a time visuallylow series− mass$( [ 2 is 4 split 5 ] . intoMuch a of 0 the . 1 5 M {\odot } ) $number companionhuman of smaller intervention . contiguous This can is be segments removedcurrently whichusing a are hierarchical Fourier hyphen scheme transformed for selecting separately significant period events .. [ The 7 1 ] individual . This thespectraapproach shortest are displayed was binary recently as a period applied two hyphen to for a search dimensional any knownof the openglobular radio parenthesis cluster pulsar M frequency 62 . resultingThe majority versus in the time discovery of closing binary ofparenthesis three millisecond new image period pulsars .. Orbitally modulatedwithpulsars orbital . One periods of the new less discoveries than –a M day 62 F found , a faint in 2 . recent 3 - ms pulsar globular in a 4 . cluster 8 - hr orbit searches – was detectable would not have been discoveredpulsaronly signals using without appear the dynamic as the sinusoidal power use spectrum signalsof acceleration in technique this plane . as searches shown in Figure . 1 .. 4 period FigureFor 14 : the .. Dynamic shortest power orbital spectra periods showing , the two assumption recent pulsar of a discoveriesconstant acceleration in the globular during cluster the ob M 62- servation Forshowing intermediateclearly fluctuation breaks down orbitalfrequency . In as thisperiods a functioncase , , a of in particularly time the period range efficient Figure 30 providedmin algorithm−− byseveral has Adam been Chandler devel hours - period, another promising tech − niqueThis technique is the has dynamic been used power by various spectrum groups searchwhere spectra shown are in inspected Figure visually 1 4 open . Here square the bracket time 2 4 series 5 closing is square split bracket into period a numberMuch of of the smaller human intervention contiguous can be segments removed using which a hierarchical are Fourier scheme− fortransformed selecting significant separately . \quad The individual spectraevents open are square displayed bracket 7 as 1 closing a two square− dimensional bracket period ( .. frequency This approach versus was recently time applied ) image to a .search\quad of theOrbitally globular cluster modulated M 62 pulsarLiving signals Reviews appear in Relativity as sinusoidal signals in this plane as shown in Figure 1 \quad 4 . resultinght tp : / / w w w . l i vi ngre v i e w s . or g / lrr - 2008 - 8 in the discovery of three new pulsars period One of the new discoveries endash M 62 F comma a faint 2 period 3 hyphen ms pulsar in \noindenta 4 periodFigure 8 hyphen 14 hr orbit : \quad endashDynamic was detectable power only spectra using the showing dynamic twopower recent spectrum pulsar technique discoveries period in the globular cluster M 62 showingFor the shortest fluctuation orbital periods frequency comma as .. the a assumptionfunction of of a timeconstant . acceleration Figure provided during the by ob Adam hyphen Chandler . servation clearly breaks down period .. In this case comma .. a particularly efficient algorithm has been devel hyphen Thishline technique has been used by various groups where spectra are inspected visually [ 2 4 5 ] . MuchLiving of Reviews the human in Relativity intervention can be removed using a hierarchical scheme for selecting significant eventsht tp : slash [ 7 slash1 ]w . w\quad w periodThis l i vi approach ngre v i e wwas s period recently or g slash applied lrr hyphen to 2008 a search hyphen of 8 the globular cluster M 62 resulting in the discovery of three new pulsars . One of the new discoveries −− M62F , a faint 2 . 3 − ms p u l s a r in a 4 . 8 − hr o r b i t −− was detectable only using the dynamic power spectrum technique .

For the shortest orbital periods , \quad the assumption of a constant acceleration during the ob − servation clearly breaks down . \quad In this case , \quad a particularly efficient algorithm has been devel −

\ [ \ r u l e {3em}{0.4 pt }\ ]

\noindent Living Reviews in Relativity

\noindent http : //www. l i vi ngrev i ews . org/ lrr − 2008 − 8 BinaryBinary and and Millisecond Millisecond Pulsars Pulsars .... 27 27 \noindenthline Binary and Millisecond Pulsars \ h f i l l 27 oped open square bracket 7 8 comma .. 3 1 2 comma .. 1 7 2 comma 3 1 5 closing square bracket which is optimised to finding binaries with\ [ \ periodsr u l e {3em so short}{0.4 that pt }\ many] orbitsoped can [ 7take 8 , place 3 1 during 2 , 1 an 7 2 observation , 3 1 5 ] which period is optimised.. This quotedblleft to finding phase binaries modulation with periods quotedblright so short that technique many exploits the fact thatorbits the Fourier can take components place during are an modulated observation by . the This orbit “ to phase create modulation a family of ” techniqueperiodic sidebands exploits the fact that the \noindentaroundFourier theoped componentsnominal [ 7 spin 8 are frequency , modulated\quad of3 the 1 by 2 pulsar the , orbit\quad period to create1 While 7 2 a this family, 3 technique 1 of 5 periodic ] haswhich so sidebands far is not optimised resulted around in the any to nominal finding binaries with periods so short that many orbitsnewspin discoveries can frequency take comma of place the the pulsar existence during . While of an short this observation technique period binaries has . so\ in farquad 47 not TucanaeThis resulted open‘‘ in phase any square modulation bracket 5 6 closing ’’ technique square bracket exploits comma Terzan the fact 5that opennew square the discoveries Fourier bracket 3 , the1 components 7 closingexistence square of are short bracket modulated period and binaries the by in the 47 Tucanae orbit [to 5 6 create ] , Terzan a 5 family [ 3 1 7 ] andof periodicthe sidebands around1 11 hyphen 1 -the min min nominal X - X ray hyphen binary spin ray X frequency binary 1820 − X303 1 820 in of NGC minus the 6624 303 pulsar [ in 3 5 NGC 4 . ] , While 6624 suggests open this that square theretechnique bracket are more 3 has5 ultra4 closing so - compact far square not bracket resulted comma in suggests any that thereradio are binary more pulsars ultra hyphen that await compact discovery . \noindentradio3 binary . 2new pulsars Correcting discoveries that await the discovery , the observed existence period pulsar of sample short period binaries in 47 Tucanae [ 5 6 ] , Terzan 5 [ 3 1 7 ] and the 3 periodIn the 2 following .. Correcting , we the review observed common pulsar techniques sample to account for many of the aforementioned selection effects \noindentIn theand following form1 1 a less− commamin biased X we− picture reviewray of common binary the true techniques X pulsar $ 1 population to 820 account .− for many303 of$ the in aforementioned NGC 6624 [ selection 3 5 4 ] , suggests that there are more ultra − compact radioeffects3 . binary and 2 . form 1 pulsars a Scale less biased factor that picture determination await of the discovery true pulsar population. period 3 periodA very 2 perioduseful approach 1 .. Scale [ factor 2 9 9 , determination 3 8 9 ] , is to define a scaling factor ξ as the ratio of the total Galactic volume \noindentA veryweighted useful3 by. approach 2 pulsar\quad density openCorrecting square to the bracket volume the 2 in 9 observed which9 comma a pulsar 3 pulsar8 9 isclosing detectable sample square : bracket comma is to define a scaling factor xi as the ratio of the total Galactic \noindent In the following , we review common techniques to account for many of the aforementioned selection volume weighted by pulsar density to the volume in whichRR Σ( aR, pulsar z)RdRdz is detectable : effectsEquation: and open form parenthesis a less 4 closing biased parenthesis pictureξ(P,L) .. = of xi open theG parenthesis true pulsar P comma population L closing .parenthesis = integral(4) integral sub G Capital P,LΣ(R, z)RdRdz Sigma open parenthesis R comma z closing parenthesis R dR dz divided by. P comma L Capital Sigma open parenthesis R comma z closing \noindent 3 . 2 . 1 \quad Scale factor determination parenthesisHere R, Σ( dRR, dz z) sub is the period assumed pulsar space density distribution in terms of galactocentric radius R and height Hereabove comma the Capital Galactic Sigma plane openz. Note parenthesis that ξ is R primarily comma z a closing function parenthesis of period P isand the assumedluminosity pulsarL such space that density short distribution in terms of galactocentric\noindent A radius very useful approach [ 2 9 9 , 3 8 9 ] , is to define a scaling factor $ \ xi $ as the ratio of the total Galactic volume- period weighted / low - luminosityby pulsar pulsars density have smaller to the detectable volume volumes in which and a pulsar is detectable : R andtherefore height higher aboveξ thevalues Galactic than plane their z long period - period .. Note / high that - xi luminosity is primarily counterparts a function . of period P and luminosityIn practice L such, that ξ is shortcalculated hyphen for period each pulsar slash separately low hyphen using luminosity a Monte pulsars Carlo have simulation smaller to detectable model the volumes volume and \ begintherefore{ a l i higher g n ∗} xi values than their long hyphen period slash high hyphen luminosity counterparts period of the Galaxy probed by the major surveys [ 2 6 8 ] . For a sample of Nobs observed pulsars above a minimum \ xiIn practice( commaP , xi is L calculated ) = for\ eachf r a c pulsar{\ int separately\ int using{ aG Monte}\Sigma Carlo simulation( R to model , z ) R dR dz }{ P luminosity Lmin, the total number of pulsars in the Galaxy ,Lthe volume\Sigma of the Galaxy( R probed , by z the major ) R surveys dR open dz square} { bracket. }\ tag 2 6∗{ 8$ closing ( 4square ) bracket $} period For a sample of N sub obs observed\end{ a l pulsars i g n ∗} above a minimum luminosity L sub minimum comma thei total=1 number of pulsars in the Galaxy \noindent Here $ , \Sigma ( R , zX )ξi $ is the assumed pulsar space density distribution in terms of galactocentric radius Equation: open parenthesis 5 closing parenthesis ..N NG sub= G = sum from i = 1 to N sub obs xi i divided by f i(5) sub comma $ R $ and height above the Galactic plane $fi z, . $ \quad Note that $ \ xi $ is primarily a function of period where f is the model hyphen dependent .... quotedblleft beamingNobs fraction quotedblright .... discussed below in Section 3 period 2 period 3 period$ P $ .... and Note that where f is the model - dependent “ beaming fraction ” discussed below in Section 3 . 2 . 3 . Note that luminositythis estimate applies $ L $ tothose such pulsars that with short luminosities− period gtrsim / low L sub− minimumluminosity period pulsars .. Monte have Carlo simulations smaller detectable have volumes and this estimate applies to those pulsars with luminosities L . Monte Carlo simulations have shown this shown this method to be reliable comma as long as N sub obs& ismin reasonably large open square bracket 2 2 2 closing square bracket period method to be reliable , as long as N is reasonably large [ 2 2 2 ] . \noindent3 period 2therefore period 2 .. The higher small hyphen $ \ xiobs number$ values bias than their long − period / high − luminosity counterparts . 3 . 2 . 2 The small - number bias For small samples of observationally hyphen selected objects comma the detected sources are likely to be those For small samples of observationally - selected objects , the detected sources are likely to be those with larger Inwith practice larger hyphen $ , than\ xi hyphen$ is average calculated luminosities for period each .. The pulsar sum of separately the scale factors using open a parenthesis Monte Carlo 5 closing simulation parenthesis to comma model - than - average luminosities . The sum of the scale factors ( 5 ) , therefore , will tend to underestimate thereforethe volume comma of will the tend Galaxy to probed by the major surveys [ 2 6 8 ] . For a sample of $ N { obs }$ observed pulsars the true size of the population . This “ small - number bias ” was first pointed out [ 1 7 4 , 1 7 8 ] for aboveunderestimate a minimum the true luminosity size of the population $ L {\ periodmin This} quotedblleft, $ the total small hyphen number number of pulsars bias quotedblright in the .. Galaxy was first pointed out open the sample of double neutron star binaries where we know of only five systems relevant for calculations of the square bracket 1 7 4 comma merging rate ( see Section 3 . 4 . 1 ) . Only when N 10 does the sum of the scale factors become a \ begin1 7 8{ closinga l i g n ∗} square bracket for the sample of double neutronobs star& binaries where we know of only five systems relevant good indicator of the true population size . N for{ calculationsG } = of\sum the mergingˆ{ i rate = open 1 } parenthesis{ N { obs see Section}}\ f ..r a 3 c {\ periodxi 4 periodi }{ 1f closing i } parenthesis{ , }\ tag period∗{$ Only ( when 5 )N sub$} obs Despite a limited sample size , it has been demonstrated [ 1 9 0 ] that rigorous confidence intervals of N gtrsim\end{ 1a l 0 i g does n ∗} the sum of the G can be derived using Bayesian techniques . Monte Carlo simulations verify that the simulated scale factors become a good indicator of the true population size period number of detected objects N closely follows a Poisson distribution and that N = \noindentDespite a limitedwhere sample $ f $ size is commadetected the it model has been− demonstrateddependent \ openh f i l square l ‘‘bracket beaming 1 9 fraction 0detected closing square ’’ \ bracketh f i l l thatdiscussed rigorous belowconfidence in Section 3 . 2 . 3 . \ h f i l l Note that αN , where α is a constant . By varying the value of N in the simulations , the mean of this Poisson intervals G G distribution can be measured . The Bayesian analysis [ 1 9 0 ] finds , for a single object , the probability \noindentof N sub Gthis can be estimate derived using applies Bayesian to techniques those pulsars period Monte with Carlo luminosities simulations verify $ \ thatgtrsim the simulated L {\min } . $ \quad Monte Carlo simulations have density function of the total population is shownnumber this of detected method objects to be N sub reliable detected ,closely as long follows as a Poisson $ N distribution{ obs }$ and is that reasonably N sub detected large = [ 2 2 2 ] . alpha N sub G comma where alpha is a constant period2 .. By varying the value of N sub G in the simulations comma the mean of this P (NG) = α NG exp(−αNG). (6) \noindentPoisson distribution3 . 2 . can 2 \ bequad measuredThe small period ..− Thenumber Bayesian b i a analysis s open square bracket 1 9 0 closing square bracket finds comma for a single object comma the \noindentprobabilityFor density small function samples of the totalof observationally population is − selected objectsLiving , the Reviews detected in Relativity sources are likely to be those withLine l1 a P r g open e r − parenthesisthan − average N subht tp G closing : luminosities / / parenthesis w w w . .=\ alpha lquad i vi toThe ngrevthe power sum i e of of w 2 sthe N . sub scale org G exponent / lrr factors - open2008 ( parenthesis - 5 8 ) , therefore minus alpha , N will sub tend to Gunderestimate closing parenthesis the period true open size parenthesis of the 6 closing population parenthesis . This Line 2 ‘‘hline small − number bias ’’ \quad was first pointed out [ 1 7 4 , 1Living 7 8 ] Reviews for the in Relativity sample of double neutron star binaries where we know of only five systems relevant forht tp calculations : slash slash w w of .. thew period merging l i vi ngrev rate i e ( w see s period Section org slash\quad lrr hyphen3 . 4 2008 . 1hyphen ) . 8Onlywhen $N { obs }\ gtrsim 1 0 $ does the sum of the scale factors become a good indicator of the true population size .

Despite a limited sample size , it has been demonstrated [ 1 9 0 ] that rigorous confidence intervals o f $ N { G }$ can be derived using Bayesian techniques . Monte Carlo simulations verify that the simulated

\noindent number of detected objects $ N { detected }$ closely follows a Poisson distribution and that $ N { detected } = $

\noindent $ \alpha N { G } , $ where $ \alpha $ is a constant . \quad By varying the value of $ N { G }$ in the simulations , the mean of this Poisson distribution can be measured . \quad The Bayesian analysis [ 1 9 0 ] finds , for a single object , the probability density function of the total population is

\ [ \ begin { a l i g n e d } P(N { G } ) = \alpha ˆ{ 2 } N { G }\exp ( − \alpha N { G } ) . ( 6 ) \\ \ r u l e {3em}{0.4 pt }\end{ a l i g n e d }\ ]

\ hspace ∗{\ f i l l } Living Reviews in Relativity

\ hspace ∗{\ f i l l } ht tp : / / w w \quad w. l i vi ngrev i ews . org / lrr − 2008 − 8 28 ....28 Duncan R period Lorimer Duncan R . Lorimer \noindenthline 28 \ h f i l l Duncan R . Lorimer Figure 15 : Small hyphen number bias of the scale factor estimates derived from a synthetic population of sources \ [ where\ r u l e the{3em true}{ number0.4 pt }\ of sources] is known period .. Left panel : .. An edge hyphen on view of a model Galactic source populationFigure 15period : Small .. Right - number panel bias : .. of The the thick scale linefactor shows estimates N sub derived G comma from thea synthetic true number population of objects of sources in the where model Galaxy comma plottedthe true against number N sub of sources ob served is known comma . the Left number panel detected : An edge by a - flux on view hyphen of a limited model Galactic survey periodsourceThe population thin solid line shows N sub est \noindent Figure 15 : Small − number bias of the scale factor estimates derived from a synthetic population of sources comma. the Right panel : The thick line shows NG, the true number of objects in the model Galaxy , plotted against where the true number of sources is known . \quad Left panel : \quad An edge − on view of a model Galactic source medianNobserved sum, ofthe the number scale factors detected comma by a flux as a- limited function survey of N . sub The obs thin from solid a linelarge shows numberNest of, Montethe median Carlo sum trials of theperiod Dashed population . \quad Right panel : \quad The thick line shows $ N { G } , $ the true number of objects in the model Galaxy , linesscale show factors 25 and , as 75 a percent function percentiles of Nobs from of the a large N sub number est distribution of Monte Carlo period trials . Dashed lines show 25 and 75% plotted against $ N { ob served } , $ the number detected by a flux − limited survey . The thin solid line shows Adoptingpercentiles the necessaryof the Nest assumptionsdistribution required . in the Monte Carlo population about the underlying $ Npulsar{Adoptinge distribution s t } the, necessary $ comma the this assumptions technique canrequired be used in the to place Monte interesting Carlo population constraints about on the the size underlying and comma pulsar as medianwe shalldistribution sum see later of , thethis comma technique scale birth factorsrate can of be the used , underlying toas place a function interesting population of constraints period $ N { onobs the size}$ and from , as we a shall large see number later of Monte Carlo trials . Dashed lines3 period, birth show 2 rateperiod 25 of and 3the .. underlyingThe $ 75beaming population\% correction$ percentiles . of the $ N { e s t }$ distribution . The3 quotedblleft . 2 . 3 Thebeaming beaming fraction correction quotedblright f in Equation open parenthesis 5 closing parenthesis is the fraction of 4 pi steradians swept out\noindent byThe a pulsar “ beamingAdopting quoteright fraction the s ” necessaryf in Equation assumptions ( 5 ) is the fraction required of 4π insteradians the Monte swept outCarlo by a population pulsar ’ s radio about the underlying pulsarradiobeam beam distribution during during one one rotation rotation , this . period Thus techniquef ..is Thus the probabilityf canis the be probability used that the to that beam place the cuts beam interesting the cuts line - the of - line sight constraints hyphen of an arbitrarilyof hyphen on sight the size and , as ◦ weof shallanpositioned arbitrarily see observer later positioned . , birth A observer na ¨ı ve rate period estimate of .. theAfor naf underlyingofdieresis-dotlessi roughly 20% population assumes ve estimate a circular for . f of beam roughly of width 20 percent∼ 10 assumesand a a circular beamrandomly of width distributed thicksim 1 inclination 0 to the power angle of between circ and the a spinrandomly and magnetic distributed axes inclination [ 3 6 5 ] . angle Observational between the evidence spin and magnetic \noindentaxessummarised open3 square . 2 in bracket .Figure 3 \quad 31 6 5 closing suggestsThe beaming square that shorter bracket correction period period pulsars .. Observational evidence summarised in Figure 1 6 .. suggests that shorter periodhave pulsars wider beams and therefore larger beaming fractions than their long - period counterparts [ 2 6 9 , \noindenthave2 wider 43,The beams 37,360]. ‘‘ and beaming therefore fraction larger beaming ’’ fractions $ f $ than in Equation their long hyphen ( 5 ) period is the counterparts fraction open of square $ 4 bracket\ pi 2$ 6 9 comma steradians swept out by a pulsar ’ s radio2 .. 4 3beamWhen comma during most .. 3 of 7 commathese one beaming rotation 3 6 0 closing models . square\quad were originallybracketThus period $ proposed f $ is, the the sample probability of millisecond that pulsars the was beam. 5 cuts the line − o f − s i g h t ofWhen anand arbitrarilymost hence of their these predictions beaming positioned models about the were observer beaming originally fractions . \ proposedquad ofA short comma na - period $ the\ddot sample pulsars{\imath of relied millisecond} largely$ ve on pulsars extrapolations estimate for $ f $ of roughly $ 20wasfrom lesssim\% the$ 5 normal andassumes hence pulsars their a circular . predictions An analysis about of thea large beaming sample fractions of millisecond of short pulsar hyphen profiles period [ pulsars 2 0 3 relied ] suggests beamlargelythat of on their width extrapolations beaming $ \sim fraction from1 the lies normal between 0 ˆ{\ pulsars 50circ and period} 10%$. and .. AnIndependent a analysis randomly of constraints a large distributed sample on f offor millisecond millisecondinclination pulsars angle between the spin and magnetic axespulsarcome [ profiles 3 from 6 5 deep open ] . square\Chandraquad bracketObservationalobservations 2 .. 0 3 closing of the evidence globular square bracket cluster summarised 47 suggests Tucanae in that [Figure 1 their 2 6 ] beaming and 1 6 radio\quad fraction pulsarsuggests surveys lies between that 50 and shorter 1 0 percent period pulsars period[ .. 5 Independent 6 ] which suggest that f > 0.4 and likely close \noindentconstraintsto unityhave on [ 1 f for wider millisecond 3 5 ]beams . pulsars The and large cometherefore beaming from deep fraction larger .. Chandra and beaming narrow observations pulses fractions often of the observed globularthan stronglytheir long suggests− aperiod counterparts [ 2 6 9 , clusterfan 47 beam Tucanae model open for millisecond square bracket pulsars 1 26 [ 2 closing 6 1 ] . square bracket and radio pulsar surveys open square bracket 5 6 closing square bracket which\noindent suggest3 . 32 that\quad The f greater population4 3 0 period, \quad 4 and of3 normal 7likely , 3 close 6 and 0 ] millisecond . pulsars to unity3 . 3 open . 1 square Luminosity bracket 1 distributions .... 3 5 closing and square local bracket number period estimates .... The large beaming fraction and narrow pulses often observed Whenstrongly mostBased suggests onof a a these number beaming of all - sky models surveys carriedwere originally out in the 1 990 proposed s , the scale , factor the sample approach of has millisecond been used to pulsars wasfanderive beam $ \ lesssim model the characteristics for millisecond 5 $ of and the pulsars hence true open normal their square and predictions millisecondbracket 2 6pulsar 1 closing about populations square the bracket beaming and is period based fractions on the sample of short of − period pulsars relied largely3 periodpulsars 3on .. withinThe extrapolations population 1 . 5 kpc of of the normal from Sun [ and the2 millisecond 4 normal 4 ] . Within pulsars this region . \quad , theAn selection analysis of a large sample of millisecond pulsar3 period profiles 3 period 1 .. [ Luminosity 2 \quad 0 distributions 3 ] suggests and local that number their estimates beaming fraction lies between 50 and $ 1 0 \% . $Based\quad on a numberIndependent of all hyphen sky surveys carried out in the 1 990 s comma the scale factor approach has been constraintsused to derive on the characteristics $ f $ for of millisecond the true normal pulsars and millisecond come pulsar from populations deep \quad andChandra is observations of the globular clusterLiving 47 Reviews Tucanae in Relativity [ 1 2 6 ] and radio pulsar surveys [ 5 6 ] which suggest that $ f > 0 . 4 $ basedht on tp the : sample / / w of w pulsarsw . l within i vi ngre 1 period v i 5 e kpc w s of . the or Sun g open / lrr square - 2008 bracket - 8 2 .. 4 4 closing square bracket period .. Within this regionand likely comma the close selection hline \noindentLiving Reviewsto unity in Relativity [ 1 \ h f i l l 3 5 ] . \ h f i l l The large beaming fraction and narrow pulses often observed strongly suggests a ht tp : slash slash w w w period l i vi ngre v i e w s period or g slash lrr hyphen 2008 hyphen 8 \noindent fan beam model for millisecond pulsars [ 2 6 1 ] .

\noindent 3 . 3 \quad The population of normal and millisecond pulsars

\noindent 3 . 3 . 1 \quad Luminosity distributions and local number estimates

\noindent Based on a number of all − sky surveys carried out in the 1 990 s , the scale factor approach has been used to derive the characteristics of the true normal and millisecond pulsar populations and is based on the sample of pulsars within 1 . 5 kpc of the Sun [ 2 \quad 4 4 ] . \quad Within this region , the selection

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\noindent Living Reviews in Relativity

\noindent http : //www. l i vi ngrev i ews . org/ lrr − 2008 − 8 BinaryBinary and and Millisecond Millisecond Pulsars Pulsars .... 29 29 \noindenthline Binary and Millisecond Pulsars \ h f i l l 29 Figure 1 6 : .. Beaming fraction plotted against pulse period for four different beaming models : .. Narayan \ [ ampersand\ r u l e {3em Vivekanand}{0.4 pt }\ 1 983] open parenthesis NV 83 closing parenthesis open square bracket 2 6 9 closing square bracket comma Lyne ampersandFigure Manchester 1 6 : 1Beaming 988 open fraction parenthesis plotted LM against 88 closing pulse parenthesis period for four open different square beaming bracket models 2 4 3 closing : Narayan square bracket& comma Biggs 1 9 90 open parenthesisVivekanand JDB 1 983 90 ( closingNV 83 ) parenthesis [ 2 6 9 ] , Lyne open& squareManchester bracket 1 988 3 7 ( closing LM 88 )square [ 2 4 3 bracket ] , Biggs and 1 9 90 ( JDB 90 ) [ 3 7 ] \noindentTaurisand ampersand TaurisFigure& Manchester Manchester 1 6 : \quad 1 1 998 998 (Beaming TMopen 98 parenthesis ) [ 3 fraction 6 0 ] . TM 98 plotted closing parenthesis against open pulse square period bracket for 3 6 four 0 closing different square bracket beaming period models : \quad Narayan $effects\&$effects are Vivekanandare well well understood understood 1 and 983 and easier (NV83 easier to quantify to quantify) [ than2 6 than in 9 the ] in ,the rest Lyne rest of the of $ the Galaxy\&$ Galaxy period Manchester . These These calculations calculations 1 988 (LM88 ) [ 2 4 3 ] , Biggs 1 9 90 ( JDB90 ) [ 3 7 ] and Taurisshouldshould therefore $ therefore\&$ give Manchester give a reliable a reliable local 1local pulsar 998 pulsar (TM98 population population ) estimate [estimate 3 6 period 0 ]. . The 430 hyphenThe MHz 430 luminosity - MHz luminosity distributions distributions obtained obtained from this from analysis this areanalysis shown are in shown Figure in 1 Figure 7 period 1 7 For . For 2 \noindentthethe normal normaleffects pulsars pulsars comma are , integrating well integrating understood the the corrected corrected and distribution distribution easier above to above quantify 1 mJy 1 mJy kpc kpc thanand to dividingthe in power the by of restπ 2× and of dividing the Galaxy by pi times . These calculations 2 2 1.5) kpc yields surface ,assuming abeaming 3 open( parenthesis foralocalluminosities to the power of 1 periodabove 5 sub density 430 to the power2 . The of same closing parenthesismodelanalysis to the power for [ of7], 2of156 sub± hyphen MHz to the power \noindentfor 430−shouldMHz therefore give a reliable local1mJykpc pulsar population estimate .the of kpc to the power1pulsars of 2 tokpc the−2 power of yields a lo cal luminosities to the power of surface above density 1 mJy kpc to the power of 2 sub 3millisecond − period to the powerpulsars of comma, assum assuming The same to the power of a beaming model analysis for open square bracket the to the power of 3 ing a mean beaming fraction of 75%[203], leads to a lo cal surface density of 38 ± 16 pulsars kpc−2 7\ hspace closing square∗{\ f i lbracket l }The comma 430 − ofMHz 1 56 luminosity plusminux 3 millisecond distributions sub pulsars obtained comma to from the power this of analysis 1 pulsars sub are assum shown sub in hyphen Figure to the 1 7 . For also for 430 - MHz luminosities above 1 mJy kpc2. power of kpc to the power of minus 2 3 . 3 . 2 Galactic population and birth - rates \noindenting a meanthe beaming normal fraction pulsars of 75 percent , integrating open square the bracket corrected 2 0 3 closing distribution square bracket above comma 1 leads mJy to a $ lo kpc cal surface ˆ{ 2 } density$ and of 38 dividing by Integrating the lo cal surface densities of pulsars over the whole Galaxy requires a knowledge of the presently plusminux$ \ pi 1\times 6 pulsars$ kpc to the power of minus 2 rather uncertain Galactocentric radial distribution [ 1 6 3 , 2 2 0 ] . One approach is to assume that pulsars also for 430 hyphen MHz luminosities above 1 mJy kpc to the power of 2 period have a radial distribution similar to that of other stellar populations and to scale the \noindent3 period 3 period$ ( 2{ ..f Galactic o r }ˆ{ population1 . and 5 } birthˆ{ ) hyphen ˆ{ 2 rates}} { 430 }ˆ{ kpc ˆ{ 2 }} { − MHz }ˆ{ y i e l d s } a l o lo cal number density with this distribution in order to estimate the total Galactic population . c a lIntegrating{ luminosities the lo cal surface}ˆ{ s densitiesu r f a c e of}$ pulsars above over the$ density whole Galaxy{ 1 requires mJy a knowledge kpc ˆ{ of2 the}}ˆ{ , assuming } { . }$ The The corresponding lo cal - to - Galactic scaling is 10 ± 250kpc2[318]. This implies a population of ∼ 160, 0 $ samepresently ˆ{ rathera beaming uncertain} Galactocentricmodel{ a n a radial l y s i s distribution}$ f o r open $ [ square{ the bracket}ˆ{ 13 6} 3 comma7 ] 2 2 0 , closing o f square 1 bracket 56 \ periodpm One3 { millisecond }ˆ{ 1 active normal pulsars and ∼ 40, 0 millisecond pulsars in the Galaxy . approachp u l s a r s is} to{ assumep u l s a r s , } { assum }ˆ{ kpc ˆ{ − 2 }} { − }$ Based on these estimates , we are in a position to deduce the corresponding rate of formation that pulsars have a radial distribution similar to that of other stellar populations and to scale the or birth - rate required to sustain the observed population . From the P – P˙ diagram in Figure 3 , \noindentlo cal numbering density a mean with beaming this distribution fraction in order of to $ estimate 75 \% the total [ Galactic 2 0 population 3 ] period , $ leads to a lo cal surface density of we infer a typical lifet ime for normal pulsars of ∼ 107 yr , corresponding to a Galactic birth rate of ∼ 1 per $ 38The corresponding\pm 1 lo 6 cal$ hyphenp u l s a tor s hyphen$ kpc Galactic ˆ{ − scaling2 }$ is 1 0 plusminux 250 kpc to the power of 2 open square bracket 3 1 8 closing 60 yr – consistent with the rate of supernovae [ 3 8 1 ] . As noted in Section 2 . 2 , the square bracket period .. This implies a population of millisecond pulsars are much older , with ages close to that of the Universe τ ( we assume here τ = 13.8 \noindentthicksim 1a 60 l s commao f o r 0 430 active− normalMHz luminosities pulsars and thicksim above 40 1comma mJy 0 $ millisecond kpc ˆ{u pulsars2 } . in $ the Galaxyu period Gyr [ 4 0 5 ] ) . Taking the maximum age of the millisecond pulsars to be τ , we infer a mean birth rate of Based on these estimates comma we are in a position to deduce the correspondingu rate of formation at least 1 per 345 , 0 yr . This is consistent , within the uncertainties , of other studies of the millisecond \noindentor birth hyphen3 . 3 rate . required 2 \quad toGalactic sustain the observed population population and period birth ....− Fromr a t e the s P endash P-dotaccent diagram in Figure .... 3 comma pulsar population [ 1 0 9 , 3 5 7 ] and with the birth - rate of low - mass X - ray we infer a typical lifet ime for normal pulsars of thicksim 1 0 to the power of 7 yr comma corresponding to a Galactic birth rate \noindentof thicksimIntegrating 1 per 60 yr endash the consistent lo cal surface with the rate densities of supernovae of pulsars .. open square over bracket the whole 3 8 .. 1 Galaxy closing square requires bracket a period knowledge .. As of the notedpresently in Section rather .. 2 period uncertain 2 comma the Galactocentric radial distribution [ 1 6 3 , 2 2 0 ] . One approach is to assume thatmillisecond pulsars pulsars have are a much radial older commadistribution with ages similarclose to that to of that the Universe of other tauLiving sub stellar u Reviews open parenthesispopulations in Relativity we assume and to here scale the tau sub u = 1 3 period 8 Gyrht open tp square: / / bracket w w 4 w 0 . 5 closing l i vi square ngrev bracket i e w closing s . org parenthesis / lrr - period 2008 .. - Taking 8 the maximum age of the\noindent millisecondlo pulsars cal numberto be tau density sub u comma with we inferthis a distribution in order to estimate the total Galactic population . mean birth rate of at least 1 per 345 comma 0 yr period .. This is consistent comma within the uncertainties comma of other \noindentstudies ofThe the millisecond corresponding pulsar population lo cal − opento square− Galactic bracket 1 scaling 0 9 comma is .. 3 $ 5 1 7 closing 0 square\pm bracket250 and kpc with ˆ{ the2 } birth[ hyphen 3 rate1 of 8 low ]hyphen . $mass\quad X hyphenThis ray implies a population of $hline\sim 1 60 , 0$ active normal pulsars and $ \sim 40 , 0 $ millisecond pulsars in the Galaxy . Living Reviews in Relativity \ hspaceht tp :∗{\ slashf i slash l l }Based w w .. on w period these l i estimatesvi ngrev i e w , s weperiod are org in slash a lrrposition hyphen 2008 to deducehyphen 8 the corresponding rate of formation \noindent or b i r t h − rate required to sustain the observed population . \ h f i l l From the $ P $ −− $ \dot{P} $ diagram in Figure \ h f i l l 3 ,

\noindent we infer a typical lifet ime for normal pulsars of $ \sim 1 0 ˆ{ 7 }$ yr , corresponding to a Galactic birth rate o f $ \sim 1 $ per 60 yr −− consistent with the rate of supernovae \quad [ 3 8 \quad 1 ] . \quad As noted in Section \quad 2 . 2 , the

\noindent millisecond pulsars are much older , with ages close to that of the Universe $ \tau { u } ( $ we assume here $ \tau { u } = 1 3 . 8$Gyr[405]). \quad Taking the maximum age of the millisecond pulsars to be $ \tau { u } , $ we i n f e r a mean birth rate of at least 1 per 345 , 0 yr . \quad This is consistent , within the uncertainties , of other studies of the millisecond pulsar population [ 1 0 9 , \quad 3 5 7 ] and with the birth − r a t e o f low − mass X − ray

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\ hspace ∗{\ f i l l } Living Reviews in Relativity

\ hspace ∗{\ f i l l } ht tp : / / w w \quad w. l i vi ngrev i ews . org / lrr − 2008 − 8 30 ....30 Duncan R period Lorimer Duncan R . Lorimer \noindenthline 30 \ h f i l l Duncan R . Lorimer Figure 1 7 : Left panel : The corrected luminosity distribution open parenthesis solid histogram with error bars closing parenthesis for normal\ [ \ r u l e {3em}{0.4 pt }\ ] pulsarsFigure period 1 7 The : Left corrected panel : distribution The corrected before luminosity the beaming distribution model ( solid has histogram been applied with iserror shown bars by ) for the normal dot hyphen dashed linepulsars period . .. The Right corrected panel :distribution .. The correspondingbefore the beaming distribution model for has millisecond been applied pulsars is shown period by the .. In dot both - dashed cases linecomma . the observed \noindentdistributionRight panelFigure is shown : The1 by 7 corresponding the : Left dashed panel line distribution and : the The thickfor corrected millisecond solid line pulsars is luminosity a power . Inlaw both with distribution cases a slope , the of observed minus ( solid 1 distribution period histogram with error bars ) for normal Theis difference shown by between the dashed the line observed and the and thick corrected solid line distributions is a power law highlights with a slope the severe of −1 under. The difference hyphen sampling between theof \noindentlowobserved hyphenpulsars luminosity and corrected . pulsars The distributions corrected period highlights distribution the severe under before - sampling the of beaming low - luminosity model pulsars has . been applied is shown by the dot − dashed l ibinaries n ebinaries . \ openquad [ 2 squareRight 3 1 bracket , 1 panel 8 82 ].. .: 3\ 1quad commaThe 1 .. corresponding 8 8 closing square bracket distribution period for millisecond pulsars . \quad In both cases , the observed distribution3 period3 . 4 4 .. The The is population shown population by of relativistic the of dashed relativistic binaries line and binaries the thick solid line is a power law with a slope of $ − 1Although .Although $ no radio no radio pulsar pulsar has has so far so been far been observed observed in orbit in orbit around around a black a black hole hole companion companion comma , we we now know of Thenowseveral difference know of double several betweenneutron double st neutron the ar and observed st neutron ar and starneutron and – correctedwhite star endashdwarf binaries distributions white dwarf which binaries will mergehighlights which due will to merge gravitational the severe under − sampling o f lowdue−wave toluminosity gravitational emission within wave pulsars a emission reasonable . within timescale a reasonable . The timescale current sample period of .. objects The current is shown sample as a functionof objects of orbital is shownperiod as and a function eccentricity of orbital in Figure period 1 8 and . Iso eccentricity chrones showing in Figure various 1 8 period coalescence Iso chrones times showingτg are calculated various using \noindentcoalescencethe expressionb times i n a r i tau e s sub [ 2 g are\quad calculated3 1 , using 1 \quad the expression8 8 ] . Equation: open parenthesis 7 closing parenthesis .. tau sub g simeq 9 period 83 times 1 0 to the power of 6 yr parenleftbigg P sub b divided by\noindent hr parenrightbigg3 . 4 to\quad the powerThe ofpopulation 8 slash 3 parenleftbigg of relativistic m sub 1 plus binaries m sub 2 divided by M sub odot parenrightbigg minus 2 slash 3 6 Pb 8/3 m1 + m2 µ 2 7/2 parenleftbigg mu divided by Mτg sub' 9 odot.83 × parenrightbigg10 yr( ) ( minus 1 parenleftbig) − 2/3( 1) − minus1(1 − ee to) the, power of 2 parenrightbig(7) to the power of 7 slash hr M M 2\noindent comma Although no radio pulsar has so far been observed in orbit around a black hole companion , we now know of several double neutron st ar and neutron star −− white dwarf binaries which will merge wherewhere m subm 1and andm m subare the2 are masses the masses of the of two the stars two stars, µ = commam m / mu(m =+ mm sub) is 1 the m sub “ reduced 2 slash mass open ” parenthesis , P is m sub 1 plus m sub 2 due to gravitational1 2 wave emission within a reasonable1 2 1 timescale2 . \quad The currentb sample of objects closingthe parenthesis binary period is the andquotedbllefte is the eccentricityreduced mass . quotedblright This formula comma is a good analytic approximation ( within a few is shown as a function of orbital period and eccentricity in Figure 1 8 . Iso chrones showing various P subpercent b is the ) to binary the numerical period and solution e is the of eccentricity the exact equations period .. for Thisτ [294 formula, 295] is a. good analytic approximation coalescence times $ \tau { g }$ are calculatedg using the expression open parenthesisIn addition within to tests a few of strong percent - field closing gravity parenthesis through to observations the numerical of relativistic solution of binary the exact systems equations ( see for Section tau sub g open square bracket 2 9 4 comma4 . 4 ) 2 , estimates 9 5 closing of square their Galactic bracket populationperiod and merger rate are of great interest as one of the prime sources \ begin { a l i g n ∗} In additionfor current to tests gravitational of strong wave hyphen detectors field gravity such as through GEO 600 observations [ 2 6 5 ] , LIGO of relativistic [ 5 1 ] , VIRGO binary systems [ 1 5 3 ] and TAMA \tau { g }\simeq 9 . 83 \times 1 0 ˆ{ 6 } yr ( \ f r a c { P { b }}{ hr } ) ˆ{ 8 / open[ 2 parenthesis 7 3 ] . see In Section the following .. 4 period , we review4 closing empirical parenthesis determinations comma estimates of the popof their - ulation Galactic sizes population and merging and merger rate are of great 3 } ( \ f r a c { m { 1 } + m { 2 }}{ M {\odot }} ) − 2 / 3 ( \ f r a c {\mu }{ M {\odot }} interestrates as of binaries where at least one component is visible as a radio ) − 1 ( 1 − e ˆ{ 2 } ) ˆ{ 7 / 2 } , \ tag ∗{$ ( 7 ) $} onepulsar of the .prime sources for current gravitational wave detectors such as GEO 600 open square bracket 2 6 5 closing square bracket comma \end{ a l i g n ∗} LIGO open3 . 4 square . 1 bracket Double 5 1 neutron closing square star binaries bracket comma VIRGOAs discussed open square in Section bracket 2 1 . 52 3, double closing neutron square bracket star ( DNS and TAMA) binaries open are square expected bracket to be 2 rare .. 7 . 3 closing This is square cert bracket period .. In the \noindent where $ m { 1 }$ and $ m { 2 }$ are the masses of the two stars $ , \mu = m { 1 } followingainly comma the case we review ; as summarized empirical determinations in Table 1 ,only of the around pop hyphen ten DNS binaries are currently known . Although m { 2 } / ( m { 1 } + m { 2 } ) $ is the ‘‘ reduced mass ’’ , ulationwe only sizes see and both merging neutron rates stars of binaries as pulsars where in J at737 least− 3039[2 one component 39], we are is “visible certain as ” a of radio the identification in five $ P { b }$ is the binary period and $ e $ is the eccentricity . \quad This formula is a good analytic approximation pulsarother period systems from precise component mass measurements from pulsar timing observations ( see Section 4 ( within a few percent ) to the numerical solution of the exact equations for $ \tau { g } [ 2 9 3 period. 4 ) .4 period The other 1 .. Double systems neutron listed in star Table binaries 1 have eccentric orbits , mass 4As , discussed 2 9 in Section 5 2] period . $ 2 comma double neutron star open parenthesis DNS closing parenthesis binaries are expected to be rare period .. This is Incert addition ainly the to case tests semicolon of as strong summarized− field in Table gravity .. 1 comma through only around observations ten DNS binaries of relativistic are currently known binary period systems (Although seeLiving Section we Reviews only\quad see in Relativity both4 neutron . 4 ) stars, estimates as pulsars inof J their 737 minus Galactic 3039 open population square bracket and 2 3 merger 9 closing rate square are bracket of commagreat we interest are as quotedblleftoneht of tp the certain : prime / /quotedblright w sourcesw w . l of ifor the vi current ngre v i gravitationale w s . or g / wave lrr - detectors 2008 - 8 such as GEO 600 [ 2 6 5 ] , LIGO [ 5 1 ] , VIRGOidentification [ 1 5 in 3 five ] and other TAMA systems [ 2from\quad precise7 component 3 ] . \quad mass measurementsIn the following from pulsar , we timing review empirical determinations of the pop − ulationobservations sizes open and parenthesis merging see rates Section of .. 4 binaries period 4 closing where parenthesis at least period one .. component The other systems is visible listed in as Table a ..radio 1 have eccentric orbits comma mass \noindenthline p u l s a r . Living Reviews in Relativity \noindentht tp : slash3 slash . 4 w. w 1 w\quad periodDouble l i vi ngre neutron v i e w s period star orbinaries g slash lrr hyphen 2008 hyphen 8 \noindent As discussed in Section 2 . 2 , double neutron star ( DNS ) binaries are expected to be rare . \quad This i s cert ainly the case ; as summarized in Table \quad 1 , only around ten DNS binaries are currently known . Although we only see both neutron stars as pulsars in J $ 737 − 3039 [ 2 3 9 ] ,$ weare ‘‘certain ’’ofthe identification in five other systems from precise component mass measurements from pulsar timing observations ( see Section \quad 4 . 4 ) . \quad The other systems listed in Table \quad 1 have eccentric orbits , mass

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\noindent http : //www. l i vi ngrev i ews . org/ lrr − 2008 − 8 BinaryBinary and and Millisecond Millisecond Pulsars Pulsars .... 3 1 3 1 \noindenthline Binary and Millisecond Pulsars \ h f i l l 3 1 Figure 18 : .. The relativistic binary merging plane period .. Top : .. Orbital eccentricity versus period for eccentric \ [ binary\ r u l e systems{3em}{ involving0.4 pt }\ neutron] stars period Bottom : Orbital period distribution for the massive white dwarf endash pulsarFigure binaries 18 : periodThe .. Isocrones relativistic show binary coalescence merging plane times . assuming Top : neutron Orbital stars eccentricity of 1 period versus 4 period M sub for odot eccentric and white dwarfs of 0 periodbinary 3 systems M sub odot involving period neutron stars . Bottom : Orbital period distribution for the massive white dwarf – pulsar \noindent Figure 18 : \quad The relativistic binary merging plane . \quad Top : \quad Orbital eccentricity versus period for eccentric functionsbinaries and . periastron Isocrones advance show coalescence measurements times assuming that are neutron consistent stars with of 1 a.4 DNSM and identification white dwarfs comma of 0.3 butM . binaryfor whichfunctions systems there and is periastron presently involving not advance sufficient neutron measurements component stars . that mass Bottom are informationconsistent : Orbital towith confirm a period DNS their identification distribution nature period , but for for which the massive white dwarf −− pulsarOnethere further binaries is DNSpresently candidate . not\quad sufficient commaIsocrones the component 95 hyphen show mass ms coalescence pulsar information J 1 753 to times minus confirm 2243 assuming their open nature parenthesis neutron . One see stars further Table of ..DNS 3 closing $ 1 parenthesis . 4 comma M {\odot }$ hasand recently whitecandidate been dwarfs , dis the hyphen 95 of - ms pulsar J 1753 − 2243( see Table 3 ) , has recently been dis - $covered 0covered . open [ 3 1 square 8 7 M ] .bracket{\ Althoughodot 1 8 7the} closing mass. $ square function bracket for this period pulsar Although is lower the than mass the function DNS systems for this listed pulsar in Table is lower than the DNS systems listed in1 , a neutron star companion cannot be ruled out in this case . Further observations should soon clarify the \noindentTablenature .. 1 commafunctions of this system a neutron and . starWe periastron companionnote , however advancecannot , that be theruled measurements 1 3out . 6 in - thisday caseorbital that period period are .. consistent Further of this system observations with means a should that DNS identification , but forsoon whichit clarify will not there the contribute nature is of presently to this gravitational system notperiod wave sufficient .. inspiral We note rate comma component calculations however mass discussed comma information that below the . 1 3 period to confirm 6 hyphen daytheir orbital nature period . of this Onesystem furtherDespite means DNS that the it uncertainties candidate will not contribute in , theidentifying to 95 gravitational− DNSms pulsar binaries wave J ,inspiral $ for 1 the rate purposes753 calculations− of determining discussed2243 ( the $ Galactic see Table \quad 3 ) , has recently been dis − belowmerger period rate , the systems for which τg is less than τu( i . e . PSRs J 737 − 3039, B 1534 + 12, \noindentDespiteJ 1756 thecovered− uncertainties2251, J 1906 [ 1 in + 8 746identifying 7, ]B .1913 Although DNS + 16 binaries and theB 2127 comma mass + 11 .. function C for ) are the primarily purposes for this of determininginterest pulsar . the is Of lower these PSR than the DNS systems listed in TableGalacticB 2127\quad merger + 111 C rate , is a in comma neutron the process the systems star of being companion for ej which ected tau from cannot sub the g globular is be less ruled than cluster tau out Msub 1 in u 5 open this [ 3 0 parenthesis 5 case , 3 0 . 1\ iquad ]period andFurther eis period PSRs observations J 737 minus should 3039soon commathought clarify B 1to 534 make the plus only nature 1 2 a comma negligible of this contribution system to . the\quad mergerWe rate note [ 2 9 , 7 however ] . The general , that approach the 1 with 3 . the 6 − day orbital period of this systemJ 1remaining 756 means minus systems2251 that comma itis to will J derive 1 906 not scale plus contribute 746 factors comma for each B to 1 9 object gravitational1 3 plus , 1 construct 6 and B wave 2 the 1 27 probability plusinspiral 1 1 C density closing rate function parenthesis calculations of are primarily discussed of interest periodbelowtheir .... . Of total these population PSR ( as outlined in Section 3 . 2 . 1 ) and then divide these by a reasonable estimate for B 2the 1 27 lifet plus ime 1 1 . C Getting is in the such process estimates of being is , ej however ected from , difficult the globular . It has cluster been M proposed 1 5 .... open [ 1 7 8square ] that bracket the o bs 3 0 5 comma .... 3 0 .... 1 closingDespiteervable square the bracketlife uncertainties times ....for and these is systems in identifying are determined DNS by binaries the timescale , on\quad for the purposes of determining the Galacticthoughtwhich to the merger make current only rate orbital a negligible , period the contribution systems is reduced for by to a the which factor merger of $ two rate\tau [ 7open ] .{ square Belowg }$ bracket this is point less 2 9 , 7 the thanclosing orbital square $ smearing\tau bracket{ u period} ($ .. The i general .e.PSRsJ approach$ 737 selection− effect3039 discussed ,$B$1 in Section 3 . 534 1 . 3 will+ render 1 the2 binary ,$ undetectable by current surveys . More withrecent the remaining work [ 7 systems 3 ] has issuggested to derive that scale a significant factors for population each object of comma highly.. eccentric construct binary the probability systems could easily \noindentdensityevade function detectionJ $ of 1 their due 756 tototal their population− short2251 lifetimes open ,$J$1 parenthesis before gravitational as outlined 906 wave in + Section inspiral 746 .. 3. period ,$B$1 If this 2 period selection 1 closing effect 9 parenthesis is 1 3 + and then 1 divide 6$ theseandB bysignificant $2 ,1 then 27 the merger + 1rate estimates 1$ C) quoted are below primarily could easily of be interest underestimated . \ h f by i l la factorOf these of a few PSR . a reasonable estimate for the lifet ime period .. Getting such estimates is comma however comma difficult period .. It has been \noindentproposed openB $ square 2 bracket 1 27 1 7 8 + closing 1 square 1 $ bracket C is that in the the o bs process ervable life of times being for theseej ected systems from are determined the globular by the timescale clusterM1 5 \ h f i l l [ 3 0 5 , \ h f i l l 3 0 \ h f i l l 1 ] \ h f i l l and i s on \noindent thought to make only a negligible contribution to theLiving merger Reviews rate in [ Relativity 2 9 7 ] . \quad The general approach which the current orbital periodht is tp reduced : / /by w a wfactor w of . two l open i vi square ngrev bracket i e w 7 s closing . org square / lrr bracket - 2008 period - 8 .. Below this point comma thewith orbital the remaining systems is to derive scale factors for each object , \quad construct the probability densitysmearing function selection effect of discussed their total in Section population 3 period 1 period ( as 3 outlined .. will render in the Section binary undetectable\quad 3 . by 2 current . 1 ) and then divide these by asurveys reasonable period .. estimate More recent for work the .. open lifet square ime bracket . \quad 7 3 closingGetting square such bracket estimates has suggested is , that however a significant , difficult population of. \ highlyquad I t has been eccentricproposed [ 1 7 8 ] that the o bs ervable life times for these systems are determined by the timescale on binary systems could easily evade detection due to their short lifetimes before gravitational wave \noindentinspiral periodwhich .. If the this selectioncurrent effect orbital is significant period comma is reduced then the merger by a rate factor estimates of two quoted [7 below ] . could\quad Below this point , the orbital smearingeasily be underestimated selection effect by a factor discussed of a few period in Section 3 . 1 . 3 \quad will render the binary undetectable by current surveyshline . \quad More recent work \quad [ 7 3 ] has suggested that a significant population of highly eccentric binaryLiving Reviews systems in Relativitycould easily evade detection due to their short lifetimes before gravitational wave i nht s p tp i r : a slash l . slash\quad w wIf .. thisw period selection l i vi ngrev effect i e w s period is significant org slash lrr hyphen , then 2008 the hyphen merger 8 rate estimates quoted below could easily be underestimated by a factor of a few .

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\ hspace ∗{\ f i l l } Living Reviews in Relativity

\ hspace ∗{\ f i l l } ht tp : / / w w \quad w. l i vi ngrev i ews . org / lrr − 2008 − 8 32 ....32 Duncan R period Lorimer Duncan R . Lorimer \noindenthline 32 \ h f i l l Duncan R . Lorimer Table .. 1 : .. Known and likely DNS binaries period .. Listed are the pulse period P comma orbital period P sub b comma orbital \ [ eccentricity\ r u l e {3em e}{ comma0.4 pt characteristic}\ ] age tau sub c comma and expected binary coalescence timescale tau sub g due to gravitational waveTable emission 1 calculated : Known from and Equation likely DNS open binaries parenthesis . 7Listed closing are parenthesis the pulse period periodP, Toorbital distinguish period betweenPb, orbital definite and candidate DNS systemseccentricity comma e, characteristic age τc, and expected binary coalescence timescale τg due to gravitational \noindentwe alsowave list emissionTable whether calculated\quad the masses1 from : of Equation\quad both componentsKnown ( 7 ) . To and distinguish have likely been between determined DNS binariesdefinite via and the candidate . measurement\quad DNSListed systems of two are or , the pulse period $ P , $morewe orbital post also hyphenlistwhether period Keplerian the $ masses P parameters{ ofb both} components as, described $ o r bhave i in t a Section been l determined 4 period via 4 period the measurement of two or more post - eccentricityhlineKeplerian parameters $ e as , described $ characteristic in Section 4 . 4 . age $ \tau { c } , $ and expected binary coalescence timescale $ \Tabletau ignored!{ g }$ due to gravitational hline \noindentThe resultswave of the emission most recent calculated DNS merger rate from estimates Equation of this ( kind 7 ) open . To square distinguish bracket 1 8 between9 closing square definite bracket and are summarised candidate in DNS systems , the left panel of Figure .. 1 9 period .. The combinedTable Galactic ignored! merger rate comma dominated by the double pulsar \noindentand J 1 906we plus also 746 is list found whether to be 1 1 8 the sub minus masses 79 to of the both power components of plus 1 74 Myr have to the been power determined of minus 1 comma via the where measurement the uncertainties of two or reflectmore the post 95 percent− Keplerian confidence parameters as described in Section 4 . 4 . level using the techniques summarised in Section 3 period 2 period 2 period Extrapolating this number to include DNS \ [ binaries\ r u l e { detectable3em}{0.4 by pt }\ LIGO] in other galaxies open square bracket 2 9 7 closing square bracket comma the expected event rate is 49 sub minus 3 3 toThe the results power of of the plus most 73 times recent 1 DNS 0 to mergerthe power rate of estimates minus 3 yr of to this the kind power [ 1 8of 9 minus ] are summarised 1 in the left for initialpanel of LIGO Figure and 265 1 9 sub . minusThe combined 1 78 to the Galactic power merger of plus rate 39 0 , yrdominated to the power by the of double minus 1 pulsar for advanced LIGO period Future prospects +174 −1 for detectingand J gravitational1906 + 746 is found to be 118−79 Myr , where the uncertainties reflect the 95% confidence level using wavethe emission techniques from summarised binary neutron in Section star inspirals 3 . 2 . 2 are . Extrapolating therefore very this encouraging number to comma include especially DNS if the \ vspace ∗{3 ex }\ centerline {\ framebox[.5 \ l i n e w i d t h ] {\ t e x t b f { Table ignored!+73 }}}\−3vspace−1 ∗{3 ex} populationbinaries of detectable highly eccentric by LIGO systems in other is significant galaxies [ 2 open 9 7 ] square , the expected bracket 7 event 3 closing rate square is 49−33 bracket× 10 periodyr Since much of the uncertainty in +390 −1 the ratefor initial LIGO and 265−178yr for advanced LIGO . Future prospects for detecting gravitational wave estimatesemission is due from to binary our ignorance neutron of star the inspirals underlying are distribution therefore very of double encouraging neutron , especiallystar systems if the comma population of futurehighly gravitational eccentric systemswave detection is significant could ultimately [ 7 3 ] . Since constrain much the of the properties uncertainty of this in exciting the rate binary estimates is due to \ [ \ r u l e {3em}{0.4 pt }\ ] speciesour periodignorance of the underlying distribution of double neutron star systems , Althoughfuture the gravitational double pulsar wave system detection J 737 could minus ultimately 3039 will constrain not be important the properties for ground of this hyphen exciting based binary de hyphen tectorsspecies until . its final coalescence in another 85 Myr comma it may be a useful calibration source for the The results of the most recent DNS merger rate estimates of this kind [ 1 8 9 ] are summarised in future space hyphenAlthough based detector the double LISA pulsar open system square J bracket 737 − 3039 2 7 2 will closing notbe square important bracket for period ground .. It- based is calculated de - open square bracket 1 the left panel of Figure \quad 1 9 . \quad The combined Galactic merger rate , dominated by the double pulsar 7 5 closingtectors square until bracket its final that coalescence a 1 hyphen in another yr observation 85 Myr with , it may LISA be a useful calibration source for the future space would- based detect detector open parenthesis LISA [ 2 7 albeit 2 ] . with It is S slashcalculated N thicksim [ 1 7 5 2 ] closing that a parenthesis 1 - yr observation the continuous with LISA emission would at detect a frequency of 0 period 2 mHz \noindent andJ $1 906 + 746$ isfoundtobe $1 1 8ˆ{ + 1 74 } { − 79 } Myr ˆ{ − based on( albeit the with S / N ∼ 2) the continuous emission at a frequency of 0 . 2 mHz based on the current orbital 1 } , $ where the uncertainties reflect the $ 95 \% $ confidence currentparameters orbital parameters. Although periodthere is Although the prospect there of is using the prospect LISA to detectof using similar LISA systems to detect through similar their systems continuous level using the techniques summarised in Section 3 . 2 . 2 . Extrapolating this number to include DNS throughemission their , continuous current calculations emission comma[ 1 7 5 ] current suggest calculations that significant open ( square S / N > bracket5) detections 1 7 5 closing are not square likely bracket . Despite suggest that significant open parenthesisthese S limitations slash N greater , it is 5 likely closing that parenthesis LISA observations will be able \noindent binaries detectable by LIGO in other galaxies [ 2 9 7 ] , the expected event rate is $ 49 ˆ{ + detectionsto place are independent not likely period constraints Despite on thesethe Galactic limitations DNS comma binary it population is likely that after LISA several observations years of will be able 73 } { − 3 3 }\times 1 0 ˆ{ − 3 } yr ˆ{ − 1 }$ to placeoperation independent . constraints on the Galactic DNS binary population after several years of operation3 . 4 . period 2 White dwarf – neutron star binaries \noindent for initial LIGO and $ 265 ˆ{ + 39 0 } { − 1 78 } yr ˆ{ − 1 }$ for advanced LIGO . Future prospects for detecting gravitational 3 periodAlthough 4 period the 2population .. White dwarf of white endash dwarf neutron – neutron star binaries star ( WDNS ) binaries in general is substantial , the wave emission from binary neutron star inspirals are therefore very encouraging , especially if the Althoughfraction the which population will merge of white due to dwarf gravitational endash neutron wave emission star open isparenthesis small . Like WDNS the DNS closing binaries parenthesis , binaries in general is substantial population of highly eccentric systems is significant [ 7 3 ] . Since much of the uncertainty in the rate commathe observed WDNS sample suffers from small - number statistics . From Figure 1 8 , we note that estimatesthe fraction is which due will to merge our due ignorance to gravitational of the wave underlying emission is small distribution period Like the of DNS double binaries neutron comma star systems , the observed WDNS sample suffers from small hyphen number statistics period .... From Figure .... 1 8 comma we note that \noindenthline future gravitational wave detection could ultimately constrain the properties of this exciting binary Living Reviews in Relativity Living Reviews in Relativity ht tp : / / w w w . l i vi ngre v i e w s . or g / lrr - 2008 - 8 \noindentht tp : slashs p slash e c i e sw w . w period l i vi ngre v i e w s period or g slash lrr hyphen 2008 hyphen 8 \ hspace ∗{\ f i l l }Although the double pulsar system J $ 737 − 3039 $ will not be important for ground − based de −

\noindent tectors until its final coalescence in another 85 Myr , it may be a useful calibration source for the future space − based detector LISA [ 2 7 2 ] . \quad It is calculated [ 1 7 5 ] that a 1 − yr observation with LISA would detect ( albeit with S / N $ \sim 2 ) $ the continuous emission at a frequency of 0 . 2 mHz based on the current orbital parameters . Although there is the prospect of using LISA to detect similar systems through their continuous emission , current calculations [ 1 7 5 ] suggest that significant ( S / N $ > 5 ) $ detections are not likely . Despite these limitations , it is likely that LISA observations will be able

\noindent to place independent constraints on the Galactic DNS binary population after several years of

\noindent operation .

\noindent 3 . 4 . 2 \quad White dwarf −− neutron star binaries

\noindent Although the population of white dwarf −− neutron star ( WDNS ) binaries in general is substantial , the fraction which will merge due to gravitational wave emission is small . Like the DNS binaries ,

\noindent the observed WDNS sample suffers from small − number statistics . \ h f i l l From Figure \ h f i l l 1 8 , we note that

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\noindent Living Reviews in Relativity

\noindent http : //www. l i vi ngrev i ews . org/ lrr − 2008 − 8 BinaryBinary and and Millisecond Millisecond Pulsars Pulsars .... 33 33 \noindenthline Binary and Millisecond Pulsars \ h f i l l 33 Figure 19 : The current best empirical estimates of the coalescence rates of relativistic binaries involving \ [ neutron\ r u l e { stars3em}{ period0.4 pt ..}\ The] individual contributions from each known binary system are shown as dashed lines comma whileFigure the solid 19 : lineThe shows current the best total empirical probability estimates density of the function coalescence on a logarithmicrates of relativistic and open binaries parenthesis involving inset closing parenthesis linear scale period neutron stars . The individual contributions from each known binary system are shown as dashed lines , while the \noindentThesolid left line panelFigure shows shows the 19the total : most The probability recent current density analysis best function for empirical DNS on a binaries logarithmic estimates open and square ( inset of bracket ) linear the1 scale coalescence 8 9 . closing The left square panel rates bracketshows of comma relativistic while the rightbinaries involving panel showsthe most the recent analysis for DNS binaries [ 1 8 9 ] , while the right panel shows the equivalent results for NS – WD \noindentequivalentbinariesneutron results [ 1 9 1 ]for . Figures starsNS endash provided . \ WDquad by binaries ChungleeThe individual open Kim square . bracket contributions 1 9 1 closing from square each bracket known period binary Figures provided system by are Chunglee shown Kim as dashed lines , periodwhile the solid line shows the total probability density function on a logarithmic and ( inset ) linear scale . Thehline left panel shows the most recent analysis for DNS binaries [ 1 8 9 ] , while the right panel shows the equivalent results for NS −− WD binaries [ 1 9 1 ] . Figures provided by Chunglee Kim . Living Reviews in Relativity Living Reviews in Relativity ht tp : slash slash w w .. w period l i vi ngrev i e w s period org slash lrr hyphen 2008 hyphen 8 \ [ \ r u l e {3em}{0.4 pt }\ ] ht tp : / / w w w . l i vi ngrev i e w s . org / lrr - 2008 - 8

\ hspace ∗{\ f i l l } Living Reviews in Relativity

\ hspace ∗{\ f i l l } ht tp : / / w w \quad w. l i vi ngrev i ews . org / lrr − 2008 − 8 34 ....34 Duncan R period Lorimer Duncan R . Lorimer \noindenthline 34 \ h f i l l Duncan R . Lorimer only three WDNS systems are currently known that will merge within tau sub u comma PSRs J 75 1 plus 1 807 open square bracket 2 3 5 closing\ [ \ r u square l e {3em bracket}{0.4 comma pt }\ ] J 1only 757 minus three WDNS5322 open systems square are bracket currently 1 0 known0 closing that square will merge bracket within .... andτu, JPSRs 1 14 1J minus751 + 1807[235] 6545 open, square bracket 1 8 3 closing square bracketJ period 1757 − ....5322 Applying [100] the same and Jtechniques 1141 − 6545 as used [183] for. the DNSApplying the same techniques as used for the DNS \noindentpopulationpopulationonly comma , the three the merging merging WDNS rate rate systems contributions contributions are of currently of the the three three systems systems known can can that be be calculated calculated will merge [ open 1 9 within square bracket 1 $ ] and\tau 1 9are ....{ 1 closingu } square, $ PSRs bracket J $75 1 + 1 807 [ 2 3 5 ] ,$ +5 −1 and areshown in Figure 1 9 . The combined Galactic coalescence rate is 4−3Myr ( at 68% confidence showninterval in Figure ) . 1 9 period .... This The result combined is not Galactic corrected coalescence for beaming rate and is therefore 4 sub minus should 3 to be the regarded power of as plus a lower 5 Myr to the power of minus 1\noindent openlimit parenthesis onJ the $ totalat 1 68 event percent 757 rate confidence− . Although5322 the [ orbital 1 frequencies 0 0 of] these $ objects\ h f i l latand coalescence J $ are 1 too 14 low to 1 be − 6545 [ 1 8interval 3detected ] closing by . parenthesis$LIGO\ h , f they i l l period doApplying fall .... within This the the result band same is not planned techniques corrected for LISA foras beaming [ 2 used7 2 ] .and Unfortunatelyfor therefore the DNS should , an extrapolation be regarded as a lower limitof on the the Galactic total event event rate rate period out to Although distances theat which orbital such frequencies events would of these be detectable objects at by coalescence LISA does are not too suggest \noindentlowthat to be these detectedpopulation systems by LIGO will , be the comma a major merging they source do fallrate of detectionwithin contributions the [ band 1 9 1 planned ] . Similarof for the LISA three opensystems square bracket can 2 be 7 2 calculated closing square bracket[ 1 9 period\ h f i l l 1 ] and are Unfortunatelyconclusions comma were an reached by considering the statistics of low - mass X - ray binaries [ 7 7 ] . \noindentextrapolation3 . 5shown of Going the in Galactic Figure further event 1 9 rate . out\ h f to i l distances l The combined at which such Galactic events would coalescence be detectable rate is $ 4 ˆ{ + 5 } { − 3 } Myrby ˆ LISA{Good − does starting1 not} suggest points( $ atfor that further $ these 68 systemsreading\% $ canwillconfidence be afound major in source other ofreview detection articles open [ 3 square 0 0 , 1 bracket 8 9 ] . 1 Our 9 1 closing cov - square bracket period .. Similarerage of compact object coalescence rates has concentrated on empirical methods . Two software packages \noindentconclusionsare freelyi n were t available e r v reached a l ) which . by\ consideringh allow f i l l theThis user the resultto statistics synthesize is of low not and hyphen search corrected massradio X pulsar for hyphen beamingpopula ray binaries- tions and [ open therefore2 8 square 7 , 3 bracket should 7 7 be closing regarded square as a lower bracket9 period 4 , 3 2 2 ] . An alternative approach is to undertake a full - blown Monte Carlo simulation of the most \noindent3 periodlikely 5 evolutionarylimit .. Going on further the scenarios total described event in rate Section . Although 2 . 6 . the In this orbital scheme frequencies , a population of primordial these objects at coalescence are too lowGood tobinaries starting be detected is synthesizedpoints for by further with LIGO a reading number , they can of underlyingbedo found fall in withindistribution other review the functions articles bandopen planned : primary square mass for bracket LISA, binary 3 0 [ 0 mass comma2 7 ratio 2 1 ] 8 .9 closing Unfortunately square bracket , an periodextrapolation, Our orbital cov hyphenperiod of distribution the Galactic etc . event The evolution rate outof both to stars distances is then fol at - lowed which to give such a predicted events sample would be detectable byerage LISAof of binary compact does systems not object suggest of allcoalescence the various that rates thesetypes has . concentrated systems Although will selectionon empirical be effects a major methods are not source period always .. of t Two aken detection software into account [ 1 in 9 1 ] . \quad S i m i l a r packagesthis approach are freely , theavailable final census which allowis usually the user normalized to synthesize to the and star search formation radio rate pulsar . popula hyphen \noindenttions openconclusions squareNumerous bracket 2 populationwere .. 8 7 reached comma syntheses .. 3 by 9 4 ( considering commamost often 3 2 to2 closing populations the square statistics of bracket binaries periodof where low An one− alternativemass or both X mem− approachray - binaries is to undertake [ 7 a 7 full ] . hyphenbers blown are Monte NSs ) Carlo can be simulation found in the literature [ 9 6 , 3 2 4 , 3 7 4 , 3 0 3 , 2 1 1 , 2 7 , 2 8 ] . A group in \noindentof theMoscow most3 likelyhas . 5 evolutionary\quad Going scenarios further described in Section .. 2 period 6 period .. In this scheme comma a population of primordialmade a web binaries interface is synthesized to their code with [ 3 a 5 number 5 ] . Although of underlying extremely distribution instructive functions , the uncertain: primary assump - tions \noindentmassabout commaGood initial binary conditions starting mass ratio , pointsthe comma physics fororbital of massfurther period transfer distribution reading and the etccan kicks period be applied found .. The to evolution inthe othercompact of bothreview object stars at articles is birth then fol hyphen [ 3 0 0 , 1 8 9 ] . Our cov − eragelowedresult toof give in compact a a wide predicted range object sample of predicted coalescence of binary event systems rates rates which of all has are the currently concentratedvarious types broader period than on .. empirical the Although empirical selection methods methods [ .1 7\quad 6 Two software packageseffects, 1 are9 1 arenot , 1 7 always freely7 ] . Ultimately t aken available into , account the detection which in this allow statistics approach the from comma user the thegravitational to final synthesize census wave is usually detectors and search normalized could provide radio far pulsar popula − t ito o n the stighter [ star 2 constraintsformation\quad 8 rate7 on , the period\quad DNS merging3 9 4 rate , 3 than 2 2 the ]. pulsar An alternative surveys from which approach these predictions is to undertake are made a full − blown Monte Carlo simulation ofNumerous the. Verymost population recently likely [ syntheses 2 evolutionary 8 9 ] the open results parenthesis from scenarios empirical most often describedpopulation to populations constraints in Section of andbinaries full\quad - where blown2 one binary . 6or both. population\quad memIn hyphen this scheme , a population ofbers primordialsynthesis are NSs codes closing binaries have parenthesis been combined is can synthesized be to found constrain in thewith a variety literature a number of input openof parameters square underlying bracket and9 physical 6 distribution comma conditions 3 2 .... . 4 functions comma The 3 7 4 : comma primary .... 3 0 3 commamassresults 2 , 1 binary .... of 1 thiscomma mass work 2 7 are ratio comma promising , 2 ....orbital , 8 with closing stringent period square constraints bracket distribution period being A placed group etc . in on\ Moscow thequad kickThe has distributions evolution , mass of - both stars is then fol − lowedmadeloss a to fractionweb give interface during a predicted to mass their transfer code sample open and square common of binary bracket envelope 3 systems 5 assumptions5 closing of square all . bracketthe various period .. types Although . \ extremelyquad Although instructive selection comma the uncertaineffects assump are not hyphen always t aken into account in this approach , the final census is usually normalized totions the about star initial formation conditions rate comma . the physics of mass transfer and the kicks applied to the compact object at birth result in a wide range of predicted event rates which are currently broader than the \ hspaceLiving∗{\ Reviewsf i l l }Numerous in Relativity population syntheses ( most often to populations of binaries where one or both mem − empiricalht tp methods : / / wopen w w square . l ibracket vi ngre 1 7 v 6 icomma e w s 1 . 9 1 or comma g / lrr 1 7 -7 closing 2008 - square 8 bracket period Ultimately comma the detection statistics from the gravitational wave \noindentdetectors couldbers provide are NSs far tighter ) can constraints be found on in the the DNS literature merging rate than [ 9 the 6 pulsar, 3 2 surveys\ h f i l l 4 , 3 7 4 , \ h f i l l 3 0 3 , 2 1 \ h f i l l 1 , 2 7 , 2 \ h f i l l 8 ] . A group in Moscow has from which these predictions are made period .. Very recently open square bracket 2 8 9 closing square bracket the results from empirical population\noindent made a web interface to their code [ 3 5 5 ] . \quad Although extremely instructive , the uncertain assump − tionsconstraints about and initial full hyphen conditions blown binary , population the physics synthesis of codes mass have transfer been combined and the to constrain kicks applied a to the compact objectvariety ofat input birth parameters result and in physical a wide conditions range of period predicted .. The results event of this rates work which are promising are currently comma with broader than the empiricalstringent constraints methods being [ 1 placed 7 6 , on 1 the 9 kick 1 , distributions 1 7 7 ] . comma Ultimately mass hyphen , the loss detection fraction during statistics mass transfer from the gravitational wave detectorsand common could envelope provide assumptions far period tighter constraints on the DNS merging rate than the pulsar surveys fromhline which these predictions are made . \quad Very recently [ 2 8 9 ] the results from empirical population constraintsLiving Reviews and in Relativity full − blown binary population synthesis codes have been combined to constrain a varietyht tp : slash of slash input w w parameters w period l i vi and ngre physical v i e w s period conditions or g slash . lrr\ hyphenquad The 2008 results hyphen 8 of this work are promising , with stringent constraints being placed on the kick distributions , mass − loss fraction during mass transfer and common envelope assumptions .

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\noindent Living Reviews in Relativity

\noindent http : //www. l i vi ngrev i ews . org/ lrr − 2008 − 8 BinaryBinary and and Millisecond Millisecond Pulsars Pulsars .... 35 35 \noindenthline Binary and Millisecond Pulsars \ h f i l l 35 4 .. Principles .. and .. Applications .. of Pulsar .. Timing \ [ Pulsars\ r u l e { are3em excellent}{0.4 pt celestial}\ ] clo cks period The period of the first pulsar open square bracket 1 4 1 closing square bracket was found to be stable to4 Principles and Applications of Pulsar Timing onePulsars part in are1 0 excellentto the power celestial of 7 cloover cks a few . The months period period of the Following first pulsar the [ 1 discovery 4 1 ] was of found the millisecond to be stable pulsar to B 1 937 plus 2 1 open square 7 bracket\noindentone 1 8 part closing4 in\quad 10 squareoverP bracket r a i n few c i p months l e s \quad . Followingand \ thequad discoveryApplications of the millisecond\quad pulsaro f Pulsar B 1937 +\ 21[18]quad Timing 13 it wasit was demonstrated demonstrated that that its its period period could could be be measured measured to to one one part part in in 1 10 0 toor the better power [ 9 of 4 1 ] .3 This or better un - rivaled open square bracket 9 4 closing square\noindentstability bracketPulsars period leads to This a are host un ofexcellent hyphen applications celestial including uses clo as time cks keepers . The , probes period of relativistic of the first gravity pulsar and natural [ 1 4 1 ] was found to be stable to rivaledgravitational stability leads wave to detectors a host of . applications including uses as time keepers comma probes of relativistic \noindentgravity4 . and 1onepart natural Observing gravitational in $1 basics wave 0ˆ detectors{ 7 }$ period over a few months . Following the discovery of the millisecond pulsar B $14 periodEach 937 1 pulsar .. + Observing is 2 typically basics1 observed [ 1 at 8 least ]$once or twice per month over the course of a year to establish its Eachbasic pulsar properties is typically . Figureobserved 2 0 at least summarises once or thetwice essential per month steps over involved the course in a of “ a time year - of - arrival ” ( TOA \noindentto establish) measurementit its was basic . demonstrated properties Pulses from period the that neutron .. Figure its star 2 period0 traverse .. summarises could the interstellar the be essential measured medium steps to before involved one being part in a received .. in quotedblleft $ at 1 the time 0 ˆ{ hyphen1 3 of} hyphen$ or better [ 9 4 ] . This un − rivaledarrivalradio quotedblright stability telescope where open leads they parenthesis areto dedispersed a host TOA ofclosing and applications added parenthesis to form measurement a including mean pulse period profileuses Pulses as. time fromthe keepers neutron , star probes traverse of the relativistic interstellar mediumgravity before andFigure natural 20 : gravitationalSchematic showing wave the detectors main stages involved . in pulsar timing observations . being receivedDuring the at the observation radio telescope , the data where regularly they are receive dedispersed a time stamp and added , usually to form based a on mean a caesium pulse t ime standard \noindentprofileor hydrogen period4 . 1 maser\quad at theObserving observatory basics plus a signal from the Global Positioning System of satellites ( GPS ; Figuresee 20 [ 9 : 3 .. ] Schematic ) . The TOA showing is defined the main as the stages arrival involved time in of pulsar some fiducialtiming observations point on the period integrated profile with \noindentDuringrespect theEach to observation either pulsar the comma start is or typically the the data midpoint regularly observed of the receive observation at a time least . stamp Since once thecomma profile or usually twice has a based st per able onmonth form a caesium at over any given the course of a year tot ime establishobserving standard frequency or its hydrogen basic ( see maserSection properties at 2the . 3 observatory ), . the\quad TOA plusFigure can a signal 2 from 0 \quad the Globalsummarises Positioning the essential steps involved in a \quad ‘ ‘ time − o f − arrivalSystembe accurately of ’’ satellites ( TOA determined open ) measurement parenthesis by cross GPS - correlation . semicolon Pulses of see from the open observed the square neutron profile bracket with star 9 3 a closing high traverse S square / N “ bracket templatethe interstellar closing ” profile parenthesis medium period before The TOA isbeing definedobtained received as the from arrival the at time addition the of radiosome ofmany fiducial telescope observations point where at the they particular are observing dedispersed frequency and . added to form a mean pulse pon r o f the i l eSuccessful integrated . pulsarprofile timingwith respect requires to eitheroptimal the TOA start precision or the midpoint which largely of the depends observation on the period signal Since - to - noise theratio profile ( Shas / Na st ) of able the form pulse at profile any given . Sinceobserving the TOA frequency uncertainty open parenthesisTOA is roughly see Section the pulse 2 period 3 closing parenthesis comma the TOA can\ centerlinewidth divided{ Figure by the 20 S : / N\quad , usingSchematic Equation ( 3 showing ) we may writethe main the fractional stages error involved as in pulsar timing observations . } be accurately determined by cross hyphen correlation of the observed profile with a high S slash N quotedblleft template quotedblright During the observation , the data regularly receive a time stamp , usually based on a caesium profile obtained from the addition of many observations at the particular) observing frequency period t ime standardTOA or hydrogenS psr maserT rec at + theT observatoryG plus∆ν a signaltint fromW the Global Positioning Successful pulsar timing' requires optimal− 1 TOA precisionsky ( which largely− 1( depends) − 1/ on2( the) signal− 1/2( hyphen)3 /2 (8) mJy K −1 . Systemto hyphen of noise satellitesP ratio open ( parenthesis GPS ; see S slash [ 9 N 3 closing ] )KJy . parenthesis The TOA ofMHz is the defined pulse profiles as period theP arrival .. Since the time TOA of uncertainty some fiducial epsilon sub point on the integrated profile with respect to either the start or the midpoint of the observation . Since TOA isHere roughly,S theis pulse the flux density of the pulsar ,T and T are the receiver and sky noise temperatures , G is thewidth profile dividedpsr byhas the a S st slash able N comma form using at any Equationrec given open observingsky parenthesis frequency 3 closing parenthesis ( see Sectionwe may write 2 . the 3 fractional ) , the error TOA as can the antenna gain , ∆ν is the observing bandwidth , tint is the integration time ,W is the pulse width and P is Equation:the pulse open period parenthesis ( we assume 8 closingW parenthesis P ). Optimal .. epsilon results sub TOA are thus divided obtained by P for simeq observations Row 1 S ofunderbar short period psr Row 2 mJy . minus 1 Row 1\noindent T underbarbe rec accuratelyplus T sub sky determined Row 2 K . parenleftbigg by cross G− dividedcorrelation by K Jy to of the the power observed of minus profile 1 to the power with of a parenrightbigg high S / N minus ‘‘ template ’’ profilepulsars obtained with large from flux densities the addition and small dutyof many cycles observations ( i . e . small W/P at the) using particular large telescopes observing with low - frequency . 1 parenleftbiggnoise receivers Capital and Delta large nu observing divided by bandwidths MHz parenrightbigg . minus 1 slash 2 parenleftbigg t sub int divided by s parenrightbigg minus 1 slash 2 parenleftbigg W divided by P parenrightbigg 3 sub period slash 2 Successful pulsarOne timing of the main requires problems optimal of employing TOA large precision bandwidths which is pulse largely dispersion depends . As ondiscussed the signal − Herein comma Section S 2 sub . 4 psr , pulses is the emitted flux density at lower of the radio pulsar frequencies comma Ttravel sub slowerrec and and T sub arrive sky later are the than receiver those and sky noise temperatures comma toG− is thenoise antenna ratio gain ( comma S / N Capital ) of Delta the nu pulse is the profile observing .bandwidth\quad Since comma the t sub TOA int is uncertainty the integration time $ \ commaepsilon W is{ theTOA pulse}$ iswidth roughly and P the is the pulse pulse period open parenthesis we assume W ll P closing parenthesis period .. Optimal results are thus obtained for observations of short period pulsars with large flux densities and small duty cycles .. open parenthesis i period e period small \noindentW slash Pwidth closing parenthesis divided by using the large S /telescopes N , using with low Equation hyphen noise ( 3 receivers ) we mayLiving and write large Reviews observing the in fractionalRelativity bandwidths errorperiod as One of the main problems of employinght tp : /large / w bandwidths w w . is l pulse i vi dispersion ngrev i eperiod w s ... As org discussed / lrr - 2008 - 8 \ beginin Section{ a l i g 2 n period∗} 4 comma pulses emitted at lower radio frequencies travel slower and arrive later than those \ f rhline a c {\ epsilon { TOA }}{ P }\simeq \ l e f t (\ begin { array }{ c} S {\underline {\}} psr \\ mJy \end{ array }\ right ) − Living1 \ Reviewsl e f t (\ inbegin Relativity{ array }{ c} T {\underline {\}} r e c + T { sky }\\ K \end{ array }\ right )( \ f r a c { G }{ K Jyht ˆ{ tp − : slash1 slash}}ˆ{ w) w} .. w − period1 l i (vi ngrev\ f r a i c e{\ w sDelta period org\nu slash}{ lrrMHz hyphen} 2008) hyphen− 1 8 / 2 ( \ f r a c { t { i n t }}{ s } ) − 1 / 2 ( \ f r a c { W }{ P } ) 3 { . } / 2 \ tag ∗{$ ( 8 ) $} \end{ a l i g n ∗}

\noindent Here $ , S { psr }$ is the flux density of the pulsar $ , T { r e c }$ and $ T { sky }$ are the receiver and sky noise temperatures , $G$ is the antenna gain $ , \Delta \nu $ is the observing bandwidth $ , t { i n t }$ is the integration time $ , W$ is the pulse width and $ P $ is the pulse period ( we assume $W \ l l P ) . $ \quad Optimal results are thus obtained for observations of short period pulsars with large flux densities and small duty cycles \quad ( i . e . small $W / P ) $ using large telescopes with low − noise receivers and large observing bandwidths .

\ hspace ∗{\ f i l l }One of the main problems of employing large bandwidths is pulse dispersion . \quad As discussed

\noindent in Section 2 . 4 , pulses emitted at lower radio frequencies travel slower and arrive later than those

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\ hspace ∗{\ f i l l } Living Reviews in Relativity

\ hspace ∗{\ f i l l } ht tp : / / w w \quad w. l i vi ngrev i ews . org / lrr − 2008 − 8 36 ....36 Duncan R period Lorimer Duncan R . Lorimer \noindenthline 36 \ h f i l l Duncan R . Lorimer emitted at higher frequencies period .. This process has the effect of quotedblleft stretching quotedblright the pulse across a finite \ [ receiver\ r u l e { bandwidth3em}{0.4 comma pt }\ ] increasing W and therefore increasing epsilon sub TOA period .. For normal pulsars comma dispersion canemitted largely be at compensatedhigher frequencies for by . the This incoherent process dedispersion has the effect process of “ stretching outlined ” in the Section pulse 3 across period a finite1 period receiver Thebandwidth short periods , increasing of millisecondW and pulsars therefore offer increasingthe ultimateTOA in timing. For precision normal pulsars period In , dispersion order to fully can largely be \noindentexploitcompensated thisemitted comma for a by at better the higher incoherent method frequencies of dedispersion dispersion removal . process\quad is outlined requiredThis in process period Section .. Technical3 has . 1 . the difficulties effect in of building ‘‘ stretching ’’ the pulse across a finite receiverdevicesThe with bandwidth short very periodsnarrow , channel of increasing millisecond bandwidths pulsars $W$ require offer and the another ultimate therefore dispersion in timing increasing removal precision technique . $ In\ orderperiodepsilon to .. fully In { exploitTOA } . $ \quad For normal pulsars , dispersion canthethis largelyprocess , a better of becoherent method compensated dedispersion of dispersion for open removal by square the is bracket incoherentrequired 1 . 2 9 Technicalcomma dedispersion 2 .. difficulties 2 6 closing process in squarebuilding bracketoutlined devices the with incoming in very Section signals 3 are . 1 dedispersed . over thenarrow whole channel bandwidths require another dispersion removal technique . In Thebandwidth shortthe process periods using of a coherent filter of which millisecond dedispersion has the inverse [ pulsars 1 2 9transfer , 2 offer 2 function 6 ] the the toincoming ultimate that of signals the interstellar in are timing dedispersed medium precision over period the . whole In order to fully exploitThebandwidth signal this processing using , a a better can filter be which done method has online the of either inverse dispersion using transfer high function speed removal devices to that is such of required the as interstellar field programmable . \quad mediumTechnical . The signal difficulties in building devicesgateprocessing arrays with open can very square be done narrow bracket online 6channel either4 comma using bandwidths 2 9 high .... 1 speed closing devices require square such bracket another as field or completelyprogrammable dispersion in software removal open technique square bracket . 3\quad 4 3 commaIn 3 5 0 closinggate square arrays bracket [ 6 4 , period 2 9 Off1 ] or hyphen completely line data in software reduction [ 3 comma 4 3 , 3 while 5 0 ] . disk Off hyphen - line data space reduction , while disk - \noindentlimitedspace commathe allows process for more of coherent flexible analysis dedispersion schemes open [ square 1 2 9bracket , 2 2\quad 0 closing2 6 square ] the bracket incoming period signals are dedispersed over the whole bandwidthFigurelimited 2 1 : , using.... allows A 1 for a 20 filtermore mu s flexible window which analysis centred has schemes on the a coherently inverse [ 2 0 ] . hyphen transfer dedispersed function giant to pulse that from of the the Crab interstellar pulsar medium . TheshowingFigure signal high 2 processing1 hyphen : intensity canA nanosecond120 beµ s done window bursts online centred period on either Figurea coherentlyusing provided - dedispersed high by Tim speed Hankins giant pulsedevices open from square the such Crab bracket as pulsar field 1 3 0 closing programmable square bracket period showing high - intensity nanosecond bursts . Figure provided by Tim Hankins [ 1 3 0 ] . \noindentThe maximumgate time arraysThe resolution maximum [ 6 obtainable 4 time , 2 resolution 9 via\ h coherent f i l l obtainable1 dedispersion ] or via completely coherent is the inverse dedispersion in softwareof the is total the inverse[ 3 4 of 3 the , 3 total 5 0 ] . Off − line data reduction , while disk − space receiverreceiver bandwidth bandwidth period . .. The The current current state state of the art art is is the the detection detection open [ 1 3 square 0 ] of bracket features 1 3on 0 nanosecond closing square bracket of features on nanosecond\noindenttimescaleslimited in pulses , from allows the 33 for - ms more pulsar flexible B 531 + 21 analysis in the Crab schemes nebula shown [ 2 in 0 Figure ] . 2 1 . Simple light timescalestravel - in time pulses arguments from the can 33 be hyphen made ms to showpulsar that B 531 , in plus the 2 absence 1 in the of Crab relativistic nebula beaming shown in Figure 2 1 period \noindentSimpleeffects lightFigure [ 1 travel 2 1 ] ,hyphen 2 these 1 : incredibly time\ h f arguments i l l brightA $ can bursts 1 be 20 originatemade to\mu show from$that regions s window comma less than in centred the 1 absencem inon size of a . relativistic coherently beaming− dedispersed giant pulse from the Crab pulsar effects4 . open 2 square The bracket t iming 1 2 1model closing square bracket comma these incredibly bright bursts originate from regions less than 1 m in size period\noindentTo modelshowing the rotational high − behaviourintensity of the nanosecond neutron st ar bursts we ideally . Figure require TOAs provided measured by Tim by an Hankins inertial [ 1 3 0 ] . 4 periodobserver 2 .. . The An t iming observatory model lo cated on Earth experiences accelerations with respect to the neutron star due \ hspaceTo modelto∗{\ the the Earthf i l rotational l } ’The s rotation maximum behaviour and orbital time of the motion resolution neutron around st ar weobtainable the ideally Sun and require is via therefore TOAs coherent measurednot dedispersion by an is the inverse of the total inertialin an observer inertial period frame . .. An observatory To a very good lo cated approximation on Earth experiences , the solar accelerations system centre with - of respect - mass ( to barycentre the ) \noindentneutroncan be starreceiver regarded due to theas bandwidth an Earth inertial quoteright frame . \quad . s rotationThe It and current is now orbital standard motionstate practice around of the [ the 1 art5 Sun 1 ] to is and transform the is therefore detection the notobserved [ 1 3 0 ] of features on nanosecond timescalesin anTOAs inertial to thisin frame pulsesframe period using from .... a planetary To the a very 33 ephemeris− goodms approximation pulsar such as B the $ comma JPL 531 DE the 405 + solar [ 3 2 5 system 2 ] 1 . The $ centre transformationin thehyphen Crab of hyphen nebula mass shown open in parenthesis Figure 2 1 . barycentreSimplebetween closinglight barycentric parenthesis travel (−T )time and observed arguments (t) takes can the be form made to show that , in the absence of relativistic beaming can be regarded as an inertial frame period .... It is now standard practice open square bracket 1 5 1 closing square bracket to transform \noindent effects [ 1 2 1 ] , these incredibly bright bursts originate from regions less than 1 m in size . the observed sˆ sˆ 2 2 r . ( r. ) − | r | TOAs to this frame usingT − t a= planetary ephemeris+ such as the JPL DE 405 open+ ∆t squarerel − ∆t bracketDM. 3 5 2 closing(9) square bracket period The transformation\noindent 4 . 2 \quad The t imingc model 2cd betweenHere barycentricr is the position open parenthesisof the observatory T closing with parenthesis respect to and theobserved barycentre open, sˆ parenthesisis a unit vector t closing in the parenthesis direction of takes the form \noindent To model the rotational behaviour of the neutron st ar we ideally require TOAs measured by an Equation:the pulsar open at parenthesis a distance d 9and closingc is parenthesis the speed of .. light T minus . The t = first r underbar term on the sub right period hand sub side hline of to Equation the power ( 9 of ) circumflex-s divided by c inertial observer . \quad An observatory lo cated on Earth experiences accelerations with respect to the plus openis the parenthesis light travel sub time hline from r period the observatory sub hline to to the the power solar system of s-circumflex barycentre closing . Incoming parenthesis pulses to from the power all but of the 2 minus bar sub hline r bar neutron star due to the Earth ’ s rotation and orbital motion around the Sun and is therefore not to the powernearest of pulsars 2 divided can by be 2 approximated cd plus Capital by Delta plane t wavefronts sub rel minus . Capital The second Delta term t sub , DM which period represents the delay Heredue r underbar to spherical is the wavefronts position ,of yields the observatory the parallax with and respect hence to the barycentre comma circumflex-s underbar is a unit vector in the \noindentdirection ofin the an pulsar inertial at a distance frame d and . \ ch is f i the l l speedTo a of very light periodgood approximationThe first term on the , theright solarhand system centre − o f − mass ( barycentre ) side of Equation open parenthesis 9 closing parenthesis is the light travel time from the observatory to the solar system barycentre period \noindentIncoming pulsescan be from regarded all but the as nearest an inertial pulsars can frame be approximated . \ h f i l lbyIt plane is wavefronts now standard period .. practice The [ 1 5 1 ] to transform the observed Living Reviews in Relativity second term comma which represents the delay due to spherical wavefronts comma yields the parallax and hence \noindenthlineht tpTOAs : / / to w thisw w . frame l i vi using ngre va i planetary e w s . or ephemeris g / lrr - such 2008 -as 8 the JPL DE 405 [ 3 5 2 ] . The transformation Living Reviews in Relativity \noindentht tp : slashbetween slash w w barycentric w period l i vi ngre $ ( v i e T w s period ) $ andor g slash observed lrr hyphen $ 2008 ( hyphen t ) 8 $ takes the form \ begin { a l i g n ∗} T − t = \ f r a c { r {\underline {\}} { . }ˆ{\hat{ s }} {\ r u l e {3em}{0.4 pt }}}{ c } + \ f r a c { ( {\ r u l e {3em}{0.4 pt }} r . {\ r u l e {3em}{0.4 pt }}ˆ{\hat{ s }} ) ˆ{ 2 } − \mid {\ r u l e {3em}{0.4 pt }} r \mid ˆ{ 2 }}{ 2 cd } + \Delta t { r e l } − \Delta t { DM } . \ tag ∗{$ ( 9 ) $} \end{ a l i g n ∗}

\noindent Here $ r {\underline {\}}$ is the position of the observatory with respect to the barycentre $ , \hat{ s } {\underline {\}}$ is a unit vector in the direction of the pulsar at a distance $ d $ and $ c $ is the speed of light . The first term on the right hand side of Equation ( 9 ) is the light travel time from the observatory to the solar system barycentre . Incoming pulses from all but the nearest pulsars can be approximated by plane wavefronts . \quad The second term , which represents the delay due to spherical wavefronts , yields the parallax and hence

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\noindent Living Reviews in Relativity

\noindent http : //www. l i vi ngrev i ews . org/ lrr − 2008 − 8 BinaryBinary and and Millisecond Millisecond Pulsars Pulsars .... 37 37 \noindenthline Binary and Millisecond Pulsars \ h f i l l 37 d period This has so far only been measured for five nearby millisecond pulsars open square bracket 3 2 9 comma .. 3 7 3 comma .. 2 1 3 comma\ [ \ r u .. l e 3{ 43em 2 comma}{0.4 pt .. 2}\ 1 5] closing square bracket period Thed. termThis Capital has so Deltafar only t sub been rel measured represents for the five Einstein nearby and millisecond Shapiro pulsars corrections [ 3 2 due 9 , to 3 general 7 3 , relativistic 2 1 3 , 3 time 4 2 , delays2 1 in 5 ] the . The solar term system ∆trel ..represents open square the bracketEinstein 1 and 7 closing Shapiro square corrections bracket due period to general .. Since relativistic measurements time delays can be carried out at different observing\noindentin the solar$ d system . $ [ This 1 7 ] has. Since so far measurements only been can measured be carried forout at five different nearby observing millisecond frequencies pulsars [ 3 2 9 , \quad 3 7 3 , \quad 2 1 3 , \quad 3 4 2 , \quad 2 1 5 ] . Thefrequencies termwith different with$ \Delta different dispersive dispersivet delays{ r e , delays l TOAs}$ comma are represents generally TOAs referred are the generally Einstein to the referred equivalent and to the Shapiro time equivalent that correctionswould time be observed due to general relativistic time delays in the solar system \quad [ 1 7 ] . \quad Since measurements can be carried out at different observing thatat would infinite be frequency observed at . infinite This transformation frequency period is the .. This term transformation ∆tDM ( see also is the term Capital Delta t sub DM open parenthesis see also frequenciesEquation open with parenthesis different 1 closing dispersive parenthesis closing delays parenthesis , TOAs period are generally referred to the equivalent time thatFollowing would the be accumulation observed of at a number infinite of TOAs frequency comma a .surprisingly\quad This simple transformation model is usually suffi is hyphen the term $ \Delta t { DM } ( $cient see to account a l s o for the TOAs during the time spanEquation(1)) of the observations. and to predict the arrival t imes of subsequent pulses period The model is a Taylor expansion of the rotational frequency Capital Omega = 2 pi slash P Following the accumulation of a number of TOAs , a surprisingly simple model is usually suffi - cient to \ beginabout{ a l model i g n ∗} value Capital Omega sub 0 at some reference epoch T sub 0 period The model pulse phase account for the TOAs during the time span of the observations and to predict the arrival t imes of subsequent EquationEquation: open ( parenthesis 1 ) 1 ) 0 closing . parenthesis .. phi open parenthesis T closing parenthesis = phi 0 plus open parenthesis T minus T pulses . The model is a Taylor expansion of the rotational frequency Ω = 2π/P about a model value Ω at sub\end 0{ closinga l i g n parenthesis∗} Capital Omega sub 0 plus 1 divided by 2 open parenthesis T minus T sub 0 closing parenthesis0 to the power of 2 sub some reference epoch T . The model pulse phase Omega-dotaccent 0 plus period0 period period comma Followingwhere T is the the barycentric accumulation time and of phi a number 0 is the pulse of TOAs phase at , aT sub surprisingly 0 period Based simple on this simplemodel model is usually comma and suffi − cient to account for the TOAs during the time span1 of the observations and to predict the arrival using initial estimates of the position comma dispersion measure and pulse2 ˙ period comma a quotedblleft t iming residual quotedblright is t imes of subsequent pulsesφ( .T The) = φ0 model + (T − is T0)Ω a0 Taylor+ (T − expansion T0) Ω 0 + ..., of the rotational frequency(10) $ \Omega = calculated for each TOA as the difference between the observed2 and predicted pulse phases period 2 A\ setpi of t iming/ P residuals $ for the nearby pulsar B 1 1 33 plus 1 6 spanning almost 1 0 years is shown where T is the barycentric time and φ0 is the pulse phase at T . Based on this simple model , and using initial aboutin Figure a model 2 .. 2 period value .. Ideally $ \Omega comma{ the0 residuals}$ at should some have reference0 a zero mean epoch and be $ free T from{ 0 any} systematic. $ The model pulse phase estimates of the position , dispersion measure and pulse period , a “ t iming residual ” is calculated for each trends open parenthesis see Panel a of Figure 2 2 closing parenthesis period To reach this point comma however comma the model needs to TOA as the difference between the observed and predicted pulse phases . be\ begin refined{ a in l i ag n ∗} A set of t iming residuals for the nearby pulsar B 1133 + 16 spanning almost 1 0 years is shown in Figure 2 \phibootstrap( fashion T period ) = .. Early\phi sets of0 residuals + (will exhibit T − a numberT { of0 trends} ) indicating\Omega a systematic{ 0 } + \ f r a c { 1 }{ 2 } ( 2 . Ideally , the residuals should have a zero mean and be free from any systematic trends ( see Panel a of T error− inT one{ or0 more} of) the ˆ{ model2 {\ parametersdot{\Omega comma}}} or a0 parameter + .not incorporated . . , into\ tag the∗{ model$ ( period 1 0 ) $} Figure 2 2 ) . To reach this point , however , the model needs to be refined in a bootstrap fashion . Early \endFrom{ a l Equation i g n ∗} open parenthesis 1 0 closing parenthesis comma an error in the assumed Capital Omega sub 0 results in a linear slope with sets of residuals will exhibit a number of trends indicating a systematic error in one or more of the model time period A parabolic parameters , or a parameter not incorporated into the model . \noindenttrend resultswhere from an $ error T $ in Omega-dotaccent is the barycentric sub 0 open time parenthesis and $ see\phi Panel b0 of Figure$ is .... the 2 2 pulseclosing parenthesis phase at period $T ....{ Additional0 } . $ From Equation ( 1 0 ) , an error in the assumed Ω results in a linear slope with time . A parabolic effectsBased will on arise this if the simple model , and 0 trend results from an error in Ω˙ ( see Panel b of Figure 2 2 ) . Additional effects will arise if the usingassumed initial position estimates of the pulsar of open the0 parenthesis position the unit, dispersion vector circumflex-s measure underbar and pulse in Equation period open , parenthesis a ‘‘ t iming 9 closing residual parenthesis ’’ is assumed position of the pulsar ( the unit vectors ˆ in Equation ( 9 ) ) used in the barycentric time closingcalculated parenthesis for used each in the TOA barycentric as the time difference between the observed and predicted pulse phases . calculation is incorrect . A position error results in an annual sinusoid ( see Panel c of Figure 2 2 ) . calculation is incorrect period .... A position error results in an annual sinusoid open parenthesis see Panel c of Figure .... 2 2 closing A proper motion produces an annual sinusoid of linearly increasing magnitude ( see Panel d of Aparenthesis set of period t iming residuals for the nearby pulsar B $ 1 1 33 + 1 6 $ spanning almost 1 0 years is shown Figure 2 2 ) . inA Figureproper motion 2 \quad produces2 . an\quad annualIdeally sinusoid of , linearly the residuals increasing magnitude should haveopen parenthesis a zero mean see Panel and d be of free from any systematic After a number of iterations , and with the benefit of a modicum of experience , it is possible to identify trendsFigure 2 ( 2 see closing Panel parenthesis a of period Figure 2 2 ) . To reach this point , however , the model needs to be refined in a and account for each of these various effects to produce a “ t iming solution ” which is phase coherent over the bootstrapAfter a number fashion of iterations . \quad commaEarly and with sets the of benefit residuals of a modicum will of exhibit experience a comma number it is of possible trends to indicating a systematic whole data span . The resulting model parameters provide spin and astrometric information with a precision erroridentify in and one account or more for each of of the these model various parameters effects to produce , or a quotedbllefta parameter t iming not solution incorporated quotedblright into which the is modelphase . which improves as the length of the data span increases . For example , t iming observations of the original coherent over the whole data span period The resulting model parameters provide spin and astrometric millisecond pulsar B 1937 + 21, spanning almost 9 years ( exactly \ hspaceinformation∗{\ f i with l l }From a precision Equation which improves ( 1 0 ) as, the an length error of the in data the span assumed increases $ period\Omega For example{ 0 }$ comma results in a linear slope with time . A parabolic 1 65 , 7 1 1 , 423 , 279 rotations ! ) , measure a period of 1.5578064688197945 ± 0.4 ms [ 1 8 5 , t iming observations of the original millisecond pulsar B 1 937 plus 2 1 comma spanning almost 9 years open parenthesis exactly 1 8 1 ] defined at midnight UT on December 5 , 1 988 ! Measurements of other parameters are no less impressive \noindent1 65 commatrend 7 1 1 comma results 423 commafrom an 279 error rotations in ! closing $ \dot parenthesis{\Omega comma} { 0 measure} ( a $ period see of Panel 1 period b 5578064688 of Figure 1 97945\ h f i plusminux l l 2 2 ) . \ h f i l l Additional effects will arise if the , with astrometric errors of ∼ 3µ arcsec being presently possible for the bright millisec - 0 period 4 ms open square bracket 1 8 5 comma \noindentond pulsarassumed J 437 − position4715[388]. of the pulsar ( the unit vector $ \hat{ s } {\underline {\}}$ in Equation ( 9 ) ) used in the barycentric time 1 84 1 closing . 3 square Timing bracket stability defined at midnight UT on December 5 comma 1 988 ! Measurements of other parameters are no less impressive comma with astrometric errors of thicksim 3 mu arcsec being presently possible for the bright millisec hyphen Ideally , after correctly applying a timing model , we would expect a set of uncorrelated timing residuals \noindentond pulsarcalculation J 437 minus 471 is 5 open incorrect square bracket . \ h f3 i 8 l l 8 closingA position square bracket error period results in an annual sinusoid ( see Panel c of Figure \ h f i l l 2 2 ) . with a zero mean and a Gaussian scatter with a standard deviation consistent with the 4 period 3 .. Timing stability measurement uncertainties . As can be seen in Figure 2 3 , this is not always the case ; the residuals of many \noindentIdeally commaA proper .. after motion correctly producesapplying a timing an annual model comma sinusoid .. we of would linearly expect a set increasing of uncorrelated magnitude timing ( see Panel d of pulsars exhibit a quasi - periodic wandering with time . residuals with a zero mean and a Gaussian scatter with a standard deviation consistent with the Such “ timing noise ” is most prominent in the youngest of the normal pulsars [ 2 5 3 , 8 3 ] and \noindentmeasurementFigure uncertainties 2 2 ) period . As can be seen in Figure 2 3 comma this is not always the case semicolon the residuals present at a lower level in the much older millisecond pulsars [ 1 8 5 , 9 ] . While the physical processes of of many pulsars exhibit a quasi hyphen periodic wandering with time period this phenomenon are not well understood , it seems likely that they may be connected to super - fluid processes AfterSuch a .. number quotedblleft of timing iterations noise quotedblright , and with .. is the most benefit prominent of in athe modicum youngest of of the experience normal pulsars , ..it open is square possible bracket to 2 .. 5 3 and temperature changes in the interior of the neutron star [ 3 ] , or to processes in commaidentify 8 3 closing and square account bracket for and each of these various effects to produce a ‘‘ t iming solution ’’ which is phase the magnetosphere [ 7 5 , 7 4 ] . coherentpresent at overa lower the level whole in the much data older span millisecond . The resulting pulsars open modelsquare bracket parameters 1 8 5 comma provide .. 9 closing spin square and astrometric bracket period While the The relative dearth of timing noise for the older pulsars is a very important finding . It implies that the physicalinformation processes with a precision which improves as the length of the data span increases . For example , measurement precision presently depends primarily on the particular hardware constraints tof iming this phenomenon observations are not of well the understood original comma millisecond it seems likely pulsar that they B may $ 1 be connected 937 + to super 2 hyphen 1 , $ spanning almost 9 years ( exactly fluid processes and temperature changes in the interior of the neutron star open square bracket 3 closing square bracket comma or to processes\noindent in 1 65 , 7 1 1 , 423 , 279 rotations ! ) , measure a period of $ 1 . 5578064688 1 97945 \pm 0 . 4$ms[185, the magnetosphere open square bracket 7 5 comma .. 7 .. 4 closing square bracket periodLiving Reviews in Relativity The relative dearth of timinght noise tp for : the / / older w w pulsars w . is al very i vi important ngrev i finding e w s period. org It / implies lrr - 2008 - 8 \noindentthat the measurement1 8 1 ] defined precision presentlyat midnight depends UT primarily on December on the particular 5 , 1 988 hardware ! Measurements constraints of other parameters are no less impressivehline , with astrometric errors of $ \sim 3 \mu $ arcsec being presently possible for the bright millisec − Living Reviews in Relativity \noindentht tp : slashond slash pulsar w w .. J w period $ 437 l i vi− ngrev471 i e w s period5 [ org 3slash 8lrr hyphen 8 ]2008 hyphen.$ 8 \noindent 4 . 3 \quad Timing stability

\noindent I d e a l l y , \quad after correctly applying a timing model , \quad we would expect a set of uncorrelated timing residuals with a zero mean and a Gaussian scatter with a standard deviation consistent with the

\noindent measurement uncertainties . As can be seen in Figure 2 3 , this is not always the case ; the residuals of many pulsars exhibit a quasi − periodic wandering with time .

\ hspace ∗{\ f i l l }Such \quad ‘‘ timing noise ’’ \quad is most prominent in the youngest of the normal pulsars \quad [ 2 \quad 5 3 , 8 3 ] and

\noindent present at a lower level in the much older millisecond pulsars [ 1 8 5 , \quad 9 ] . While the physical processes of this phenomenon are not well understood , it seems likely that they may be connected to super − fluid processes and temperature changes in the interior of the neutron star [ 3 ] , or to processes in

\noindent the magnetosphere [ 7 5 , \quad 7 \quad 4 ] .

The relative dearth of timing noise for the older pulsars is a very important finding . It implies that the measurement precision presently depends primarily on the particular hardware constraints

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\ hspace ∗{\ f i l l } ht tp : / / w w \quad w. l i vi ngrev i ews . org / lrr − 2008 − 8 38 ....38 Duncan R period Lorimer Duncan R . Lorimer \noindenthline 38 \ h f i l l Duncan R . Lorimer Figure 22 : Timing model residuals for PSR B 1 1 33 plus 1 6 period Panel a : Residuals obtained from the best hyphen fitting \ [ model\ r u l e which{3em}{ includes0.4 pt period}\ ] comma period derivative comma position and proper motion period Panel b : Residuals obtained whenFigure the period 22 : derivativeTiming model term residuals is set to for zero PSR period B 1133 Panel + c 16 :. ResidualsPanel a : showing Residuals the obtained effect offrom a 1 the hyphen best - arcmin fitting position errormodel period which .. Panel includes d : period .. Residuals , period obtained derivative neglecting , position and the proper proper motion motion . Panelperiod b .. : Residuals The lines obtained in Panels when b endash the d show the \noindentexpectedperiod behaviour derivativeFigure term22in the : is timingTiming set to zero residuals model . Panel for cresiduals : each Residuals effect showing period for PSRB Data the effect provided $ of 1 a 1 by - 1 arcmin Andrew 33 position Lyne + perioderror 1 . 6 Panel . $ Panel a : Residuals obtained from the best − f i t t i n g modelhlined : which Residuals includes obtained period neglecting , the period proper derivativemotion . The , lines position in Panels and b – d proper show the motion expected .behaviour Panel b : Residuals obtained whenLivingin the the Reviews timing period in residuals Relativity derivative for each effect term . Data is provided set to by zero Andrew . LynePanel . c : Residuals showing the effect of a 1 − arcmin position e rht r o tp r : . slash\quad slashPanel w w w d period : \quad l i vi ngreResiduals v i e w s period obtained or g slash neglecting lrr hyphen the 2008 proper hyphen 8 motion . \quad The lines in Panels b −− d show the expected behaviour in the timing residuals for each effect . Data provided by Andrew Lyne .

\ [ \ r uLiving l e {3em Reviews}{0.4 in pt Relativity}\ ] ht tp : / / w w w . l i vi ngre v i e w s . or g / lrr - 2008 - 8

\noindent Living Reviews in Relativity

\noindent http : //www. l i vi ngrev i ews . org/ lrr − 2008 − 8 BinaryBinary and and Millisecond Millisecond Pulsars Pulsars .... 39 39 \noindenthline Binary and Millisecond Pulsars \ h f i l l 39 Figure 23 : .. Examples of timing residuals for a number of normal pulsars period .. Note the varying scale on \ [ the\ r u ordinate l e {3em axis}{0.4 comma pt }\ the] pulsars being ranked in increasing order of timing quotedblleft activity quotedblright period Data taken from the Figure 23 : Examples of timing residuals for a number of normal pulsars . Note the varying scale on the Jodrellordinate Bank axis timing , the programpulsars being open ranked square in bracketincreasing 3 order 3 5 comma of timing .. “ 1 activity 4 6 closing ” . Data square taken bracket from the period Jodrell Figure Bank provided by Andrew Lyne period\noindenttiming programFigure [ 233 3 5 : ,\quad 1 4 6 ]Examples . Figure provided of timing by Andrew residuals Lyne . for a number of normal pulsars . \quad Note the varying scale on thehline ordinate axis , the pulsars being ranked in increasing order of timing ‘‘ activity ’’ . Data taken from the JodrellLiving Reviews Bank intiming Relativity program [ 3 3 5 , \quad 1 4 6 ] . Figure provided by Andrew Lyne . ht tp : slash slash w w .. w period l i vi ngrev i e w s period org slash lrr hyphen 2008 hyphen 8 \ [ \ r u l e {3em}{0.4 pt }\ ] Living Reviews in Relativity ht tp : / / w w w . l i vi ngrev i e w s . org / lrr - 2008 - 8

\ hspace ∗{\ f i l l } Living Reviews in Relativity

\ hspace ∗{\ f i l l } ht tp : / / w w \quad w. l i vi ngrev i ews . org / lrr − 2008 − 8 40 ....40 Duncan R period Lorimer Duncan R . Lorimer \noindenthline 40 \ h f i l l Duncan R . Lorimer of the observing system period Consequently comma a large effort in hardware development is now being made \ [ to\ r improve u l e {3em the}{ precision0.4 pt }\ of] these observations using comma in particular comma coherent dedispersion outlined in Sectionof the 4 period observing 1 period system Much . Consequently progress in this, a large area effort has been in hardware made by development groups at Princeton is now being open madesquare to bracket improve 3 0 6 closing square bracket commathe Berkeley precision open of squarethese observations bracket 3 7 using 7 closing , in particularsquare bracket , coherent comma dedispersion outlined in Section 4 . 1 . Much \noindentJodrellprogress Bankof in open the this areasquare observing has bracket been system made 3 7 9by closing groups. Consequently square at Princeton bracket [, 3 comma a 0 6 large ] , UBCBerkeley effort open [ 3 square 7 in 7 ] hardware , bracket 3 7development 6 closing square is bracket now being comma made Swinburneto improveJodrell open Bank thesquare [ 3 precision 7bracket 9 ] , UBC 3 5 of [9 3 closing 7 these 6 ] , square Swinburne observations bracket [ 3 5 and 9 ] andATNF using ATNF open , in[ square1 3 particular ] . From bracket high 1 3 ,quality closing coherent observations square dedispersion bracket period .... outlined From high in qualitySectionspanning observations 4 . over 1 . a Much decade progress [ 3 2 7 , 3 2 in 8 , this 1 8 5 area ] , these has groups been have made demonstrated by groups that at the Princeton timing st ability [ 3 0 6 ] , Berkeley [ 3 7 7 ] , spanningof millisecond over a decade pulsars open over square such brackettimescales 3 2 is 7 commacomparable 3 2 8 to comma terrestrial .. 1 8 atomic 5 closing clo square cks . bracket comma these groups have demonstrated that\noindent theFigure timingJodrell 24 st :abilityThe Bank fractional [ 3 stability 7 9 ] of ,UBC three millisecond [ 3 7 6 pulsars ] , Swinburne compared to [ an 3 atomic 5 9 clock] andATNF . Both PSRs [ 1 B 3 ] . \ h f i l l From high quality observations of millisecond1855 + 9 and pulsars B 1937 over + 21suchare timescales comparable is , comparable or j ust slightly to terrestrial worse than atomic , the atomic clo cks clock period behaviour over timescales \noindentFigureof a 24 few :spanning The years fractional [ 2 5 over4 ] . stability a More decade of recent three [ millisecondtiming 3 2 7 of , the 3 pulsars millisecond 2 8 compared , \quad pulsar to1 J an 8437 atomic5− ]4715[388] , clock these periodindicates groups Both that PSRshave it is demonstrated that the timing st ability ofB 1millisecondinherently 855 plus 9 aand very pulsars B stable 1 937 clock plus over . 2Data 1 such are for comparable the timescales latter pulsar comma provided is or comparable j ust byslightly Joris Verbiest worse to terrestrial . than comma the atomic atomic clock clo cksbehaviour . over timescalesThis of phenomenal a few years open stability square is demonstrated bracket 2 5 4 closing in Figure square 2 bracket4 which period shows ..σz More[254, 380] recent, a timing parameter of the closely millisecond pulsar J 437 minus 4715\noindent openresembling squareFigure bracket the Allan 24 3 :8 variance 8 The closing fractional used square by bracket the clostability indicates ck community of three to estimate millisecond the stability pulsars of atomic compared clo cks [ 3 to an atomic clock . Both PSRs Bthat $6 1it 2 is ,1 inherently 855 ] . Both + a very PSRs 9 $ stable B andB 1937 clock + 21 period $ and 1 Data B 937 1855 for + the + 9 seem latter 2 to pulsar be1 $ limited provided are by comparable aby power Joris Verbiestlaw component , or period j ust which slightly worse than , the atomic clock behaviour over timescales of a few years [ 2 5 4 ] . \quad More recent timing of the millisecond pulsar J $ 437 − Thisproduces phenomenal a minimum stability in isσ demonstratedz after 2 yr and in 5Figure yr respectively 2 .. 4 which . This shows is mostsigma likely sub z a open result square of a small bracket amount 2 5 4 ofcomma 3 8 0 closing square 4715 [ 3 8 8 ]$ indicates bracketintrinsic comma atiming parameter noise [ 1 8 5 ] . The σz based on timing observations [ 3 8 8 ] of the bright millisecond pulsar thatcloselyJ it 437 resembling is− 4715 inherently is the now Allan 1 –2 a variance orders very of used stable magnitude by the clock clo smaller ck . community Datathan the for other to the estimate two latter pulsars the stability orpulsar the atomic of provided clo ck ! by Joris Verbiest . atomic4 . clo 4 cks openTiming square binary bracket pulsars3 6 2 comma 1 closing square bracket period .. Both PSRs B 1 937 plus 2 1 and B 1 855 plus 9 seem to beThis limited phenomenalFor by binary a power pulsars stability law , the t iming is model demonstrated introduced in Section Figure 4 2 .\ 2quad needs4 to which be extended shows to incorporate $ \sigma the{ z } [ 2 5 4component ,additional 3 which 8 motion produces 0 of ] the a pulsar minimum ,$ as aparameter it in orbits sigma the sub common z after 2 centre yr and - of 5 yr - mass respectively of the binary period system This is . most Describing likely a closelyresultthe of binary a resembling small orbit amount using the of Kepler intrinsic Allan ’ timings variance laws noiseto refer open used the square TOAs by the bracket to the clo 1 binary 8ck 5 closing community barycentre square requires to bracket estimate periodfive additional The the sigma stability sub z based of on timing atomic clo cks [ 3 6 2 , 1 ] . \quad BothPSRsB $1 937 + 2 1$ andB $1 855 + 9$ observationsmodel open parameters square bracket : the 3 orbital 8 8 closing period squarePb, bracketprojected semi - major orbital axis x, orbital eccentricity e, seem to be limited by a power law of thelongitude bright millisecond of periastron pulsarω and J 437the epochminus of4715 periastron is now 1 passage endashT 20 orders. This of descriptionmagnitude smaller , using fivethan “ the Keplerian componentotherparameters two pulsars which ” , or is produces theidentical atomic to cloa that minimum ck used ! for in spectroscopic $ \sigma binary{ starsz }$ . Analogous after 2 to yr the and radial 5 velocity yr respectively curve . This is most likely a result4 periodin a of spectroscopic 4 .. a Timing small binary binary amount pulsars , for of binary intrinsic pulsars the timing orbit is noise described [ 1 by 8 the 5 apparent ] . The pulse $ period\sigma against{ z time}$ based on timing observations [ 3 8 8 ] ofFor the. binary An bright examplepulsars millisecond comma of thisthe is shown t iming pulsar in Panelmodel J a introduced of $ Figure 437 in− 2 Section 5 .4715 Alternatively .. 4 $ period is now2 , needs when 1 −− to radial be2 extended orders accelerations to of incorporate magnitude can smaller than the otherthebe additional two measured pulsars motion , the of or orbit the the pulsar can atomic also as it be orbits clo theck common ! centre hyphen of hyphen mass of the binary system period Describing the binary orbit using Kepler quoteright s laws to refer the TOAs to the binary barycentre requires \noindentfive additional4 . model 4 \quad parametersTiming : .. binary the orbital pulsars period P sub b comma .. projected semi hyphen major orbital axis x comma orbital eccentricity e comma .. longitude of periastron omega and the epoch of periastron passage T sub 0 period .. This \noindentLivingFor Reviews binary in Relativity pulsars , the t iming model introduced in Section \quad 4 . 2 needs to be extended to incorporate descriptionht tp : comma / / w using w w five . quotedblleft l i vi ngre Keplerian v i e w parameters s . or g quotedblright / lrr - 2008 comma - 8 is identical to that used for spectroscopic binary thestars additional period Analogous motion to the of radial the velocity pulsar curve as in it a orbitsspectroscopic the binary common comma centre for binary− o f pulsars− mass the of orbit the binary system . Describingis described by the the binary apparent orbit pulse period using against Kepler time ’ period s laws .. An to example refer of the this TOAsis shown to in the Panel binary a barycentre requires fiveof Figure additional .. 2 5 period model .. Alternatively parameters comma : \ ..quad whenthe radial orbital accelerations period can be $ measured P { b comma} , .. $ the\quad orbit canprojected also be semi − major orbital axis $ xhline , $ orbitalLiving Reviews eccentricity in Relativity $ e , $ \quad longitude of periastron $ \omega $ and the epoch of periastron passage $ Tht tp{ :0 slash} slash. $ w\ wquad w periodThis l i vi ngre v i e w s period or g slash lrr hyphen 2008 hyphen 8 description , using five ‘‘ Keplerian parameters ’’ , is identical to that used for spectroscopic binary stars . Analogous to the radial velocity curve in a spectroscopic binary , for binary pulsars the orbit is described by the apparent pulse period against time . \quad An example of this is shown in Panel a o f Figure \quad 2 5 . \quad Alternatively , \quad when radial accelerations can be measured , \quad the orbit can also be

\ [ \ r u l e {3em}{0.4 pt }\ ]

\noindent Living Reviews in Relativity

\noindent http : //www. l i vi ngrev i ews . org/ lrr − 2008 − 8 BinaryBinary and and Millisecond Millisecond Pulsars Pulsars .... 4 1 4 1 \noindenthline Binary and Millisecond Pulsars \ h f i l l 4 1 visualised in a plot of acceleration versus period as shown in Panel b of Figure 2 .. 5 period This method is \ [ particularly\ r u l e {3em useful}{0.4 for pt determining}\ ] binary pulsar orbits from sparsely sampled data open square bracket 1 1 5 closing square bracket period Figurevisualised 25 : Panel in a a plot : Keplerian of acceleration orbital fit versus to the period 669 hyphen as shown day in binary Panel pulsar b of Figure J 407 plus 2 1 5 607 . This open method square bracket is 2 3 3 closing square bracketparticularly period Panel useful b : Orbital for determining binary pulsar orbits from sparsely sampled data [ 1 1 5 ] . \noindentfit inFigure the periodvisualised 25 : hyphenPanel a acceleration : in Keplerian a plot orbital plane of fit for acceleration to the the globular 669 - day cluster binaryversus pulsar pulsar period 47 J 407 Tuc as+ S 1607[233] open shown square. inPanel bracket Panel b : Orbital 1 b 1 5of closing fit Figure square 2 \ bracketquad period5 . This method is particularlyConstraintsin the period on the useful - acceleration masses for of planethe determining pulsar for the m globular sub p binary and cluster the pulsar pulsar orbiting 47 Tuccompanion orbits S [ 1 1 from 5 m ] . sub sparsely c can be placed sampled by data [ 1 1 5 ] . combiningConstraints x and P on sub the b to masses obtain of the the mass pulsar functionmp and the orbiting companion mc can be placed by combining x \noindent Figure 25 : Panel a : Keplerian orbital fit to the 669 − day binary pulsar J $ 407 + 1 Equation:and Pb opento obtain parenthesis the mass 1 1 function closing parenthesis .. f sub mass = 4 pi to the power of 2 divided by G x to the power of 3 divided by P sub607 b to [ the power 2 3 of 2 = 3 open ] parenthesis .$ Panelb:Orbital m sub c sine i closing parenthesis to the power of 3 divided by open parenthesis m sub p plus m fit in the period − acceleration plane for the globular cluster pulsar 47 Tuc S [ 1 1 5 ] . sub c closing parenthesis to the power of 2 sub comma4π2 x3 (m sin i)3 where G is Newton quoteright s gravitationalf constant= and= i is thec open parenthesis initially unknown closing(11) parenthesis angle between the mass G P 2 (m + m )2 Constraintsorbital plane onand the the plane masses of the of sky the open pulsar parenthesis $ im periodb { p ep period}$c and an, orbit the viewed orbiting edge hyphen companion on corresponds $ m { toc i =}$ 90 to can the be power placed by ofcombining circ closing parenthesis $ x $ andperiod $P .. In { b }$ to obtain the mass function where G is Newton ’ s gravitational constant and i is the ( initially unknown ) angle between the orbital plane the absence of further information comma the standard practice is to consider a random distribution of and the plane of the sky ( i . e . an orbit viewed edge - on corresponds to i = 90◦). In the absence of \ begininclination{ a l i g anglesn ∗} period .. Since the probability that i is less than some value i sub 0 is p open parenthesis less i sub 0 closing parenthesis further information , the standard practice is to consider a random distribution of inclination angles . Since =f 1 minus{ mass cos open} = parenthesis\ f r a c { i4 sub 0\ closingpi ˆ{ parenthesis2 }}{ G }\ commaf r a c { x ˆ{ 3 }}{ P ˆ{ 2 } { b }} = \ f r a c { ( m { c } the probability that i is less than some value i is p(< i ) = 1− cos (i ), the 90% confidence interval for i is \ sinthe 90i percent ) ˆ confidence{ 3 }}{ interval( m for{ ip is 26} to+ the m0 power{ c of0} circ) less ˆ{ i less2 0}} 90Row{ , 1}\ circtag Row∗{$ 2 period ( 1 90 an 1 assumed ) $} pulsar mass comma ◦ the\end 90{ percent26a l◦ i g< n i∗}< confidence90 F or an assumed pulsar mass , the 90% confidence interval for m can be obtained by solving . c interval for m sub c can be obtained by solving Equation open parenthesis 1 1 closing parenthesis for i = 26 to the power of circ and Case \noindent where $ G $ is Newton◦ ’ s gravitational constant and $ i $ is the ( initially unknown ) angle between the 1 circ CaseEquation 2 period ( 1 1 ) for i = 26◦ and 90 orbitalAlthough plane most of and the presently the plane known of binary the. sky pulsar ( systems i . e can . an be adequately orbit viewed timed usingedge − on corresponds to $ i = 90 ˆ{\ circ } )Kepler . $ Although quoteright\quad mostIn s laws of thecomma presently there knownare a number binary pulsarwhich requiresystems an can additional be adequately set of timed quotedblleft using Kepler post hyphen ’ s laws Keplerian quotedblright .. openthe parenthesis absence, there are PK a of number closing further which parenthesis information require pa an hyphen additional , the set standard of “ post - Keplerian practice ” is ( PK to ) consider pa - rameters a which random have distribution of inclinationrametersa distinct which functional angles have a distinct . form\quad for functional aSince given form relativistic the for probability a given theory relativistic of gravity that theory [ 9 $ 2 of] i . gravity $ In is general open less square relativity than bracket some ( GR 9 value )2 theclosing square$ i { bracket0 }$ period i s ..$ In pPK ( formalism< i gives{ 0 the} relativistic) = advance 1 − of$ periastron cos $ ( i { 0 } ) , $ thegeneral $ 90relativity\% open$ confidence parenthesis GR interval closing parenthesis for $ thei $ PK formalismi s $ 26 gives ˆ{\ thec i relativisticr c } < advancei < of periastron\ l e f t .90\ begin { array }{ c}\ c i r c \\ . \end{ array }For\ r i g h t . $ an assumed pulsar mass , the $ 90 \% $ confidence Equation: open parenthesis 1 2 closing parenthesisP .. omega-dotaccent = 3 parenleftbigg P sub b divided by 2 pi parenrightbigg minus interval for $m { c }$ canω˙ be= 3( obtainedb ) − 5/3( byT M solving)2/3(1 − e Equation2)−1, ( 1 1 ) for $ i(12) = 26 ˆ{\ circ }$ and 5 slash 3 open parenthesis T sub odot M closing2 parenthesisπ to the power of 2 slash 3 open parenthesis 1 minus e to the power of 2 closing parenthesis$\ l e f t .90 to\ begin the power{ a l i of g n minus e d } & 1 comma\ circ \\ &.thethe time time\end dilation dilation{ a l i and g n eand gravitational d }\ gravitationalright . $ redshift redshift parameter parameter Equation: open parenthesis 1 3 closing parenthesis .. gamma = e parenleftbigg P sub b divided by 2 pi parenrightbigg 1 slash 3 T sub odot toAlthough the power most of 2 slash of 3the M to presently the power of known minus 4binary slash 3 m pulsar sub c open systems parenthesis can mbe sub adequately p plus 2 m sub timed c closing using parenthesis comma Kepler ’ s laws , there are a numberPb which2/3 require−4/3 an additional set of ‘‘ post − Keplerian ’’ \quad ( PK ) pa − the rate of orbital decay due to gravitationalγ = e( radiation)1/3T M mc(mp + 2mc), (13) 2π rametersEquation: which open parenthesis have a 1 distinct 4 closing parenthesis functional .. P-dotaccent form for sub a b given = minus relativistic 1 92 pi divided by theory 5 parenleftbigg of gravity P sub [b divided 9 2 ] by . 2\quad pi In parenrightbigggeneralthe rate relativity minus of orbital 5 slash decay ( 3 GR parenleftbigg due ) to the gravitational PK 1 plus formalism 73 radiation divided gives by 24 e the to the relativistic power of 2 plus 37 advance divided by of 96 periastron e to the power of 4 parenrightbigg parenleftbig 1 minus e to the power of 2 parenrightbig to the power of minus 7 slash 2 T sub odot to the power of 5 slash 3 m sub p m sub c M\ begin to the{ powera l i g n of∗} minus 1 slash 3 \dot{\omega} =˙ 3 (192π\ f rP ab c { P { b73}}{2 237 4\ pi }2 −)7/2 5−/3 5− /1/3 3 ( T {\odot } M ) ˆ{ 2 and the two Shapiro delayPb = parameters− ( ) − 5/3(1 + e + e )(1 − e ) T mpmcM (14) /Line 3 } 1 r =( T sub 1 odot− me sub ˆ{ c open52 }2 parenthesisπ ) ˆ{ − 1 5241 closing} ,96 parenthesis\ tag ∗{$ (Line 21 hline 2 ) $} \end{ a l i g n ∗} Livingand Reviews the two in Shapiro Relativity delay parameters ht tp : slash slash w w .. w period l i vi ngrev i e w s period org slash lrr hyphen 2008 hyphen 8 \noindent the time dilation and gravitational redshift parameter r = T mc (15) \ begin { a l i g n ∗} \gamma = e ( \ f r a c { P { b }}{ 2 \ pi } ) 1 / 3Living T ˆ Reviews{ 2 /in Relativity 3 } {\odot } M ˆ{ − 4 / 3 } m { c } ( mht{ tpp :} /+ / w 2w m w .{ lc i} vi), ngrev i\ tag e w∗{ s$ . ( org 1 / lrr 3 - 2008) $} - 8 \end{ a l i g n ∗}

\noindent the rate of orbital decay due to gravitational radiation

\ begin { a l i g n ∗} \dot{P} { b } = − \ f r a c { 1 92 \ pi }{ 5 } ( \ f r a c { P { b }}{ 2 \ pi } ) − 5 / 3 ( 1 + \ f r a c { 73 }{ 24 } e ˆ{ 2 } + \ f r a c { 37 }{ 96 } e ˆ{ 4 } ) ( 1 − e ˆ{ 2 } ) ˆ{ − 7 / 2 } T ˆ{ 5 / 3 } {\odot } m { p } m { c } M ˆ{ − 1 / 3 }\ tag ∗{$ ( 1 4 ) $} \end{ a l i g n ∗}

\noindent and the two Shapiro delay parameters

\ [ \ begin { a l i g n e d } r = T {\odot } m { c } ( 1 5 ) \\ \ r u l e {3em}{0.4 pt }\end{ a l i g n e d }\ ]

\ hspace ∗{\ f i l l } Living Reviews in Relativity

\ hspace ∗{\ f i l l } ht tp : / / w w \quad w. l i vi ngrev i ews . org / lrr − 2008 − 8 42 ....42 Duncan R period Lorimer Duncan R . Lorimer \noindenthline 42 \ h f i l l Duncan R . Lorimer and \ [ Equation:\ r u l e {3em open}{0.4 parenthesis pt }\ ] 1 6 closing parenthesis .. s = x parenleftbigg P sub b divided by 2 pi parenrightbigg minus 2 slash 3 T sub odot to the powerand of minus 1 slash 3 M to the power of 2 slash 3 m sub c to the power of minus 1 which describe the delay in the pulses around superior conjunction where the pulsar radiation \noindenttraverses theand gravitational well of its companion period In the above expressions comma all masses are in solar Pb −1/3 2/3 −1 units comma M equiv m sub p plus m subs c= commax( ) − x equiv2/3T a subM p sinm i slash c comma s equiv sin i and T(16) sub odot equiv GM sub odot 2π c slash\ begin c to{ a the l i g power n ∗} of 3 = 4 period 925490947 mu s period .. Some scombinations =which x describe comma ( \ thef r or a delay c all{ commaP in{ theb of pulses}}{ the PK around2 parameters\ pi superior} have) conjunction now− been2 where measured / the 3 pulsar for T a ˆ number{ radiation − of1 binarytraverses / pulsar 3 the} {\odot } M ˆ{ 2 /systems 3 gravitational} periodm ˆ{ − Further well1 of PK}its{ companion parametersc }\ tag .∗{ due In$ the to( aboveaberration 1 expressions 6 and ) relativistic $} , all masses deformation are in solar open square bracket 9 0 closing square bracket are \end{ a l i g n ∗} 3 not listedunits ,M ≡ mp + mc, x ≡ ap sin i/c, s ≡ sin i and T ≡ GM /c = 4.925490947µ s . hereSome but may combinations soon be important , or all , forof the the PK double parameters pulsar open have square now been bracket measured 2 0 1 closing for a number square bracket of binary period pulsar \noindent4 periodsystems 5which .. . Testing Further describe general PK parameters relativity the delay due to in aberration the pulses and relativistic around deformation superior [ conjunction9 0 ] are not listed where the pulsar radiation traversesThehere key butpoint the may in thegravitational soon PK be definitions important introducedwell for the of double its in the pulsar companion previous [ 2 0 section1 ] . . In is thethat comma above given expressions the precisely , all masses are in solar measured4 . 5 Keplerian Testing parameters general comma relativity .. the only two unknowns are the masses of the pulsar and its \noindentcompanionThe keyu comma n point i t s in m $ the sub , PK p M and definitions m\ subequiv c introduced periodm ..{ Hence inp the} comma previous+ from m section{ a measurementc } is that, ,given x of j ust\ theequiv two precisely PK parametersa measured{ p }$ open s iparenthesis n $ i e period/ c , s \equiv $ sin $i$ and $T {\odot }\equiv GM {\odot } / c ˆ{ 3 } = 4 . 925490947 g periodKeplerian comma omega-dotaccent parameters , the and only gamma two unknowns closing parenthesis are the masses of the pulsar and its companion , mp and mc. \muone$Hence can s solve . ,\ fromquad for a the measurementSome two masses of and j ust comma two PK using parameters Equation ( opene . g ., parenthesisω˙ and γ) 1 1 closing parenthesis comma find the orbital inclination anglecombinations ione period can .... solve If , for or the all two , masses of the and PK , using parameters Equation ( have 1 1 ) , now find the been orbital measured inclination for angle a numberi. ofIf binary pulsar systemsthreethree open . ( orparenthesis Further more ) PK PK or parameters more parameters closing are parenthesis measured due to PK , aberration the parameters system is “and are overdetermined measured relativistic comma ” and the deformation can system be used is quotedblleft to [ 9 0 ] overdetermined are not listed quoted- blrighttest and GR can (be or used , more to generally , any other theory of gravity ) by comparing the third PK parameter with the \noindenttestpredicted GR openhere value parenthesis but based may on or soon the comma masses be more important determined generally from for comma the the otherany double other two . theory pulsar of gravity [ 2 0 closing 1 ] . parenthesis by comparing the third PK parameter The first binary pulsar used to test GR in this way was PSR B 1913 + 16 discovered by Hulse & Taylor in \noindent 4 . 5 \quad Testing general relativity with1 the 974 predicted [ 1 5 0 ] . value Measurements based on the of masses three PK determined parameters from (ω ˙ the,γ and otherP˙b two) were period obtained from Thelong first - binary term timing pulsar observationsused to test GR at Arecibo in this way [ 3 6 was 6 , PSR 3 6 7 B , 1 3 9 9 1 3 1 plus ] . 1 The 6 discovered measurement by Hulse of orbital decay , \noindentampersandwhichThe corresponds Taylor key in 1 point 974 to a open shrinkage in square the of PK bracket about definitions 1 3 5 . 0 2 closing mm per square introduced orbit bracket , is seen period in most the .. dramatically Measurements previous as section of the three gradually PK is parameters that , given open parenthesis the precisely omega-dotaccentmeasuredincreasing Keplerian sub shift comma in orbital parameters gamma phase and for dotaccent-P periastron , \quad passagesthe sub b only closing with two respect parenthesis unknowns to a non were are - obtaineddecaying themassesfrom orbit shown of in the Figure pulsar and its companionlong2 hyphen 6 . This term $ , figure timing m includes{ observationsp } recent$ and atArecibo Arecibo $ m data open{ takenc square} since. bracket $ the\quad upgrade 3 6 6Hence comma of the telescope, 3 6from 7 comma a in measurement the 3 9 mid .. 1 1 closing 990 s .of square j ust bracket two period PK parameters The ( e . g measurement$ . , The\ ofdot measurement orbital{\omega decay} of comma$ orbital and which decay $ \gamma in the B 1913) $ + 16 system , obtained from observations span - ning correspondsa 30 - yr to baseline a shrinkage [ 3 9 of 1 about ] , is 3 within period 0. 22% mm of per the orbit GR predictioncomma is seen and most provided dramatically the first as indirect the gradually evidence \noindentincreasingfor theone shift existence incan orbital of solve gravitational phase for for the periastron waves two . massesHulse passages andand with Taylor respect , using were to awarded a Equation non hyphen the 1 ( 993 decaying 1 Nobel 1 ) orbit , Physics find shown prize the [ orbital 3 inclination angle $ iin Figure6 . 8 $, 2 1\..h4 6 f 9period i l , l I 3 f This 6 3 ]figure in recognition includes recent of their Arecibo discovery data of taken this since remarkable the upgrade laboratory of the for telescope testing in GR . A thesimilar mid 1 990 , though s period less precise , test of GR from this combination of PK parameters has recently been performed \noindentThein measurement thethree double neutron of( orbital or more star decay binary ) PKin the PSR parameters B 1 B 9 2127 1 3 plus +are 11 1 C 6 measuredsystem in the globular comma , the obtained cluster system M from 1 5 isobservations [ 1 ‘‘ 5 8 overdetermined ] . span For hyphen this ’’ and can be used to ningsystem a 30 hyphen , the measurement yr baseline open uncertainties square bracket permit 3 a 9 test 1 closing of GR square to 3% precision bracket comma which is is unlikely within 0 to period improve 2 percent due to of the GR prediction and provided\noindentvarious the firsttest kinematic indirect GR (contaminations or , more including generally the acceleration , any other of the theory binary system of gravity in the cluster ) by ’ s comparing gravitational the third PK parameter withevidencepotential the for predicted the . existence value of gravitational based on waves the period masses Hulse determined and Taylor were from awarded the other the 1 993 two Nobel . PhysicsFive prize PK open parameters square bracket have been 3 6 measured 8 comma for .. the 1 4 double 9 comma pulsar .. 3 discussed 6 3 closing in detail square below bracket and infor recognition the double of their discovery of this The first binary pulsar used to test GRin this way wasPSRB $ 1 9 1 3 + 1 6 $ discovered by Hulse remarkableneutron laboratory star system for PSR B 1534 + 12[351] where the test of GR comes from mea - surements ofω ˙ ,γ and s. In $testing\&$this GR system Taylor period , the A in agreement similar 1 974 comma between [ 150 though theory ] less . and precise\quad observation commaMeasurements test is within of GR 0. of from7%[351] three this. This combination PK test parameters will of improve PK parameters in $ the ( \ hasdot{\omega} { , } \gammarecentlyfuture$ been andas the performed t$ iming\dot in baseline{P the} double{ extendsb } neutron) and $ a star more were binary significant obtained PSR B measurement 2 from 1 27 plus 1 of 1r Ccan in the be made globular . cluster M 1 5 openCurrently square the bracket best binary 1 5 8 pulsar closing system square for bracket testing period GR in .. the For strong this system - field comma regime theis the measurement double pulsar uncertainties J permit a test of GR\noindent to 3737 percent− 3039long precision. −Interm this system timing , where observations two independent at pulsar Arecibo clo cks [ 3can 6 be 6 timed , 3 6, five 7 PK , 3 parameters 9 \quad of1 the ] . The measurement of orbital decay , which correspondswhich22 is . 7unlikely - ms to pulsar to a improve shrinkage “ A ” due have to been of various about measured kinematic 3 . as 2 well contaminations mm as per two orbit additional including , isconstraints the seen acceleration most from the dramatically of measured mass as the gradually increasingthefunction binary system and shift projected inthe in cluster orbital semiquoteright - major phase axis s for gravitational of the periastron 2 . 7 -potential s pulsar passages period “ B ” . A with useful respect means of to summarising a non − thedecaying orbit shown inFive Figurelimits PK parameters so 2 far\quad is Figure have6 .2 been 7 Thismeasured which figure shows for theincludes the allowed double pulsar regions recent discussed of Arecibo parameter in detail data space below in taken terms and since of the masses the upgrade of the of the telescope in thefor themidtwo double pulsars 1 990 neutron . s The . star shaded system regions PSR are B 1 excluded 534 plus by 1 2 the open requirement square bracket that sin 3 5i 1 closing < 1. squareFurther bracket constraints where the test of GR comes from mea hyphenare shown as pairs of lines enclosing permitted regions as Thesurements measurementpredicted of omega-dotaccentby GR of . The orbital measurement sub decay comma [ in 2 gamma 0 the1 ] of B andω ˙ = $ s 16 period1.899 ± 9 In0.01 this 1 deg system 3yr−1 +gives comma 1the the total 6 agreement $ system system between , obtained theory and from observation observations is span − withinning a 30 − yr baseline [ 391 ] , is within $0 . 2 \% $ of the GR prediction and provided the first indirect evidence0 period 7 for percent the open existence square bracket of gravitational 3 5mass 1 closingM = square 2.5871 waves± bracket0.2 .M Hulse period. and This Taylortest willimprove were awarded in the future the as 1 the 993 t Nobeliming baseline extendsPhysics and prizea more significant [ 3 6 8 , \quad 1 4 9 , \quad 3 6 3 ] in recognition of their discovery of this remarkable laboratory for testing GR . A similar , though less precise , test of GR from this combination of PK parameters has measurementLiving Reviews of r can in Relativitybe made period recentlyCurrently thebeen best performed binary pulsar in system the doublefor testing neutron GR in the star strong binary hyphen PSRB field regime $ 2is the 1 double 27 + 1 1 $ C in the globular cluster ht tp : / / w w w . l i vi ngre v i e w s . or g / lrr - 2008 - 8 Mpulsar 1 5 [ J 7371 5 minus 8 ] 3039 . \quad periodFor .. In this this system system comma , the where measurement two independent uncertainties pulsar clo cks can permit be timed a comma test of five GR PK to $ 3 \% $ p r eparameters c i s i o n of the 22 period 7 hyphen ms pulsar quotedblleft A quotedblright have been measured as well as two additional constraints from whichthe measured is unlikely mass function to improve and projected due tosemi various hyphen major kinematic axis of the contaminations 2 period 7 hyphen including s pulsar quotedblleft the acceleration B quotedblright of period Athe useful binary means system in the cluster ’ s gravitational potential . of summarising the limits so far is Figure 2 7 .. which shows the allowed regions of parameter space Fivein terms PK parameters of the masses have of the twobeen pulsars measured period ..for The the shaded double regions pulsar are excluded discussed by the requirement in detail below and forthat the sin i double less 1 period neutron .. Further star constraints systemPSRB are shown $ as 1 pairs 534 of lines + enclosing 1 permitted 2 [ regions 3 5 as 1 ] $ where the test ofGRcomes frommea − surementspredicted by of GR period$ \dot The{\omega measurement} { , open}\ squaregamma bracket$ and 2 0 1 closing $ s square . $ bracket In this of omega-dotaccent system , the = agreement 1 6 period 899 between plusminux theory and observation is within 0 period$ 0 0 1 . deg 7 yr to\ the% power [ of 3 minus 5 1 gives 1 the ] total . $ systemThis test will improve in the future as the t iming baseline extends and a more significant measurementLine 1 mass M of = 2 period$ r $ 5871 can plusminux be made 0 period . 2 M sub odot period Line 2 hline Living Reviews in Relativity Currentlyht tp : slash the slash best w w binary w period pulsar l i vi ngre system v i e w s for period testing or g slash GR lrr in hyphen the 2008 strong hyphen− field 8 regime is the double pulsar J $ 737 − 3039 . $ \quad In this system , where two independent pulsar clo cks can be timed , five PK parameters of the 22 . 7 − ms pulsar ‘‘ A ’’ have been measured as well as two additional constraints from the measured mass function and projected semi − major axis of the 2 . 7 − s pulsar ‘‘ B ’’ . A useful means of summarising the limits so far is Figure 2 7 \quad which shows the allowed regions of parameter space in terms of the masses of the two pulsars . \quad The shaded regions are excluded by the requirement that s i n $ i < 1 . $ \quad Further constraints are shown as pairs of lines enclosing permitted regions as

\noindent predicted by GR . The measurement [ 2 0 1 ] of $ \dot{\omega} = 1 6 . 899 \pm 0 . 0 1$ deg $yrˆ{ − 1 }$ gives the total system

\ [ \ begin { a l i g n e d } mass M = 2 . 5871 \pm 0 . 2 M {\odot } . \\ \ r u l e {3em}{0.4 pt }\end{ a l i g n e d }\ ]

\noindent Living Reviews in Relativity

\noindent http : //www. l i vi ngrev i ews . org/ lrr − 2008 − 8 BinaryBinary and and Millisecond Millisecond Pulsars Pulsars .... 43 43 \noindenthline Binary and Millisecond Pulsars \ h f i l l 43 Figure 26 : .. Orbital decay in the binary pulsar B 1 9 1 3 plus 1 6 system demonstrated as an increasing orbital \ [ phase\ r u l eshift{3em for}{ periastron0.4 pt }\ passages] with time period The GR prediction due entirely to the emission of gravita hyphen tionalFigure radiation 26 : is shownOrbital by decay the parabola in the binary period pulsar Figure B 1913 provided + 16 system by Joel demonstrated Weisberg period as an increasing orbital phase hlineshift for periastron passages with time . The GR prediction due entirely to the emission of gravita - tional radiation \noindentLivingis shown ReviewsFigure by the inRelativity parabola 26 : \ .quad FigureOrbital provided by decay Joel Weisberg in the . binary pulsar B $ 1 9 1 3 + 1 6 $ system demonstrated as an increasing orbital phaseht tp : shift slash slash for w periastron w .. w period passagesl i vi ngrev i with e w s periodtime org. The slash GR lrr prediction hyphen 2008 hyphen due entirely 8 to the emission of gravita − tional radiation is shown by the parabola . Figure provided by Joel Weisberg .

\ [ \ r u l e {3em}{0.4 pt }\ ] Living Reviews in Relativity ht tp : / / w w w . l i vi ngrev i e w s . org / lrr - 2008 - 8

\ hspace ∗{\ f i l l } Living Reviews in Relativity

\ hspace ∗{\ f i l l } ht tp : / / w w \quad w. l i vi ngrev i ews . org / lrr − 2008 − 8 44 ....44 Duncan R period Lorimer Duncan R . Lorimer \noindenthline 44 \ h f i l l Duncan R . Lorimer Figure 2 7 : quoteleft Mass endash mass quoteright diagram showing the observational constraints on the masses of the neutron stars \ [ in\ r the u l e double{3em}{ pulsar0.4 pt system}\ ] J 737 minus 3039 period Inset is an enlarged view of the small square encompassing the intersectionFigure 2 of 7 the : ‘ tightest Mass – constraints mass ’ diagram period showing Figure the provided observational by Ren constraints acute-e on Breton the masses open square of the neutron bracket stars 4 4 closing in square bracket period hlinethe double pulsar system J 737 − 3039. Inset is an enlarged view of the small square encompassing the intersection \noindentLivingof the Reviews tightestFigure in constraints Relativity 2 7 : . ‘ Figure Mass provided−− mass by Ren ’ diagrame´ Breton [ showing 4 4 ] . the observational constraints on the masses of the neutron stars inht the tp : slash double slash pulsar w w w period system l i vi J ngre $ 737v i e w s− period3039 or g slash . $ lrr hyphen Inset 2008 is an hyphen enlarged 8 view of the small square encompassing the intersection of the tightest constraints . Figure provided by Ren $ \acute{e} $ Breton [ 44 ] .

\ [ \ r uLiving l e {3em Reviews}{0.4 in pt Relativity}\ ] ht tp : / / w w w . l i vi ngre v i e w s . or g / lrr - 2008 - 8

\noindent Living Reviews in Relativity

\noindent http : //www. l i vi ngrev i ews . org/ lrr − 2008 − 8 BinaryBinary and and Millisecond Millisecond Pulsars Pulsars .... 45 45 \noindenthline Binary and Millisecond Pulsars \ h f i l l 45 The measurement of the projected semi hyphen major axes of both orbits gives the mass ratio R = \ [ 1\ periodr u l e {3em 71 plusminux}{0.4 pt }\ 0 period] 0 1 period The mass ratio measurement is unique to the double pulsar system and rests on the basic assumptionThe measurement that momentum of the projected is conserved semi period - major .. This axes constraint of both orbits should gives apply the to massany reasonable ratio R = 1.71 ± theory0.01 of. The gravity mass period ratio .. measurement The intersection is unique between to the the double lines for pulsar omega-dotaccent system and andrests R on yield the the basic masses assumption of A and B as Them measurement subthat A momentum = 1 period of is3381 the conserved plusminux projected . 0 This period semi constraint 7− M submajor should odot axes and apply m of subto both any B = reasonable 1 orbits period 2489 theory gives plusminux of the gravity mass 0 .period ratio The 7 M sub $ R odot = period $ From $ 1 . 71 \pm 0 . 0 1 . $ The mass ratio measurement is unique to the double pulsar system and rests on the these valuesintersection comma between using Equations the lines Case forω 1 ˙ endashand R Caseyield 2 the 1 3 masses of A and B as mA = 1.3381 ± 0.7M and basic assumption that momentum is conserved . \quad −This − constraint should apply to any reasonable 1 6m closing= 1. parenthesis2489 ± 0.7M the. expectedFrom these values values of ,gamma using Equations comma P-dotaccent ( sub b comma r and s may be calculated and compared with the observedtheoryB of gravity . \quad The intersection between13 the lines for $ \dot{\omega} $ and $R$ yield the masses of AandB as $ m { A } = 1 . 3381 \pm 0 . 7 M {\odot }$ and $ m { B } = 1 . 2489 \pm values1 6 period ) the expected These four values tests of ofγ, GRP˙ allr agreeand s withmay thebe calculated theory to andwithin compared the uncertainties with the observed period Currently values . These the 0 . 7 M {\odot } . $b, From these values , using Equations $\ l e f t .( \ begin { a l i g n e d } & −− \\ t ightestfour tests constraint of GR is all the agree Shapiro with delay the theory parameter to within s where the the uncertainties observed value . Currently is in agreement the t ightest with constraint is & 1 3 \end{ a l i g n e d }\ right . $ GRthe at the Shapiro 0 period delay 5 parameterpercent levels where open squarethe observed bracket value 2 .. is 0 in1 closing agreement square with bracket GR at period the 0.5% level [ 2 0 1 ] . AnotherAnother unique unique feature feature of the double of the double pulsar systempulsar system is the interactions is the interactions between between the two the pulsars two pulsars quoteright ’ radiation \noindent 1 6 ) the expected values of $ \gamma , \dot{P} { b , } r $ and $ s $ may be calculated and compared with the observed radiationbeams beams . Specifically period Specifically , the signal commafrom A theis eclipsed signal from for 30 A s is each eclipsed orbit for by 30 the s magnetosphere each orbit by the of Bmagnetosphere [ 2 3 9 , 1 values . These four tests of GR all agree with the theory to within the uncertainties . Currently the of B8 open 4 , square 2 6 0 bracket ] and the 2 3 radio 9 comma pulses .. from1 8 .. B 4 are comma modulated 2 .. 6 0 by closing the relativistic square bracket wind andfrom the A radio pulses from B are modulated by the t ightest constraint is the Shapiro delay parameter $ s $ where the observed value is in agreement with relativisticduring wind two from phases A of the orbit [ 2 5 8 ] . These provide unique insights into plasma physics [ 1 2 5 ] GRatthe $0 . 5 \% $ l e v e l [ 2 \quad 0 1 ] . duringand two , as phases shown shownof the inorbit Figure .. open 2 7 , square a measurement bracket 2 of 5 relativistic 8 closing square spin – bracket orbit coupling period in .. the These binary provide system unique insights into plasma physicsand .. open , hence square , another bracket constraint 1 2 5 closing on GR square . By bracket careful modeling of the change in eclipse profiles of A over a four Another unique feature of the double pulsar system is the interactions between the two pulsars ’ and- comma year baseline as shown , Breton shown et in al Figure . [ 4 247 ] have comma been a measurement able to fit a remarkably of relativistic simple spinendash model 3 orbitand coupling determine in the the binary radiation beams . Specifically , the signal from A is eclipsed for 30 s each orbit by the magnetosphere systemprecession and comma of B ’hence s spin comma axis about another the constraint orbital angular on GR momentum period By carefulvector . modeling This remarkable of the change measurement in eclipse profiles o f B [ 2 3 9 , \quad 1 8 \quad 4 , 2 \quad 6 0 ] and the radio pulses from B are modulated by the relativistic wind from A of Aagrees over a , within four hyphen the 13% year measurement baseline comma uncertainty Breton , et to al the period GR prediction open square . bracket 4 4 closing square bracket have been able to fit a remarkablyIt simple took only model two 3 years for the double pulsar system to surpass the tests of GR possible from three decades \noindent during two phases of the orbit \quad [ 2 5 8 ] . \quad These provide unique insights into plasma physics \quad [ 1 2 5 ] andof determine monitoring the PSR precession B 1913 of + B 16 quoteright and over a s decade spin axis of tabout iming the PSR orbital B 1534 angular + 12. momentumOn - going vector precision period timing .. This and , as shown shown in Figure 2 7 , a measurement of relativistic spin −− orbit coupling in the binary remarkablemeasurements measurement of the agreesdouble comma pulsar withinsystem the should 1 3 percent soon provide measurement even more uncertainty stringent comma and new to the tests GR of prediction GR period system and , hence , another constraint on GR . By careful modeling of the change in eclipse profiles It took. Crucial only two to these years measurements for the double pulsarwill be system the timing to surpass of the the 2 . tests 7 - of s pulsarGR possible B , where from the observed profile of A over a four − year baseline , Breton et al . [ 4 4 ] have been able to fit a remarkably simple model 3 threeis decades significantly of monitoring affected by PSR A ’B s 1 relativistic 9 1 3 plus wind1 6 and [ 2 over 3 9 a , decade 2 5 8 of ] t. iming A careful PSR decoupling B 1 534 plus of 1 these 2 period profile .. On hyphen and determine the precession of B ’ s spin axis about the orbital angular momentum vector . \quad This goingvariations precision is timing required measurements to accurately of measure the double TOAs pulsar for this system pulsar should and determine soon provide the evenextent more to which the theory remarkable measurement agrees , within the $ 1 3 \% $ measurement uncertainty , to the GR prediction . stringent- independent and new mass tests ratio of GRR periodcan be Crucial measured to these. This measurements task is compounded will be the by timing the fact of that the 2 pulsar period B 7 ’ hyphens signal s pulsar B commais now where [ 4 4 ] the significantly observed weaker profileis compared significantly to the affected by A quoteright s relativistic wind open square bracket 2 3 9 comma .. 2 5 8 It took only two years for the double pulsar system to surpass the tests of GR possible from closingdiscovery square bracket observations period A five careful years ago [ 2 3 9 ] . This appears to be a direct result of its beam precessing out three decades of monitoringPSRB $ 1 9 1 3 + 1 6 $ and over a decade of t imingPSRB $ 1 decouplingof our line of these of sight profile . variations is required to accurately measure TOAs for this pulsar and 534 + 1 2 . $ \quad On − determineThe the relativistic extent to effects which observed the theory in hyphen the double independent pulsar system mass are ratio so R large can thatbe measured corrections period to higher .. This post task - going precision timing measurements of the double pulsar system should soon provide even more is compoundedNewtonian order by the may fact soon that need pulsar to be B quoterightconsidered s. signal For isexample now open, ω˙ may square be bracketmeasured 4 precisely4 closing enough square bracketto significantly weaker stringent and new tests of GR . Crucial to these measurements will be the timing of the 2 . 7 − s p u l s a r comparedrequire to the terms of second post - Newtonian order to be included in the compu - t ations [ 9 1 ] . In addition B , where the observed profile is significantly affected by A ’ s relativistic wind [ 2 3 9 , \quad 2 5 8 ] . A careful discovery, in contrast observations to Newtonian five years physics ago open , square GR predicts bracket that 2 3 9 the closing spins square of the bracket neutron period st ars This affect appears their orbital to be a direct result of its beam decoupling of these profile variations is required to accurately measure TOAs for this pulsar and precessingmotion via spin - orbit coupling . This effect would most clearly be visible as a contribution to the observed determine the extent to which the theory − independent mass ratio $ R $ can be measured . \quad This task outω of˙ in our a secular line of sight [ 2 6 ]period and periodic fashion [ 3 9 5 ] . For the J 737 − 3039 system , the expected contribution is compounded by the fact that pulsar B ’ s signal is now [ 4 4 ] significantly weaker compared to the Theis relativistic about an effectsorder of observed magnitude in the larger double than pulsar for PSR system B 1913 are so + 16[239]large that. correctionsAs the exact to value depends on the higherpulsars post ’ hyphen moment Newtonian of inertia order , a potential may soon measurement need to be considered of this effect period would .. For allow example the moment comma of omega-dotaccent inertia of a may be measured \noindent discovery observations five years ago [ 2 3 9 ] . This appears to be a direct result of its beam precessing preciselyneutron enough st ar to to require be determined terms of second post hyphen Newtonian order to be included in the compu hyphen out of our line of sight . t ationsfor the .. first open time square [ 9 1bracket ] . 9 1 closing Such square a measurement bracket period would .. be In invaluable addition comma for studies in contrast of the neutron to Newtonian star physics comma .. GR predictsequation that the of spins state of and the our understanding of matter at extreme pressure and densities [ 2 0 6 ] . The relativistic effects observed in the double pulsar system are so large that corrections to neutronFinally st ars affect, in the their neutron orbital star motion – white via dwarf spin binary hyphen J orbit 1141 − coupling6545, the period measurement .. This effect of P˙ wouldω˙ γ and mosts permit clearly a higher post − Newtonian order may soon need to be considered . \quad Forb, , example $ , \dot{\omega} $ be visible6% test as of a GRcontribution [ 3 5 ] . Despite to the observed this being omega-dotaccent nominally only ain relatively a secular weakopen squareconstraint bracket for GR 2 6 , closing the significantly square bracket and periodic fashion may be measured open squaredifferent bracket self gravities 3 9 5 closing of the square neutron bracket star period and white .. For dwarf permits constraints on two coupling parameters precisely enough to require terms of second post − Newtonian order to be included in the compu − thebetween J 737 minus matter 3039 and system thescalar comma gravitational the expected field contribution . These is about parameters an order are of non magnitude - existent larger in GR than , which for t a t i o n s \quad [ 9 1 ] . \quad In addition , in contrast to Newtonian physics , \quad GR predicts that the spins of the PSRdescribes B 1 9 1 gravity 3 plus 1 in 6 terms open square of a tensor bracket field 2 , 3 but 9 closing are predicted square bracket by some period alternative .. As theoriesthe exact of value gravity depends which on the pulsars quoteright neutron st ars affect their orbital motion via spin − orbit coupling . \quad This effect would most clearly momentconsider of inertia tensor comma and a scalar potential field components . The constraints provided by PSR J 1141 − 6545 for the strongly be visible as a contribution to the observed $ \dot{\omega} $ in a secular [ 2 6 ] and periodic fashion [ 3 9 5 ] . \quad For measurementnon - linear of coupling this effect parameter would allow are the currently moment the of most inertia stringent of a neutron to date st and ar to are be set determined to improve dramatically the J $ 737 − 3039 $ system , the expected contribution is about an order of magnitude larger than for forover the first thenext time five open years square of timing bracket observations 9 1 closing . square bracket period .... Such a measurement would be invaluable for studies of the neutronPSRB$1 star 9 1 3+1 6 [ 2 3 9 ] .$ \quad As the exact value depends on the pulsars ’ moment of inertia , a potential measurementequation of state of and this our understanding effect would of matter allow at the extreme moment pressure of and inertia densities of open a neutron square bracket st ar 2 0to 6 closing be determined square bracket period Finally comma in the neutron star endash white dwarf binary J 1 1 41 minus 6545 comma the measurement of P-dotaccent sub b comma dotaccent-omega\noindent for sub the comma first gamma time and [ s 9 1 ] . \ h f i l l Such a measurement would be invaluable for studies of the neutron star permit a 6 percent3The testreader of GR is openencouraged square to view bracket the beautiful 3 5 closing movies square explaining bracket the eclipse period model Despite [ 2 5 this 7 ] being nominally only a relatively weak constraint\noindent forequation GR comma of state and our understanding of matter at extreme pressure and densities [ 2 0 6 ] . the significantly different self gravities of the neutron star and white dwarf permits constraints on Finallytwo coupling , in parameters the neutron between star matter−− andwhite the scalar dwarf gravitational binary J field $ 1period 1 .. These 41 parameters− 6545 are , $ the measurement of $ \dot{P} { b , }\dot{\omega} { , }\gamma $ and $ s $ Living Reviews in Relativity non hyphen existent in GR commaht tp which : / describes / w w gravity w . l in i terms vi ngrev of a tensor i e w field s . comma org / but lrr are - predicted 2008 - 8 by some permitalternative a theories $ 6 of\% gravity$ test which of consider GR [ tensor 3 5 ] and . scalarDespite field this components being period nominally The constraints only a relatively weak constraint for GR , theprovided significantly by PSR J 1 1 different 41 minus 6545 self for the gravities strongly non of hyphen the neutron linear coupling star parameter and white are currently dwarf permits the constraints on twomost coupling stringent to parameters date and are between set to improve matter dramatically and the over scalar the next gravitational five years of timing field . \quad These parameters are nonobservations− existent period in GR , which describes gravity in terms of a tensor field , but are predicted by some alternativehline theories of gravity which consider tensor and scalar field components . The constraints provided3 sub The byPSRJ reader is encouraged $ 1 to 1 view 41 the beautiful− 6545 movies $ explainingfor the thestrongly eclipse model non − openlinear square coupling bracket 2 5 parameter7 closing square are bracket currently the mosthline stringent to date and are set to improve dramatically over the next five years of timing observationsLiving Reviews in. Relativity ht tp : slash slash w w .. w period l i vi ngrev i e w s period org slash lrr hyphen 2008 hyphen 8 \ begin { a l i g n ∗} \ r u l e {3em}{0.4 pt } \end{ a l i g n ∗}

\ centerline { $ 3 { The }$ reader is encouraged to view the beautiful movies explaining the eclipse model [ 2 5 7 ] }

\ [ \ r u l e {3em}{0.4 pt }\ ]

\ hspace ∗{\ f i l l } Living Reviews in Relativity

\ hspace ∗{\ f i l l } ht tp : / / w w \quad w. l i vi ngrev i ews . org / lrr − 2008 − 8 46 ....46 Duncan R period Lorimer Duncan R . Lorimer \noindenthline 46 \ h f i l l Duncan R . Lorimer 4 period 6 .. Pulsar t iming and neutron star masses \ [ Multiple\ r u l e {3em PK parameters}{0.4 pt }\ have] now been measured for a number of binary pulsars which provide very4 precise . 6 measurements Pulsar t iming of the neutron and neutron star masses star open masses square bracket 3 7 1 comma 3 4 5 closing square bracket period Figure .. 2 8 shows theMultiple distribution PK parameters have now been measured for a number of binary pulsars which provide very precise \noindentof massesmeasurements following4 . 6 of\quad updates the neutronPulsar to a recentstar t masses iming compilation [ 3 and 7 1 open, neutron 3 4 5 square ] . Figure star bracket masses 2 3 8 4 shows 5 closing the distribution square bracket period While the young pulsars and the doubleof masses following updates to a recent compilation [ 3 4 5 ] . While the young pulsars and the double neutron \noindent Multiple PK parameters have now been measured for a number of binary pulsars which provide neutronstar binariesstar binaries are consistent are consistent with with , or commajust below or just , the below canonical comma 1.4 theM canonical, we note 1that period the 4 millisecond M sub odot pulsars comma we note that the verymillisecondin precise binary pulsars systems measurements inbinary have , systemson average of havethe , significantly comma neutron on average star larger masses massescomma . significantly [ 3 This 7 1 provides , larger 3 4 strong masses 5 ] . support period Figure .. for This\ theirquad provides2 8 shows the distribution strongformation support through for their an formation extended through period of an accretion extended in period the past of accretion , as discussed in the in past Section comma 2 . 6 as . discussed \noindentin SectionFigureof 2 28 period masses: 6Distribution period following of neutron updates star masses to a as recent inferred compilation from timing observations [ 3 4 of5 binary ] . While pulsars the and X young pulsars and the double neutronFigure- ray 28 binary star : .. Distribution systems binaries . Figure of are neutron adapted consistent star from masses an original with as inferred version , or from providedjust timing below by observationsIngrid ,the stairs canonical . of Additional binary pulsars information $ 1 . on 4 M {\odot } , $and weglobular X hyphen note cluster that ray pulsarbinary the mass systems constraints period provided Figure adapted by Paulo from Freire an . original Error version bars show provided one - by sigma Ingrid uncertainties stairs period on Additional millisecondinformationeach mass on determination pulsars globular cluster in . binary pulsar mass systems constraints have provided , on average by Paulo Freire , significantly period .. Error largerbars show masses one hyphen . \quad This provides strongsigma uncertaintiesAlso support shown onfor on this each their diagram mass formation determination are several eccentric through period binary an extended systems in globular period clusters of accretion which have theirin the masses past , as discussed inAlso Sectionconstrained shown on 2 this from . 6 diagram measurements . are several of the eccentric relativistic binary advance systems of inperiastron globular and clusters the Keplerian which mass function . In havethese their cases masses , the constrained condition fromsin i < measurements1 sets a lower of limit the relativistic on the companion advance of periastron and the \noindent Figure 282 : 1/\3quad Distribution of neutron star masses as inferred from timing observations of binary pulsars Keplerianmass m massc > ( functionfmassM ) periodand In a these corresponding cases comma upper the limit condition on the sin pulsar i less mass 1 sets . aProbability lower limit density on the functions companion and X − ray binary systems . Figure adapted from an original version provided by Ingrid stairs . Additional massfor m both subm c greaterp and m openc can parenthesis also be estimated f sub mass in a statisticalM to the power sense by of 2assuming closing parenthesisa random to the power of 1 slash 3 and a corresponding upperinformation limit on the on pulsar globular mass period cluster Probability pulsar density mass constraints provided by Paulo Freire . \quad Error bars show one − sigmafunctions uncertainties for both m sub onp and each m sub mass c can determination also be estimated . in a statistical sense by assuming a random hline Also shownLiving Reviews on this in Relativity diagram are several eccentric binary systems in globular clusters which Livinght Reviewstp : / in / Relativity w w w . l i vi ngre v i e w s . or g / lrr - 2008 - 8 haveht tp their : slash slashmasses w w constrained w period l i vi ngre from v i measurements e w s period or g of slash the lrr hyphen relativistic 2008 hyphen advance 8 of periastron and the Keplerian mass function . In these cases , the condition sin $ i < 1 $ sets a lower limit on the companion

\noindent mass $ m { c } > ( f { mass } M ˆ{ 2 } ) ˆ{ 1 / 3 }$ and a corresponding upper limit on the pulsar mass . Probability density functions for both $ m { p }$ and $ m { c }$ can also be estimated in a statistical sense by assuming a random

\ [ \ r u l e {3em}{0.4 pt }\ ]

\noindent Living Reviews in Relativity

\noindent http : //www. l i vi ngrev i ews . org/ lrr − 2008 − 8 BinaryBinary and and Millisecond Millisecond Pulsars Pulsars .... 47 47 \noindenthline Binary and Millisecond Pulsars \ h f i l l 47 distribution of orbital inclination angles period An example of this is shown in Figure .. 2 9 for the eccentric \ [ binary\ r u l e millisecond{3em}{0.4 pulsar pt }\ in] M 5 open square bracket 1 1 8 closing square bracket where the nominal pulsar mass is 2 period 8 plusminux 0 perioddistribution 1 9 M sub odot of orbital ! .. This inclination is angles . An example of this is shown in Figure 2 9 for the eccentric binary a potentiallymillisecond outstanding pulsar in M result 5 [ 1 period 1 8 ] .. where If confirmed the nominal by the pulsar measurement mass is 2 of.8 other± 0.19 relativisticM ! This parame is a potentially hyphen \noindenttersoutstanding commadistribution these result supermassive . If ofconfirmed neutron orbital by stars the inclinationmeasurement will have important of angles other constraints relativistic . An example on parame the equation - of ters this , these of state is supermassive shown of in Figure \quad 2 9 for the eccentric binarysuperdenseneutron millisecond matter stars will period have pulsar important in M5 constraints [ 1 1 on 8 the ] equation where the of state nominal of superdense pulsar matter mass . is $ 2 . 8 \pm 0 . 1Figure 9Figure M29 : 29{\ Pulsar : odotPulsar mass} mass versus! versus $ companion\ companionquad This mass mass diagram i diagram s showing mass mass constraints constraints for for the theeccentric eccentric binary binary millisecond amillisecond potentiallypulsar B pulsar1516+2 outstanding BB 1 5[ 1 1 1 6 8 plus ] . The 2 result B allowed open parameter.square\quad bracket spaceIf confirmed 1is 1bounded 8 closing by bysquarethe dashed the bracket measurement lines whichperiod show The of the allowed otheruncertainty parameter relativistic space is bounded parame by− theters dashedon , the these lines total which mass supermassive from the measurement neutron of the stars relativistic will advance have importantof periastron . constraints Masses within the on hatched the equation region of state of superdenseshoware the disallowed uncertainty matter by the on . Keplerian the total mass mass function from the and measurement the constraint of that the sin relativistici < 1. advanceAssuming of periastron a random distribution period Massesof orbital within inclination the hatched angles region allows are the disallowed probability by density the Keplerian functions mass of the function pulsar and and companion the constraint mass to that be derived , \noindentsin ias less shown 1Figure period by the .. top 29 Assuming and : Pulsarright a hand random mass panels distribution versus . Figure companion provided of orbital by inclination Paulo mass Freire diagram angles . allows showing the probability mass constraints density for the eccentric binary millisecondfunctionsCurrently of the pulsar pulsar the largest and B companion $ measurement 1 5 mass 1 of toa radio 6 be derived +pulsar 2 comma mass $ throughB as [ shown 1 1multiple8 by ] the . PK top The parameters and allowed right hand is the parameter panels eccentric period space is bounded by the dashed lines which showFiguremillisecond the provided uncertainty pulsar by Paulo binary Freire on system the period total J 1903 mass + 327[70] from ( the see also measurement Section 2. of 9 the) . relativistic Thus , in addition advance to of periastron . MassesCurrentlychallenging within the largest models the measurement hatched of millisecond region of a pulsar radio are formation pulsar disallowed mass , this through new by multiple discovery the Keplerian PK has parameters impor mass - t ant function implications and for the constraint that s i n $ i < 1 . $ \quad Assuming a random distribution of orbital inclination angles allows the probability density is thefundamental eccentric millisecond physics . pulsar When binary placed system on the J mass 1 903 – plusradius 327 diagram open square for neutron bracket stars 7 0 [ closing 2 0 6 ] square , this 1 bracket.74M open parenthesis see also Sectionfunctionspulsar .. 2 period appears of 9the closing to pulsar be parenthesis incompatible and companion period with .. at Thus least mass comma four to equations be derived of st ate , for as superdense shown by matter the top . Futureand right hand panels . Figurein additiontiming provided measurements to challenging by Paulo are models required Freire of millisecond to consolidate . pulsar and formation verify this comma potentially this new very discovery exciting has result impor . hyphen t ant implications for fundamental physics period .. When placed on the mass endash radius diagram for neutron Currentlystars open the square largest bracket 2 measurement 0 6 closing square of bracket a radio comma pulsar this 1 mass period through 74 M sub multipleodot pulsar PK appears parameters to be incompatible with at least fouris equations the eccentric of st ate millisecond pulsar binary system J $ 1 903 + 327 [ 7 0 ] ( $ see also Section \quad 2 . 9 ) . \quad Thus , in addition to challenging models of millisecond pulsar formationLiving , Reviews this new in Relativity discovery has impor − for superdense matter periodht .. Future tp : timing / / w measurements w w . l iare vi required ngrev to i econsolidate w s . org and / verify lrr this- 2008 - 8 tpotentially ant implications very exciting for result fundamental period physics . \quad When placed on the mass −− radius diagram for neutron stars[206],thishline $1 . 74 M {\odot }$ pulsar appears to be incompatible with at least four equations of st ate forLiving superdense Reviews in Relativitymatter . \quad Future timing measurements are required to consolidate and verify this potentiallyht tp : slash slash very w w exciting .. w period result l i vi ngrev . i e w s period org slash lrr hyphen 2008 hyphen 8 \ [ \ r u l e {3em}{0.4 pt }\ ]

\ hspace ∗{\ f i l l } Living Reviews in Relativity

\ hspace ∗{\ f i l l } ht tp : / / w w \quad w. l i vi ngrev i ews . org / lrr − 2008 − 8 48 ....48 Duncan R period Lorimer Duncan R . Lorimer \noindenthline 48 \ h f i l l Duncan R . Lorimer 4 period 7 .. Pulsar t iming and gravitational wave detection \ [ We\ r u have l e {3em seen}{ in0.4 the pt Section}\ ] 4 period 4 how pulsar t iming can be used to provide indirect evidence for the existence4 . 7 of gravitational Pulsar t waves iming from and coalescing gravitational stellar hyphen wave mass detection binaries period In this final section comma we look at howWe havepulsar seen timing in the might Section soon 4 be. 4 used how pulsarto detect t iming gravitational can be used radiation to provide directly indirect period evidence The idea for to the use existence \noindentpulsarsof gravitational as4 natural . 7 gravitational\quad waves fromPulsar wavecoalescing t detectors iming stellar wasand - massfirst gravitational explored binaries in . Inthe this wavelate final 1 970 detection section s open , square we look bracket at how 3 pulsar3 0 comma .. 9 5 closing square brackettiming period might .. The soon be used to detect gravitational radiation directly . The idea to use pulsars as natural \noindentbasicgravitational conceptWe is have to wave treat seen detectors the in solar the was system first Section barycentre explored 4 . in and 4 the how a late distant pulsar 1 970 pulsar s [t 3as iming 3 opposite 0 , can 9 ends 5 ] be . of used an The basicto provide concept indirect evidence for the existenceimaginaryis to treat arm of the in gravitational space solar systemperiod The barycentre waves pulsar acts andfrom as a distant coalescingthe reference pulsar clo as stellar oppositeck at one− ends endmass of of the an binaries imaginary arm sending . arm In out in this spacefinal . section , we look atregular howThe signalspulsar pulsar whichacts timing as are the monitored reference might soonclo by anck be atobserver one used end on to of the the detect Earth arm sending over gravitational some out t regular imescale signals radiation T period which The are directly effect monitored . The idea to use pulsarsof aby passing an as observer gravitational natural on the gravitational wave Earth would over besome to wave tperturb imescale detectors theT. loThe cal spacetime effect was of first a metric passing explored and gravitational cause in a change the wave late would 1 be 970 to s [ 3 3 0 , \quad 9 5 ] . \quad The basicin theperturbconcept observed the rotationallo is cal to spacetime treat frequency metric the of solarthe and pulsar cause system period a change barycentre .. For in theregular observed pulsar and rotationala timing distant observations frequency pulsarof with as the oppositepulsar . ends of an imaginary arm in space . The pulsar acts as the reference clo ck at one end of the arm sending out typicalFor TOA regular uncertainties pulsar timing of epsilon observations sub TOA with comma typical this TOA quotedblleft uncertainties detector of quotedblrightTOA, this “ detector would be ” sensitive would be to waves with dimensionless regular signals which are monitored by an observer on the Earth over some t imescale $ T . $ The effect amplitudessensitive h to gtrsim waves epsilon with dimensionless sub TOA slash amplitudes T and frequenciesh & TOA f/T thicksimand frequencies 1 slash T openf ∼ 1 square/T [33, bracket41]. 3 3 comma 4 1 closing square bracket periodof a4 passing . 7 . 1 gravitational Probing the gravitational wave would wave be background to perturb the lo cal spacetime metric and cause a change in4 period theMany observed 7 cosmological period 1 .. rotational Probing models the predict gravitational frequency that the wave Universe of the background is pulsar presently . \ filledquad withFor a low regular - frequency pulsar stochas timing - tic observations with typicalManygravitational cosmological TOA uncertainties wave models background predict of (that GWB $ the\ )epsilon Universe produced is during{ presentlyTOA the} filled big, bang $ with this era a low [ 2 ‘‘hyphen 9 2 detector ] . frequency A significant ’’ stochas would hyphen be sensitive to waves with dimensionless amplitudestic gravitationalcomponent $ [ 3wave h 0 9 background,\ gtrsim 1 5 9 ] is open the\ epsilon gravitational parenthesis{ GWBTOA radiation} closing/ from parenthesis T$ the inspiral and produced frequenciesprior to during supermassive the $ big f black bang\sim holeera open1 square / bracket T [ 2 9 2 3 closing3 ,mergers square 4 bracket . 1 In the ] period ideal . case .. $ A , significant the change in the observed frequency caused by the GWB should be detectable in componentthe set of open timing square residuals bracket after 3 the 0 9 application comma .. of 1 an5 9 appropriate closing square model bracket for the is rotational the gravitational , astrometric radiation and from the inspiral prior to supermassive\noindent, where black4 necessary . 7 . 1 , binary\quad parametersProbing of the the pulsar gravitational . As discussed wave in Sectionbackground 4 . 2 , all other effects being holenegligible mergers period , the rms In the scatter ideal of case these comma residuals the changeσ would in be the due observed to the measurementfrequency caused uncertainties by the GWB and should intrinsic \noindentbe detectabletimingMany noise in fromthe cosmological set the of neutron timing residuals star models . after predict the application that the of an Universe appropriate is model presently for the filled with a low − frequency stochas − ticrotational gravitational comma ..For astrometric wave a GWB background with and acomma flat energy ( where GWB spectrum necessary ) produced in comma the frequency during binary parameters band thef big± f/ bangof2 the there pulsar era is an [ period additional 2 9 2.. As ] .discussed\quad inA significant Sectioncontribution .. 4 period to 2the comma timing all residuals other effectsσg[95] being. When negligiblefT  comma1, the thecorresponding rms scatter wave of these energy residuals density sigma would be due to \noindenttheis measurementcomponent uncertainties [ 3 0 and 9 , intrinsic\quad timing1 5 9 noise ] is from the the gravitationalneutron star period radiation from the inspiral prior to supermassive black holeFor a mergers GWB with . a In flat the energy ideal spectrum case in the, the frequency change band in f plusminux the observed f slash frequency2 there is an additional caused by the GWB should be detectable in the set of timing residuals after the application of an appropriate model for the contribution to the timing residuals sigma sub g open square bracket3 4 2 9 5 closing square bracket period When fT gg 1 comma the corresponding rotational , \quad astrometric and , where243 necessaryπ f gσ , binary parameters of the pulsar . \quad As discussed in wave energy density ρg = (17) 208G . Secis tion \quad 4 . 2 , all other effects being negligible , the rms scatter of these residuals $ \sigma $ would be due to Equation:An upper open limit parenthesis to ρ can 1 be 7 closingobtained parenthesis from a set .. of rho timing sub residuals g = 243pi by to assuming the power the of rms 3 f scatter to the power of 4 g sigma to the power of 2 the measurement uncertaintiesg and intrinsic timing noise from the neutron star . dividedis by entirely 208 Gsub due period to this effect (σ = σg). These limits are commonly expressed as a fraction of the energy Andensity upper limit required to rho to sub close g canthe Universebe obtained from a set of timing residuals by assuming the rms scatter \ hspaceis entirely∗{\ duef i l l to}For this effect a GWB open with parenthesis a flat sigma energy = sigma spectrum sub g closing in the parenthesis frequency period band .. These $ limits f \ arepm commonlyf / expressed 2 $ as there a is an additional fraction of the \noindent contribution to the timing residuals3H2 $ \sigma { g } [ 9 5 ] .$When$fT \gg energy density required to close the Universeρc = 0 ' 2 × 10−29h2gcm−3, (18) 1Equation: , $ the open corresponding parenthesis 1 8 closing wave parenthesis energy8πG density .. rho c = 3 H sub 0 to the power of 2 divided by 8 pi G simeq 2 times 1 0 to the power of minus 2 9 h to the power of 2 g cm to the power−1 of minus 3 comma \noindentwhere thei s Hubble constant H0 = 10h km s Mpc . where theThis Hubble technique constant was firstH sub applied 0 = 1 [0 3 h 2 km 5 ]s to to athe set power of TOAs of minus for PSR 1 Mpc B period1237 + 25 obtained from regular This technique was first applied open square bracket 3 2 5 closing square bracket to a set of TOAs for PSR B 1 237 plus 25 obtained from \ beginobservations{ a l i g n ∗} over a period of 1 1 years as part of the JPL pulsar timing programme [ 9 9 ] . This pulsar was regularchosen on the basis of its relatively low level of timing activity by comparison with the youngest pulsars , \rhoobservations{ g } over= a period\ f r a c { of 1243 1 years\ pi as partˆ{ of3 the} JPLf ˆ{ pulsar4 } timingg {\ programmesigma } openˆ{ 2 square}}{ bracket208 9 G 9} closing{ . square}\ tag ∗{ bracket$ ( period 1 7 )whose $} residuals are ultimately plagued by timing noise ( see Section 4 . 3 ) . By ascribing the This pulsar −3 −2 \end{ rmsa l i g scatter n ∗} in the residuals (σ = 240 ms ) to the GWB , the limit is ρg/ρ c . 4 × 10 h for a centre wasfrequency chosen onf the= 7 basis nHz of . its relatively low level of timing activity by comparison with the youngest pulsars comma whose residuals are ultimately plagued by timing noise open parenthesis see Section 4 period 3 closing parenthesis period \noindentThisAn limit upper , already limit well to below $ \ therho energy{ g density}$ can required be obtained to close the from Universe a set , was of further timing reduced residuals by assuming the rms scatter By ascribingfollowing the the long - term timing measurements of millisecond pulsars at Arecibo ( see Sec - tion 4 . 3 ) . rmsIn scatter the intervening in the residuals period open , more parenthesis elaborate sigmatechniques = 240 had ms been closing devised parenthesis [ 3 3 , to 4 1 the , GWB 3 5 6 comma ] to look the for limit the is rho sub g slash rho c lesssim\noindent 4 timesis 1 0 entirely to the power due of minus to this 3 h to effect the power $ of ( minus\sigma 2 for a = \sigma { g } ) . $ \quad These limits are commonly expressed as a fraction of the energylikely density signature required of a GWB in to the close frequency the spectrum Universe of the timing residuals and to address the possibility of centre“ fitting frequency out ” f = the 7 nHz signal period in the TOAs . Following [ 3 3 ] it is convenient to define This limit comma already well below the energy density required to close the Universe comma was further \ begin { a l i g n ∗} reduced following the long hyphen term timing measurements1 d log ρg of millisecond pulsars at Arecibo open parenthesis see Sec hyphen \rhotion .. 4c period = 3\ closingf r a c { parenthesis3 H ˆ{ period2 } { ..Ω0 Ing }}{= the intervening8 \ pi (19) periodG }\ commasimeq more elaborate2 \times techniques1 had 0 been ˆ{− devised2 open 9 square} h ˆ{ 2 } ρc d log f , bracketg cm 3 ˆ3{ comma − 3 .. 4} 1 comma, \ tag ..∗{ 3$ 5 6( closing 1 square 8 bracket) $} to \endlook{ a for l i g then ∗} likely signature of a GWB in the frequency spectrum of the timing residuals and to addressLiving the Reviews possibility in Relativity of .. quotedblleft fitting out quotedblright .. the signal in the TOAs period .. Following open square bracket 3 3 closing\noindentht square tpwhere : bracket / / the wit isw convenientwHubble . l i constant vi to ngre v i $ e H w s{ .0 } or= g / lrr 1 - 0 2008 h - $ 8 km $ s ˆ{ − 1 }$ Mpc . define ThisLine technique 1 Capital Omega was firstsub g = applied 1 divided by[ 3 rho 2 c 5 d ] log to rho a sub set g divided of TOAs by d for log PSRB f sub comma $ 1 open 237 parenthesis + 251 9 closing$ obtained parenthesis from regular Lineobservations 2 hline over a period of 1 1 years as part of the JPL pulsar timing programme [ 9 9 ] . This pulsar wasLiving chosen Reviews on in the Relativity basis of its relatively low level of timing activity by comparison with the youngest pulsarsht tp : slash , whose slash w residuals w w period l are i vi ngre ultimately v i e w s period plagued or g slash by timing lrr hyphen noise 2008 hyphen ( see 8 Section 4 . 3 ) . By ascribing the \noindent rms scatter in the residuals $ ( \sigma = 240 $ ms ) to theGWB, the limit is $ \rho { g } / \rho $ c $ \ l e s s s i m 4 \times 1 0 ˆ{ − 3 } h ˆ{ − 2 }$ f o r a centre frequency $ f = 7 $ nHz .

This limit , already well below the energy density required to close the Universe , was further reduced following the long − term timing measurements of millisecond pulsars at Arecibo ( see Sec − t i o n \quad 4 . 3 ) . \quad In the intervening period , more elaborate techniques had been devised [ 3 3 , \quad 4 1 , \quad 3 5 6 ] to look for the likely signature of a GWB in the frequency spectrum of the timing residuals and to address the possibility of \quad ‘‘ fitting out ’’ \quad the signal in the TOAs . \quad Following [ 3 3 ] it is convenient to d e f i n e

\ [ \ begin { a l i g n e d }\Omega { g } = \ f r a c { 1 }{\rho c }\ f r a c { d \ log \rho { g }}{ d \ log f } { , } ( 1 9 ) \\ \ r u l e {3em}{0.4 pt }\end{ a l i g n e d }\ ]

\noindent Living Reviews in Relativity

\noindent http : //www. l i vi ngrev i ews . org/ lrr − 2008 − 8 BinaryBinary and and Millisecond Millisecond Pulsars Pulsars .... 49 49 \noindenthline Binary and Millisecond Pulsars \ h f i l l 49 i period e period the energy density of the GWB per logarithmic frequency interval relative to rho c to the power of period .. With this \ [ definition\ r u l e {3em comma}{0.4 the pt power}\ ] spectrum of the GWB open square bracket 1 4 7 comma .. 4 1 closing square bracket is . Equation:i . e . the open energy parenthesis density 20 ofclosing the GWB parenthesis per logarithmic .. P open frequency parenthesis interval f closing relative parenthesis to ρc With = G this rho definitionsub g divided by 3 pi to the power of 3 f to, the the power power spectrum of 4 = H subof the 0 to GWB the power [ 1 4 7 of , 2 4Capital 1 ] is Omega sub g divided by 8 pi to the power of 4 f to the power of 5 = 1 period 34 times\noindent 1 0 to thei . power e . of the 4 Capital energy Omega density sub gh of to the the powerGWB per of 2 f logarithmic sub yr to the power frequency of minus interval 1 to the power relative of minus to 5 mu $ s\rho to the c ˆ{ . }$ \quad With t h i s power of 2 yr comma Gρ H2Ω definitionwhere f sub yr , to the the power power of spectrumP minus(f) = 1 is of frequencyg the= GWB0 ing cycles= [ 1 1.34 4 per× 710 year4 ,Ω\hquad period2f −5 4µ Thes2 1yr long, ] i s hyphen term timing(20) stability of B 1 937 plus 2 1 3π3f 4 8π4f 5 g yr−1 comma discussed \ begin { a l i g n ∗} in Sectionwhere f ....− 41 period is frequency 3 comma in cycles limits per its use year for . The periods long gtrsim - term 2 timing yr period stability Using of the B more 1937 + stable 21, discussed residuals for PSR B 1 855 plus 9 comma P ( fyr ) = \ f r a c { G \rho { g }}{ 3 \ pi ˆ{ 3 } f ˆ{ 4 }} = \ f r a c { H ˆ{ 2 } { 0 }\Omega { g }}{ 8 Kaspiin Sectionet al period open 4 . 3 square , limits bracket its use 1 for 8 5 periods closing square2 yr . bracket Using the placed more an stable upper residuals limit of for Capital PSR OmegaB 1855 +sub 9, g h to the power of 2 less \ pi ˆ{ 4 } f ˆ{ 5 }} = 1 . 34 \× 1 0 ˆ{ 4 }\Omega { g } h ˆ{ 2 } f ˆ{ − 5 } { yr ˆ{ − 1 periodKaspi 1 times et al 1 .0 [ to 1 the8 5 ]power placed of an minus upper 7 period limit of .... Ω Thish2 < limit1.1 × is10 difficult−7. to reconcileThis limit is difficult to reconcile 1 }}\mu s ˆ{ 2 } yr , \ tag ∗{$ (g 20 ) $} withwith most most cosmic cosmic string string models models for galaxyfor galaxy formation formation open [ 5 square 0 , 3 7 bracket 2 ] . 5 0 comma 3 7 2 closing square bracket period \end{ a l i g n ∗} For binaryFor binary pulsars pulsars comma , the orbital orbital period period provides provides an an additional additional clo clo ck ck for for measuring measuring the the effects effects of ofgravitational gravitationalwaves . waves In this period case , .. the In range this case of frequencies comma the is range not limited of frequencies by the time is not span limited of the by observations the time span , allowing of the \noindent where $ f { yr ˆ{ − }} 1 $ is frequency in cycles per year . The long − term timing stability of B observationsthe detection comma of waves allowing with the periods detection as large of waves as the with light periods travel as time large to as the the binary light travel system time [ 3 to3 ] the . The most $1 937 + 2 1 ,$ discussed binarystringent system results open presentlysquare bracket available 3 3 are closing based square on the bracket B 1855 period + 9 limit The most stringent results presently available are based on the B 1 855 plusΩ 9h limit2 < 2.7 × 10−4 in the frequency range 10−11 < f < 4.4 × 10−9 Hz [ 1 9 6 ] . \noindentg in Sectio n \ h f i l l 4 . 3 , limits its use for periods $ \ gtrsim 2 $ yr . Using the more stable residuals for PSRB Capital4 . 7 Omega . 2 sub Constraints g h to the power on massive of 2 less black 2 period hole 7 times binaries 1 0 to the power of minus 4 in the frequency range 1 0 to the power of minus $ 1 855 + 9 , $ 1 1 lessIn f less addition 4 period to probing 4 times the 1 0 GWB to the , power pulsar of timing minus is 9 beginning Hz open square to place bracket interesting 1 9 6 constraints closing square on the bracket existence period 4 periodof massive 7 period black 2 .. hole Constraints binaries . on massive Arecibo black data for hole PSRs binaries B 1937 + 21 and J 1713 + 747 \noindent Kaspi et al . [ 1 8 5 ] placed an upper limit of $ \Omega { g } h ˆ{ 2 } < 1 . 1 \times In additionalready maketo probing the existence the GWB of comma an equal pulsar - mass timing black is hole beginning binary to in place Sagittarius interesting A ∗ constraintsunlikely [ 2 on 1 4 ] . More 1 0 ˆ{ − 7 } . $ \ h f i l l This limit is difficult to reconcile therecently existence , of timing massive data black from hole B binaries 1855 + 9 period have .. been Arecibo used data to virtually for PSRs rule B 1 out 937 the plus existence 2 1 and J of 1 a 7 proposed1 3 plus 747 alreadysupermassive make the black existence hole of as an the equal explanation hyphen for mass the black periodic hole motion binary seenin Sagittarius at the centre A asterisk of the radio unlikely galaxy open 3 square C bracket 2 1 4 closing \noindent with most cosmic string models for galaxy formation [ 5 0 , 3 7 2 ] . square66 bracket B [ 3 period 5 8 ] . More recently commaA simulation timing of data the from expected B 1 855 modulations plus 9 have of thebeen timing used to residuals virtually for rule the out putative the existence binary system of a , For binary pulsars , the orbital period provides an additional clo ck for measuring the effects of proposedwith a supermassive total mass of black 5.4×10 hole10M as the, is shown explanation along forwith the the periodic observed motion t iming seen residuals at the in centre Figure of 3 0 . Although gravitational waves . \quad In this case , the range of frequencies is not limited by the time span of the thethe radio exact galaxy signature 3 C 66 depends B open on square the orientation bracket 3 5 and 8 closing eccentricity square of bracket the binary period system , Monte Carlo simulations observations , allowing the detection of waves with periods as large as the light travel time to the A simulationshow that of the the existence expected of modulations such a massive of theblack timing hole binary residuals is ruled for the out putative with at binary least 95% system confidence comma [ 1 6 1 ] . binary system [ 3 3 ] . The most stringent results presently available are based on the B $ 1 855 with4 a . total 7 . 3 mass A of millisecond 5 period 4 times pulsar 1 0 t to iming the power array of 1 0 M sub odot comma is shown along with the observed t iming residuals in + 9 $ l i m i t FigureA 3 0 natural period extension of the single - arm detector concept discussed above is the idea of using timing data for Althougha number the ofexact pulsars signature distributed depends over on the the whole orientation sky to and detect eccentricity gravitational of the waves binary [ 1 system 3 7 ] . Such comma a “ timing \noindent $ \Omega { g } h ˆ{ 2 } < 2 . 7 \times 1 0 ˆ{ − 4 }$ in the frequency range Montearray Carlo ” simulations would have show the advantage that the existence over a single of such arm a massivein that , black through hole a binary cross - is correlation ruled out analysis of the $ 1 0 ˆ{ − 1 1 } < f < 4 . 4 \times 1 0 ˆ{ − 9 }$ Hz [ 1 9 6 ] . withresiduals at least for95 percent pairs of confidence pulsars distributed open square over bracket the sky 1 , 6 1 it closing should square be possible bracket to period separate the timing noise of 4 periodeach pulsar7 period from 3 .. the A millisecond signature of pulsar the GWB t iming common array to all pulsars in the array . To i llustrate this , consider \noindent 4 . 7 . 2 \quad Constraints on massive black hole binaries A naturalthe fractional extension frequency of the single shift ofhyphen the i th arm pulsar detector in an concept array discussed above is the idea of using timing data for a number of pulsars distributed over the whole sky to detect gravitational waves open square bracket 1 3 7 closing square bracket period\noindent Such In addition to probing the GWB , pulsar timing is beginning to place interesting constraints on thea .. existence quotedblleft timing of massive array quotedblright black hole .. would binariesδνi have the . advantage\quad Arecibo over a single data arm for in that PSRsB comma through $1 a 937 cross hyphen + 2 correlation 1$ andJ $1 7 1 3 + 747$ = αiA(t) + Ni(t), (21) analysis of the residuals for pairs of pulsars distributedνi over the sky comma .. it should be possible to separate the timing noise of each pulsar from the signature of the GWB common to all pulsars in where α is a geometric factor dependent on the line - of - sight direction to the pulsar and the propagation \noindentthe array periodalreadyi To i make llustrate the this existence comma consider of an theequal fractional− frequencymass black shift ofhole the i binary th pulsar in in an Sagittarius array A $ \ ast $ unlikely [ 214 ] . and polarisation vectors of the gravitational wave of dimensionless amplitude A. The t iming noise intrinsic to MoreEquation: recently open parenthesis , timing 2 1data closing from parenthesis B $ 1.. delta 855 nu sub + i divided 9 $ by have nu sub been i = alpha used sub to i A virtually open parenthesis rule t closing out the parenthesis existence of a the pulsar is characterised by the function N . The result of a cross - plusproposed N sub i open supermassive parenthesis t blackclosing parenthesis hole as the commai explanation for the periodic motion seen at the centre of correlation between pulsars i and j is then thewhere radio alpha galaxy sub i .. is 3C66B a geometric [ factor 3 5 dependent8 ] . on the line hyphen of hyphen sight .. direction to the pulsar and the propagation and polarisation vectors of the gravitational wave of dimensionless amplitude A period The \ hspace ∗{\ f i l l }A simulation of the expected modulations of the timing residuals for the putative binary system , t iming noise intrinsic to the pulsar is characterised2 A by−N the functionN−A N sub i period .. The result of a cross hyphen αiαjhA i + αihj i + αjh ii + hNiNji, (22) correlation between pulsars i and j is then \noindent witha total mass of $5 . 4 \times 1 0 ˆ{ 1 0 } M {\odot } , $ is shown along with the observed t iming residuals in Figure 3 0 . Equation:where the open bracketed parenthesis terms 22 indicate closing parenthesis cross - correlations .. alpha . sub Since i alpha the sub wave j angbracketleft function and the A to noise the contributions power of 2 right angbracket plus alpha Although the exact signature depends on the orientation and eccentricity of the binary system , sub i angbracketleftfrom the two pulsarsto the power are independent of A-N sub , jthe right cross angbracket correlation plus tends alpha to α subα jhA angbracketleft2i as the to the power of N-A i right angbracket plus Monte Carlo simulations show that the existence of suchi aj massive black hole binary is ruled out angbracketleftnumber N of sub residuals i N sub becomes j right largeangbracket . Summing comma the cross - correlation functions over a large number of withwhere at the least bracketed $ terms 95 indicate\% $ crossconfidence hyphen correlations [ 1 6 1 period ] . .. Since the wave function and the noise contributions from the two pulsars are independent comma the cross correlation tends to alpha sub i alpha sub j angbracketleft A to the power\noindent of 2 right4 angbracket. 7 . 3 \ asquad the A millisecond pulsar t iming array number of residuals becomes large period Summing the cross hyphen correlation functionsLiving Reviewsover a large in Relativity number of \noindenthline A natural extensionht tp : of / the / w wsingle w .− larm i vi detector ngrev i e concept w s . org discussed / lrr - 2008above - 8is the idea of using timing dataLiving for Reviews a number in Relativity of pulsars distributed over the whole sky to detect gravitational waves [ 1 3 7 ] . Such a ht\quad tp : slash‘‘ slash timing w w array .. w period ’’ \ lquad i vi ngrevwould i e w have s period the org advantage slash lrr hyphen over 2008 a hyphensingle 8 arm in that , through a cross − correlation analysis of the residuals for pairs of pulsars distributed over the sky , \quad it should be possible to separate the timing noise of each pulsar from the signature of the GWBcommon to all pulsars in the array . To i llustrate this , consider the fractional frequency shift of the $ i $ th pulsar in an array

\ begin { a l i g n ∗} \ f r a c {\ delta \nu { i }}{\nu { i }} = \alpha { i } A ( t ) + N { i } ( t ) , \ tag ∗{$ ( 2 1 ) $} \end{ a l i g n ∗}

\noindent where $ \alpha { i }$ \quad is a geometric factor dependent on the line − o f − s i g h t \quad direction to the pulsar and the propagation and polarisation vectors of the gravitational wave of dimensionless amplitude $ A . $ The t iming noise intrinsic to the pulsar is characterised by the function $ N { i } . $ \quad The result of a cross −

\noindent correlation between pulsars $ i $ and $ j $ is then

\ begin { a l i g n ∗} \alpha { i }\alpha { j }\ langle A ˆ{ 2 }\rangle + \alpha { i }\ langle ˆ{ A−N } { j } \rangle + \alpha { j }\ langle ˆ{ N−A } i \rangle + \ langle N { i } N { j }\rangle , \ tag ∗{$ ( 22 ) $} \end{ a l i g n ∗}

\noindent where the bracketed terms indicate cross − correlations . \quad Since the wave function and the noise contributions from the two pulsars are independent , the cross correlation tends to $ \alpha { i }\alpha { j } \ langle A ˆ{ 2 }\rangle $ as the

\noindent number of residuals becomes large . Summing the cross − correlation functions over a large number of

\ [ \ r u l e {3em}{0.4 pt }\ ]

\ hspace ∗{\ f i l l } Living Reviews in Relativity

\ hspace ∗{\ f i l l } ht tp : / / w w \quad w. l i vi ngrev i ews . org / lrr − 2008 − 8 50 ....50 Duncan R period Lorimer Duncan R . Lorimer \noindenthline 50 \ h f i l l Duncan R . Lorimer Figure 30 : .. Top panel : .. Observed timing residuals for PSR B 1 855 plus 9 period .. Bottom panel : .. Simulated timing \ [ residuals\ r u l e {3em induced}{0.4 from pt }\ a putative] black hole binary in 3 C 66 B period Figure provided by Rick Jenet open square bracket 1 6 1 closing squareFigure bracket 30 period : Top panel : Observed timing residuals for PSR B 1855 + 9. Bottom panel : Simulated pulsartiming pairs residuals provides induced additional from ainformation putative black on hole this binary term as in a3 Cfunction 66 B . Figure of the provided angle on by the Rick sky Jenet open [ 1 square 6 1 ] . bracket 1 3 6 closing square bracket\noindentpulsarFigure pairs provides 30 : additional\quad Top information panel on : \ thisquad termObserved as a function timing of the angle residuals on the sky for [ 1 PSRB 3 6 ] $ 1 855 + 9 . $ \quadandand allowsBottom allows the panel the separation separation : \quad of the of the effectsSimulated effects of of clo clo cktiming ck and and ephemeris ephemeris errors errors from from the the GWB GWB open [ 1 1 square 2 ] . bracket 1 1 2 closing square bracket periodresiduals inducedA recent from analysis a putative [ 1 6 0 ] applying black the hole timing binary array concept in 3 C to 66 data B for . seven Figure millisecond provided pulsars by Rick Jenet [ 1 6 1 ] . 2 −8 A recenthas reduced analysis the open energy square density bracket limit 1 to 6 0 Ω closinggh < 1 square.9×10 bracketfor a background applying the of timing supermassive array concept black hole to data sources for seven millisecond pulsars \noindenthas. reduced The correspondingpulsar the energy pairs density limits provides on limit the to background Capital additional Omega of relic information sub gravitational g h to the waves power on this and of 2 cosmic termless 1 period as a 9function times 1 0 to of the the power angle of minus on the 8 for sky a [ 1 3 6 ] −8 −8 backgroundstrings of are supermassive 2.0 × 10 blackand 1.9 × 10 respectively . These limits can be used to constrain the merger rate of \noindentholesupermassive sourcesand period allows black The hole corresponding the binaries separation at limits high redshift on of the the background , investigate effects of inflationary of relic clo gravitational ck parameters and ephemeriswaves and and cosmic errors from the GWB [ 1 1 2 ] . stringsplace are limits 2 period on the 0 times tension 1 0 of to currently the power proposed of minus cosmic 8 and string 1 period scenarios 9 times . 1 0 to the power of minus 8 respectively period These limits can\ hspace be used∗{\ tof constrain i l l }TheA recent region the merger of analysis the gravitational [ 1 6 wave 0 ]energy applying density the spectrum timing probed array by the concept current pulsar to data tim - for seven millisecond pulsars rateing of supermassive array is shown black in Figure hole binaries 3 1 where at it high can redshift be seen comma that the investigate pulsar t iming inflationary regime parameters is complementary and to the \noindentplacehigher limitshas frequency on the reduced tension bands theof of currently LISA energy and proposed LIGO density . cosmic limit string to scenarios $ \Omega period { g } h ˆ{ 2 } < 1 . 9 \times 1 0 ˆThe{ − regionA8 number of}$ the for ofgravitational long a background- term wave timing energy projects of density supermassive are spectrum now underway probed black to by make the a current large - pulsar scale pulsar tim hyphen timing array a holeingreality array sources is . shown The . Parkes The in Figure corresponding pulsar 3 1 timing where itarray can limits [ be 1 1seen , on that 1 4 the3 the ] observesbackground pulsar t imingtwenty regimeof millisecond relic is complementary gravitational pulsars twice a month waves and cosmic to the. higher The European frequency Pulsar bands ofTiming LISA Array and LIGO [ 1 0 period ] uses the Lovell , Westerbork , Effelsberg and Nancay radio \noindentA numbertelescopesstrings of long to regularly hyphen are observeterm $2 timing a similar . projects 0 number\ aretimes now. Finally underway1 , 0 toat ˆ{ Arecibomake − a large8 and}$ Green hyphen and Bank scale $ , 1 regular pulsar . timingt iming 9 of\times 1 0 ˆ{ − 8 }array$a respectively dozen a reality or more period millisecond .The These Parkes pulsars limits pulsar is carried timing can be out array used by open a North to square constrain American bracket consortium 1the 1 comma merger [ 2 .. 6 7 1 ] 4 . 3 closingIt is expected square bracket observes twenty millisecondratethat of pulsars a supermassive combined twice analysis black of all thesehole efforts binaries could reach at high a limits redshift , investigate inflationary parameters and 2 −10 a monthof Ωgh period< 10 .. Thebefore European 201 0 [ Pulsar 1 Timing 4 3 ] . Array Looking open further square ahead bracket , the 1 0increase closing in square sensitivity bracket provided uses the by Lovell comma Westerbork comma\noindentthe Effelsberg Squareplace and Kilometre limits Array on the [ 1 5 tension 4 , 1 9 8 of ] should currently further improveproposed the cosmic limits of thestring spectrum scenarios probed by . Nancaypulsar radio timing telescopes . As to Figure regularly 3 1 observe shows a similar, the SKA number could period provide .. Finallyup to two comma orders .. of at magnitude Arecibo and Green \ hspaceBankimprovement comma∗{\ f i l regular l }The over t current region iming of capabilities a of dozen the or gravitational. more millisecond pulsarswave energy is carried density out by a North spectrum American probed by the current pulsar tim − consortium4 . 8 open Going squarefurther bracket 2 6 7 closing square bracket period .. It is expected that a combined analysis of all these efforts could reach a\noindent limitsFor furthering details array on is the shown techniques in and Figure prospects 3 1 of where pulsar timing it can , a number be seen of excellent that the reviews pulsar are available t iming regime is complementary toof the Capital[ 1 7 higher , 3 Omega 6 2 , frequency sub 3 0 g , h 3to 4 the 4 bands , power2 2 of 6 of ] LISA2 . less Two 1 and 0 audio to LIGO the files power . and of slides minus from 1 0 lectures before at201 the 0 open centennial square meeting bracket 1 .... 4 3 closing square bracketof period the American Looking furtherPhysical ahead Society comma are also the available increase inon sensitivity - line [ 1 5 provided , 3 9 9 by ] . The tests of general A numberthe Square of Kilometre long − Arrayterm open timing square projects bracket 1 are 5 4 now comma underway .. 1 9 8 closing to make square a large bracket− shouldscale further pulsar improve timing the limits of the spectrumarray a probed reality . The Parkes pulsar timing array [ 1 1 , \quad 1 4 3 ] observes twenty millisecond pulsars twice aby month pulsar . timing\quad periodThe .. European As Figure .. Pulsar 3 1 .. shows Timing comma Array the SKA [ 1 could 0 ] provide uses the up to Lovell two orders , Westerborkof magnitude , Effelsberg and NancayLiving radio Reviews telescopes in Relativity to regularly observe a similar number . \quad F i n a l l y , \quad at Arecibo and Green improvementht tp : over / / current w w w .capabilities l i vi ngreperiod v i e w s . or g / lrr - 2008 - 8 Bank4 period , regular 8 .. Going t further iming of a dozen or more millisecond pulsars is carried out by a North American consortiumFor further details [ 2 6 on 7 the ] techniques . \quad andIt prospects is expected of pulsar that timing a combined comma a number analysis of excellent of all reviews these efforts could reach a limits are available open square bracket 1 7 comma 3 6 2 comma .. 3 0 comma .. 3 4 4 comma 2 .. 2 6 closing square bracket period .. Two audio files\noindent and slideso from f $ lectures\Omega at the{ centennialg } h ˆ{ 2 } < 1 0 ˆ{ − 1 0 }$ before 201 0 [ 1 \ h f i l l 4 3 ] . Looking further ahead , the increase in sensitivity provided by meeting of the American Physical Society are also available on hyphen line open square bracket 1 5 comma .. 3 9 9 closing square bracket period\noindent The teststhe of Square general Kilometre Array [ 1 5 4 , \quad 1 9 8 ] should further improve the limits of the spectrum probed byhline pulsar timing . \quad As Figure \quad 3 1 \quad shows , the SKA could provide up to two orders of magnitude Living Reviews in Relativity \noindentht tp : slashimprovement slash w w w period over l current i vi ngre v capabilities i e w s period org . slash lrr hyphen 2008 hyphen 8 \noindent 4 . 8 \quad Going further

\noindent For further details on the techniques and prospects of pulsar timing , a number of excellent reviews are available [ 1 7 , 3 6 2 , \quad 3 0 , \quad 3 4 4 , 2 \quad 2 6 ] . \quad Two audio files and slides from lectures at the centennial meeting of the American Physical Society are also available on − l i n e [ 1 5 , \quad 3 9 9 ] . The tests of general

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\noindent http : //www. l i vi ngrev i ews . org/ lrr − 2008 − 8 BinaryBinary and and Millisecond Millisecond Pulsars Pulsars .... 5 1 5 1 \noindenthline Binary and Millisecond Pulsars \ h f i l l 5 1 Figure 31 : Summary of the gravitational wave spectrum showing the location in phase space of the pulsar \ [ timing\ r u l e array{3em}{ open0.4 parenthesis pt }\ ] PTA closing parenthesis and its extension with the Square Kilometre Array open parenthesis SKA closing parenthesisFigure period 31 : FigureSummary updated of the by gravitational Michael wave spectrum showing the location in phase space of the pulsar timing Kramerarray open ( PTA square ) and bracket its extension 1 9 8 with closing the Squaresquare Kilometre bracket from Array an ( original SKA ) . designFigure updatedby Richard by Michael Battye period Kramer [ 1 9 \noindenthline8 ] fromFigure an original 31 design : Summary by Richard of Battye the . gravitational wave spectrum showing the location in phase space of the pulsar timingLiving Reviews array in( PTA Relativity ) and its extension with the Square Kilometre Array ( SKA ) . Figure updated by Michael Kramerht tp : slash [ 1 slash9 8 w] w from .. w periodan original l i vi ngrev design i e w s periodby Richard org slash Battye lrr hyphen . 2008 hyphen 8 \ [ \ r u l e {3em}{0.4 pt }\ ] Living Reviews in Relativity ht tp : / / w w w . l i vi ngrev i e w s . org / lrr - 2008 - 8

\ hspace ∗{\ f i l l } Living Reviews in Relativity

\ hspace ∗{\ f i l l } ht tp : / / w w \quad w. l i vi ngrev i ews . org / lrr − 2008 − 8 52 ....52 Duncan R period Lorimer Duncan R . Lorimer \noindenthline 52 \ h f i l l Duncan R . Lorimer relativity discussed in Section 4 period 4 comma along with further effects comma are reviewed elsewhere in this journal \ [ by\ r Will u l e { open3em}{ square0.4 pt bracket}\ ] 4 0 0 closing square bracket and Stairs open square bracket 3 4 4 closing square bracket period A recent review by Kramerrelativity ampersand discussed Stairs in Section open square 4 . 4 bracket , along with 2 0 0 further closing effects square ,bracket are reviewed provides elsewhere a detailed in this account journal by Will of the[ 4 double 0 0 ] and pulsar Stairs period [ 3 4 Further 4 ] . A recent discussions review on by the Kramer realities & of Stairs using [ 2pulsars 0 0 ] provides as gravity a detailedwave detectors account of the \noindentcandouble be foundrelativity pulsar in other . Further review discussed discussions articles open inon the square Section realities bracket 4 of . using 3 4 2 3 , pulsars comma along as .. with 1gravity 4 comma further wave 1 detectors4 3 closingeffects can square be , found are bracket reviewed in period elsewhere in this journal byhline Willother [ review 4 0 articles 0 ] and [ 3 2 Stairs 3 , 1 4 [ , 31 4 4 3 4 ] . ] . A recent review by Kramer $ \& $ Stairs [ 2 0 0 ] provides a detailed account ofLiving the Reviews double in pulsar Relativity . Further discussions on the realities of using pulsars as gravity wave detectors canht tp be : slash found slash in w other w w period review l i vi articles ngre v i e w [ s period3 2 3 or , g\ slashquad lrr1 hyphen 4 , 1 2008 4 3 hyphen ] . 8 \ [ \ r uLiving l e {3em Reviews}{0.4 in pt Relativity}\ ] ht tp : / / w w w . l i vi ngre v i e w s . or g / lrr - 2008 - 8

\noindent Living Reviews in Relativity

\noindent http : //www. l i vi ngrev i ews . org/ lrr − 2008 − 8 BinaryBinary and and Millisecond Millisecond Pulsars Pulsars .... 53 53 \noindenthline Binary and Millisecond Pulsars \ h f i l l 53 5 .. Summary .. and .. Future .. Prospects \ [ The\ r u main l e {3em aim}{ of0.4 this pt article}\ ] was to review some of the many astrophysical applications provided by the5 present Summary sample of binary and and millisecond Future radio pulsars Prospects that are relevant to gravitational physicsThe period main aim The of topics this article covered was here to review comma some along of with the many the bibliography astrophysical and applications associated provided tables of by observational the present \noindentparameterssample5 of comma\ binaryquad should andSummary millisecond be useful\quad to radio thoseand pulsars wishing\quad that toFuture are delve relevant deeper\quad to into gravitationalProspects the vast body physics of literature . The topics that covered existshere period , along with the bibliography and associated tables of observational parameters , should be useful to those \noindentThroughwishing anThe to understanding delve main deeper aim of into of the thethis Galactic vast article body population of literature was of to radio that review pulsars exists some summarised. of the in many Section astrophysical 3 applications provided byit isthe possibleThrough present to predict an sample understanding the detection of binary of the statistics Galactic and of millisecond population terrestrial gravitational of radio radio pulsars pulsars wave summarised detectors that in to are Section nearby relevant 3 it is possible to gravitational physicsrapidlyto predict spinning . The the neutron topics detection stars covered statistics open parenthesis of here terrestrial , along see gravitational Section with 3 period the wave bibliography detectors 3 closing to parenthesis nearby and rapidly comma associated spinning as well neutron as tables coalescing of relativistic observational binaries atparameters cosmicstars ( see , Section should 3 . be 3 ) ,useful as well as to coalescing those wishing relativistic to binaries delve at cosmic deeper into the vast body of literature that e xdist i s tdist ances s . ances open ( parenthesis see Section see 3 Section . 4 ) . .. 3 Continued period 4 closing improvements parenthesis in gravitational period .. Continued wave detector improvements sensitivities in gravitational wave detector sensitivitiesshould result in a number of interesting developments and contributions in this area . These devel - opments Throughshouldand result an contributions understanding in a number might of includeinteresting of the the developments Galactic detection of population presently and contributions known of radio radio in this pulsars area pulsars period, as well summarised These as a devel population hyphen in Section of 3 itopments iscoalescing possible and contributions binary to systems predict might which theinclude have detection notthe detectionyet been statistics detected of presently as radio knownof terrestrial pulsars radio . pulsars gravitationalcomma as well wave detectors to nearby rapidlyas a population spinning ofThe coalescing neutron phenomenal binary stars timing systems ( stability see which Section of have radio not 3pulsars yet . been 3 leads ) detected , naturally as well as radio to as a largepulsars coalescing number period of relativistic applica - binaries at cosmic Thet phenomenal ions , including timing their stability use as oflaboratories radio pulsars for relativisticleads naturally gravity to a (large see Section number 4 .of 5 applica ) , constraining hyphen the \noindentt ionsequation commadist of including st ances ate of their superdense ( see use asSection matter laboratories (\ seequad Sectionfor relativistic3 . 4 4 . 6 ) ) gravity.and\quad as natural openContinued parenthesis detectors improvements ofsee gravitational Section 4 period in 5 gravitational closing parenthesis wave comma detector sensitivities constrainingshouldradiation result the ( see in Section a number 4 . 7 of ) . interesting Long - term timing developments experiments and of the contributions present sample of in millisecond this area and . These devel − opmentsequationbinary and of pulsars st ate contributions of currently superdense underway matter might appearopen include parenthesis to have the tremendous see detection Section potential 4 period of presently 6 in closing these parenthesisareas known and may radio anddetect as natural pulsars the detectors , as of well gravitational asradiation agravitational population open parenthesis wave of background coalescing see Section ( if it binary .. exists 4 period ) systemswithin 7 closing the which next parenthesis decade have . period not yet .. Long been hyphen detected term timing as radio experiments pulsars of the . present sample of millisecondThese applications will benefit greatly from the continuing discovery of new systems by the present gen- \ hspaceanderation binary∗{\ f ofpulsars i l radio l }The currently pulsar phenomenal searches underway which timing appear continue to stability have to probe tremendous new of areasradio potential of pulsarsparameter in these leadsspace areas . and Based naturally on the toresults a large number of applica − maypresented detect the in gravitational Section 3 wave. 3 , backgroundit is clear that open we parenthesis are aware ofif it only exists a few closing per parenthesiscent of the totalwithin active the next pulsar decade period \noindentThesepopulation applicationst ions in our will , Galaxy including benefit . greatly In all their likelihood from the use ,continuing then as laboratories , we discovery have not seen of new for all systems of relativistic the pulsar by the zoo . gravity The current ( seeand Section 4 . 5 ) , constraining the presentfutures generation surveys of described radio pulsar in Section searches 2 . which 1 1 will continue ultimately to probe provide new a far areas more ofparameter complete census space ofperiod the Galactic \noindentBasedpulsar on theequation population results presented . of Three st possible atein Section of “ superdenseholy .. 3 grails period ” 3 of comma matter pulsar it astronomy is( clear see that Section which we could are 4 aware soon . 6 of be ) only andfound a as few are naturalper : cent detectors of gravitational of theAn total X - active ray / pulsar radio population millisecond in ourpulsar GalaxyWhile period the In link all between likelihood millisecond comma then pulsars comma and we X - have ray bi not - seen all of \noindentthe pulsarnariesradiation zoo appears period Theto ( be current see compelling Section and futures, despite\quad surveys intensive4 . described 7 searches ) . in\quad [ Section 4 7 ] ,Long no 2 radioperiod− term pulsations 1 1 will timing ultimately have been experiments provide detected a of the present sample of millisecond andfar moreinbinary these complete binaries pulsars census . currently This of the could Galactic be underway a result pulsar of population freeappear - free toperiod absorption have Three tremendous of possible any radio quotedblleft waves potential by the holy thick in grailsthese accretion quotedblright areasand of pulsar mayastronomydisk detect , or which perhaps the could gravitational quenching soon be of found the acceleratingwave are : background potential in( the if neutron it exists star magnetosphere ) within the by infalling next decade matter . An. X hyphen The recent ray slash discovery radio of millisecond radio pulsations pulsar from While two the magnetars link between [ 6 2 millisecond , 6 1 ] demonstrates pulsars and that X hyphenradio emission ray bi hyphen Thesenariescan applications appears be found to inbe seemingly compelling will benefit unlikely comma sites despite greatly . intensive from searches the continuing open square bracket discovery 4 7 closing of new square systems bracket comma by the no radio pulsations havepresent been A generation millisecond pulsar of radioin transition pulsar between searches an X - ray which and radio continue phase would to probe be another new suchareas remarkable of parameter space . Baseddetecteddiscovery on in the these . results binaries period presented .. This incould Section be a result\quad of free3 hyphen . 3 , free it absorption is clear of thatany radio we waves are aware of only a few per cent ofby the theA pulsar thick total accretion – active black disk hole pulsar comma binary populationor perhapssystem quenching : inFollowing our of Galaxythe the accelerating wide . In variety allpotential of likelihood science in the possible neutron , fromthen the , wenew have not seen all of thestardouble pulsar magnetosphere pulsar zoo J . 737 by The infalling− 3039( current matter see Sections and period futures 2 .. . 6 The , recent surveys3 . 4 . discovery 1 described and of4 . radio 4 ) , pulsationsin a radio Section pulsar from 2with two . a1 black 1 will - hole ultimately provide a farmagnetars morecompanion complete open would square without census bracket doubt 6 of 2 comma the be a Galactic fantastic 6 1 closing gravitational pulsar square bracket population laboratory demonstrates . . Excellent Three that radio places possible emission to look ‘‘ can for holy be such found grails in seemingly ’’ of unlikely pulsar sitesastronomy periodsystems which are globular could clusters soon and be the found Galactic are centre : [ 2 9 6 ] . A millisecondA sub - millisecond pulsar in transition pulsar between: The an most X hyphen rapidly ray spinning and radio radio phase pulsar would currently be another known such is the 1 . 39 - ms \noindentremarkablePSR JAn 1748 discovery X−−2446ray period ad / in radio Terzan millisecond 5 [ 1 4 0 ] . pulsar Do neutron While stars the with link kHz between spin rates exist millisecond ? pulsars and X − ray bi − A pulsar endashSearches black hole now binary have system sensitivity : .. Followingto such objects the wide [ 4 6 variety ] and aof discovery science possible of even from one would the constrain nariesnew double appears pulsarthe to equation J be 737 compelling minus of state 3039 of open matter , despite parenthesis at high densitiesintensive see Sections . As searches 2 mentioned period 6 [ comma in 4 Section 7 ].. ,3 2 periodno . 2 ,radio the 4period R - pulsations mode 1 .. and 4 have period been 4 closing parenthesisdetectedinstability comma in these a may radio prevent binaries pulsar neutron with . a\ black starsquadhyphen fromThis reaching could such be high a resultspin rates of [ 3 8 free , 6− 6 ] .free Of course absorption , this does of any radio waves byhole thenot companion stopthick observers accretion would from without looking disk doubt for , be orsuch a fantastic perhaps objects !gravitational The quenching current laboratory generation of the period acceleratingof surveys Excellent summarized places potential in Section in 2 the neutron starto look. magnetosphere 1 1 for such continues systems toby be are more infallingglobular and moreclusters matter sensitive and the . to Galactic\ thisquad putativeThe centre recent source open squarepopulation discovery bracket . 2 of 9 6 radio closingpulsations square bracket from period two magnetarsA sub hyphen [ 6millisecond 2 , 6 1 pulsar ] demonstrates : .. The most rapidly that spinning radio emission radio pulsar can currently be found known inis the seemingly 1 period 39 unlikely hyphen sites . ms PSR J 1 748 minus 2446 ad in Terzan 5 .. open square bracket 1 .. 4 0 closing square bracket period .. Do neutron stars with kHz spin Arates millisecond exist ? pulsar in transition between an X − ray and radio phase would be another such remarkable discovery . Living Reviews in Relativity Searches now have sensitivityht to such tp : objects / / w open w square w . bracket l i vi 4 ngrev 6 closing i e square w s . bracket org / and lrr a discovery- 2008 - of 8 even one would constrain the equation of state of matter at high densities period .. As mentioned in Section 2 period 2 comma the R hyphen mode \noindentinstabilityA may p u prevent l s a r −− neutronblack stars hole from binary reachingsystem such high : spin\quad rates openFollowing square bracket the wide 3 8 comma variety .. 6 6 of closing science square bracketpossible period from the Ofnew course double comma pulsar J $ 737 − 3039 ( $ see Sections 2 . 6 , \quad 3 . 4 . 1 \quad and 4 . 4 ) , a radio pulsar with a black − holethis does companion not stop observerswould without from looking doubt for such be a objects fantastic ! The current gravitational generation of laboratory surveys . Excellent places tosummarized look for in such Section systems 2 period 1are 1 .. globular continues to clusters be more and and more the sensitive Galactic to this centre putative [source 2 9 6 ] . population period \noindenthline A sub − millisecond pulsar : \quad The most rapidly spinning radio pulsar currently known is the 1 . 39 − msPSRJLiving Reviews $1 in Relativity 748 − 2446 $ ad in Terzan 5 \quad [ 1 \quad 4 0 ] . \quad Do neutron stars with kHz spin rates exist $ ?ht $ tp : slash slash w w .. w period l i vi ngrev i e w s period org slash lrr hyphen 2008 hyphen 8 \ hspace ∗{\ f i l l } Searches now have sensitivity to such objects [ 4 6 ] and a discovery of even one would constrain

\ hspace ∗{\ f i l l } the equation of state of matter at high densities . \quad As mentioned in Section 2 . 2 , the R − mode

instability may prevent neutron stars from reaching such high spin rates [ 3 8 , \quad 6 6 ] . Of course , this does not stop observers from looking for such objects ! The current generation of surveys summarized in Section 2 . 1 1 \quad continues to be more and more sensitive to this putative source population .

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\ hspace ∗{\ f i l l } ht tp : / / w w \quad w. l i vi ngrev i ews . org / lrr − 2008 − 8 54 ....54 Duncan R period Lorimer Duncan R . Lorimer \noindenthline 54 \ h f i l l Duncan R . Lorimer The discovery of the eccentric millisecond binary pulsar J 1 903 plus 327 open square bracket 7 0 closing square bracket open parenthesis see\ [ Sections\ r u l e {3em 2 period}{0.4 9 ptand}\ 4 period] 6 closing parenthesis wasThe completely discovery unprecedented of the eccentric within millisecond the framework binary of pulsar our theories J 1903 for + 327[70](binary pulsar see Sections formation 2 . period 9 and 4 . 6 ) It thereforewas completely serves as unprecedented a stark reminder within that the we framework should quotedblleft of our theories expect for the binary unexpected pulsar formation quotedblright . It therefore ! Even though the \noindentstudyserves of radio asThe a pulsarsstark discovery reminder is now 40of that years the we shouldold eccentric comma “ expect these millisecond the experiences unexpected tell binary ” us ! Even that pulsar thoughmany exciting the J study $ discoveries 1 of radio 903 pulsars + 327 [ 7 0 ]lie ($ aheadis now see of 40 us years Sections period old , these 2 . experiences 9and4 tell . 6) us that many exciting discoveries lie ahead of us . wasPulsar completelyPulsar astronomy astronomy remains unprecedented remains an extremely an extremely within active area the active of framework modernarea of modern astrophysics of ourastrophysics and theories the and next the for decade next binary decade pulsar will un- formation . Itwill thereforedoubtedly undoubtedly continue serves continue to as produce to producea stark new new results reminder results from from currently that currently we known should known objects objects ‘‘ as expect well as aswell new the as surprisesnew unexpected . Although ’’ ! Even though the studysurprisesit is of often period radio stated .. pulsarsAlthough that we it are is is bound oftennow 40stated byyears available that we old computational are , bound these by experiencesresources availablecomputational , in my tell opinion us resources , thatpulsar many research comma exciting in is discoveries liemy aheadcurrentlyopinion commaof limited us pulsar . by a shortage research of is researcherscurrently limited , and not by a necessarily shortage of computational researchers comma resources and . not Keen necessarily students computationalmore than ever resources are needed period to .. help Keen shape students the futuremore than of this ever exciting are needed and continually to help shape evolving the future field of. Pulsarthis exciting astronomy and continually remains evolving an extremely field period active area of modern astrophysics and the next decade willhline undoubtedly continue to produce new results from currently known objects as well as new s u r p r i s e s . \quad Although it is often stated that we are bound by available computational resources , in LivingLiving Reviews Reviews in Relativity in Relativity myht opinion tp : slash slash , pulsar w w w researchperiod l i vi is ngre currently v i e w s period limited or g slash by lrr a hyphen shortage 2008 of hyphen researchers 8 , and not necessarily computationalht tp : / / resources w w w . l . i\ viquad ngreKeen v i students e w s . or more g / than lrr - ever 2008 -are 8 needed to help shape the future of this exciting and continually evolving field .

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\noindent http : //www. l i vi ngrev i ews . org/ lrr − 2008 − 8 BinaryBinary and and Millisecond Millisecond Pulsars Pulsars .... 55 55 \noindenthline Binary and Millisecond Pulsars \ h f i l l 55 6 .. Acknowledgements \ [ Many\ r u l ethanks{3em}{ to0.4 Chunglee pt }\ Kim] and Evan Kean who read and provided very useful comments on this6 revised Acknowledgements review comma .. and to Scott Ransom and Matthew Bailes for providing unpublished data givenMany in Table thanks .. 4 to period Chunglee .. I am Kim indebted and Evan to Keana number who of read colleagues and provided who comma very useful as noted comments in many on of this the revised figure \noindentcaptionsreview comma6 ,\quad and kindly toAcknowledgements Scott gave Ransom permission and to Matthew use their Bailes figures for in providing this article unpublished period .. Frequent data given use in was Table made 4 of . I NASAam quoterightindebted to s a magnificent number of colleagues Astrophysics who Data , as notedSystem in open many square of the bracket figure captions 1 3 4 closing , kindly square gave permission bracket comma the arXiv e hyphen print\noindent serviceto use openMany their square figures thanks bracket in this to article8 Chunglee 6 closing . Frequent square Kim andbracket use Evan was and made Kean of course of who read and provided very useful comments on thistheNASA .. revised Google ’ s magnificentduring review the literature , Astrophysics\quad searchesand Data to period System Scott .. [My Ransom 1 3 research 4 ] , the and is arXiv partially Matthew e - print supported Bailes service by [ for 8 West 6 ] providing and Virginia of course unpublished data givenEPSCoRthe in throughGoogle Table during a\quad Research the4 literature Challenge. \quad searches GrantI am period indebted . My .. research Finally to a comma is numberpartially I would supported of like colleagues to by thank West the whoVirginia Living , as EPSCoR Reviews noted in many of the figure captionseditorsthrough for , their a kindly Research support gave Challenge and patience permission Grant during . to Finally the use completion , theirI would of figureslike this to long thank hyphen in the thisLiving overdue article Reviews update . editors period\quad forFrequent their use was made of hlinesupport and patience during the completion of this long - overdue update . \noindentLiving ReviewsNASA in ’ Relativity s magnificent Astrophysics Data System [ 1 3 4 ] , the arXiv e − print service [ 8 6 ] and of course ht tp : slash slash w w .. w period l i vi ngrev i e w s period org slash lrr hyphen 2008 hyphen 8 \noindent the \quad Google during the literature searches . \quad My research is partially supported by West Virginia EPSCoR through a Research Challenge Grant . \quad Finally , I wouldLiving Reviews like to in thankRelativity the Living Reviews editors for their supportht tp and : patience / / w w during w . l thei vi completion ngrev i e w sof . this org /long lrr− - 2008overdue - 8 update .

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\ hspace ∗{\ f i l l } ht tp : / / w w \quad w. l i vi ngrev i ews . org / lrr − 2008 − 8 56 ....56 Duncan R period Lorimer Duncan R . Lorimer \noindenthline 56 \ h f i l l Duncan R . Lorimer A .. Tables .. of Binary .. and .. Millisecond .. Pulsars \ [ Table\ r u l e2{ :3em Parameters}{0.4 pt for}\ the] 20 isolated millisecond pulsars currently known in the Galactic disk period Four of theA pulsars open Tables parenthesis of J 609 Binary plus 2 1 30 comma and J 1 38 Millisecond plus 32 comma J 1 753 Pulsars minus 1 9 1 4 and J 2235 plus 1 506 closing parenthesis are thoughtTable to 2 be : theParameters descendants for the 20 isolated millisecond pulsars currently known in the Galactic disk . Four of the \noindentof highpulsars hyphenA ( J\quad609 mass + binaryTables 2130, J systems138\quad + period32,o fJ Binary1753 .. Listed− 1914\ arequadand the Jspinand2235 period\quad + 1506) PMillisecond commaare thought the base to\ be hyphenquad the descendantsPulsars 1 0 logarithms of of the characteristic agehigh tau sub - mass c and binary surface systems magnetic . Listed field strength are the spin B open period parenthesisP, the base see - Section 1 0 logarithms 2 period of 2 the closing characteristic parenthesis age commaτc the distance d derived from\noindent theand Cordes surfaceTable magnetic 2 : field Parameters strength B( forsee Section the 20 2 . isolated 2 ) , the distance millisecondd derived from pulsars the Cordes currently& Lasio electron known in the Galactic disk . Four of thepulsars(J $609 + 2 1 30 ,$ J $1 38 + 32 ,$ J $1 753 − 1 9 1 ampersanddensity model Lasio [ electron 8 4 , 8 density 5 ] or independently model open square( when availablebracket 8 ) ,4 and comma the transverse .. 8 5 closing speed squarevt inferred bracket from ord independentlyand a open parenthesis when4 $ available andproper J motion closing $ 2235 measurement parenthesis + ( 1 comma when 506 available and the ) ) .$ transverse Key are publications thought speed v for sub toeach t be pulsar the are descendants referenced to the bibliography . o finferred high from− mass d and binary a proper systems motion measurement . \quad Listed open parenthesis are the when spin available period closing $ P parenthesis , $ the period base Key− publications1 0 logarithms for each of the characteristic pulsarage are $ \tau { c }$ and surface magnetic field strength $ B ( $ see Section 2 . 2 ) , the distance $ d $ derived from the Cordes referenced to the bibliography period P log τc log B d vt Refs. $ \& $ Lasio electronPSR densityline − line model [ 8 4 , \quad 8 5 ] or independently ( when available ) , and the transverse speed Line 1 hline Line 2 PSR Case 1 P log tau sub c[ms] log B [log(yr)] d v sub t [log(G)] Refs period [kpc] Case [km 2/ opens] square bracket ms closing square bracket open square$ v { brackett }$ log open parenthesis yr closing parenthesis closing square bracket open square bracket log open parenthesis G closing parenthesis closinginferred square from bracket $ open d $ square and bracket a proper kp c closing motion square measurement bracket open ( square when bracket available km slash ) s . closing Key publications square bracket Line for 3hline each pulsar are referencedTable ignored! to the bibliography . Line 1 hline Line 2 hline Table ignored! \ [ \Livingbegin Reviews{ a l i g n e in d Relativity}\ r u l e {3em}{0.4 pt }\\ \ lht e f tp t . : slashPSR slash l i n e w− wl iw n e period\ begin l i{ via l ngre i g n e v d i} e&P w s period\ orlog g slash\ lrrtau hyphen{ c 2008}\ hyphenlog 8 B d v { t } Refs . \\ & [ ms ] [ \ log ( yr ) ] [ \ log (G) ] [kpc ] [km/ s ] \end{ a l i g n e d }\ right . \\ \ r u l e {3em}{0.4 pt }\end{ a l i g n e d }\ ] Living Reviews in Relativity ht tp : / / w w w . l i vi ngre v i e w s . or g / lrr - 2008 - 8

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\noindent http : //www. l i vi ngrev i ews . org/ lrr − 2008 − 8 BinaryBinary and and Millisecond Millisecond Pulsars Pulsars .... 57 57 \noindentLine 1 hlineBinary Line 2 hline and Millisecond Pulsars \ h f i l l 57 Living Reviews in Relativity \ [ \htbegin tp : slash{ a l i g slash n e d }\ w wr .. u wl e period{3em}{ l i0.4 vi ptngrev}\\ i e w s period org slash lrr hyphen 2008 hyphen 8 \ r u l e {3em}{0.4 pt }\end{ a l i g n e d }\ ] Living Reviews in Relativity ht tp : / / w w w . l i vi ngrev i e w s . org / lrr - 2008 - 8 \ hspace ∗{\ f i l l } Living Reviews in Relativity

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\noindent http : //www. l i vi ngrev i ews . org/ lrr − 2008 − 8 BinaryBinary and and Millisecond Millisecond Pulsars Pulsars .... 59 59 \noindentLine 1 hlineBinary Line 2 hline and Millisecond Pulsars \ h f i l l 59 Living Reviews in Relativity \ [ \htbegin tp : slash{ a l i g slash n e d }\ w wr .. u wl e period{3em}{ l i0.4 vi ptngrev}\\ i e w s period org slash lrr hyphen 2008 hyphen 8 \ r u l e {3em}{0.4 pt }\end{ a l i g n e d }\ ] Living Reviews in Relativity ht tp : / / w w w . l i vi ngrev i e w s . org / lrr - 2008 - 8 \ hspace ∗{\ f i l l } Living Reviews in Relativity

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\noindent http : //www. l i vi ngrev i ews . org/ lrr − 2008 − 8 BinaryBinary and and Millisecond Millisecond Pulsars Pulsars .... 6 1 6 1 \noindenthline Binary and Millisecond Pulsars \ h f i l l 6 1 References \ [ open\ r u l square e {3em bracket}{0.4 pt 1}\ closing] square bracket .. Allan comma D period W period comma .. quotedblleft The Allan Variance quotedblright commaReferences personal homepage comma Allan quoteright s Time Interval Metrology Enterprises[ 1 ] period Allan URL , D . open W . , parenthesis “ The Allan cited Variance on 7 December ” , personal 2000 homepage closing parenthesis , Allan ’ s : Time Interval Metrology \noindentht t p : slashReferences slash w w w periodEnterprises alla n s t i me. URL period ( cited c om on slash 7 December A l lan Var 2000 iance ) : slash period .. 4 period 3 open squareht bracket t p :2 closing / / w square w w . bracket alla .. n Alpar s t i comma me . M c period om / A A period l lan comma Var iance Cheng / comma. 4 . A 3 period F period comma Ruderman comma\ hspace M∗{\ period[ 2f ] i l A lAlpar} period[ 1 , M ] comma .\quad A . , and ChengAllan Shaham , A ,D . F comma . .W. , Ruderman J period , \quad , comma M . A‘‘ . quotedblleft , The and Shaham Allan A newVariance , J . class , “ A of new radio ’’ class , Case personal of radio 1 quotedblright homepage Case , 2 Allan comma ’ s Time Interval Metrology 00 Nature comma 300 comma 728 endash 730 comma open parenthesis 1 982 closing parenthesis period .. 2 period 6 comma .. 2 period 6 \ centerlinepulsars{ Enterprises . URL ( cited on 7 December 2000 ) : } comma .. 2 period, 6 period 2 open square bracket 3 closingNature square, 300 bracket, 728 – .. 730 Alpar , ( 1 comma 982 ) . M 2period . 6 , A 2 period . 6 , comma 2 . 6 . Nandkumar 2 comma R period comma and Pines \ centerline { ht t p : //www. alla n s t i me . com/Al lan Var iance / . \quad 4 . 3 } comma D period comma[ 3 ] .. quotedblleft Alpar , M . AVortex . , Nandkumar Creep and , the R . Internal , and Pines Temperature , D . , “ Vortex Creep and the Internal of NeutronTemperature Stars : Timing Noise of Pulsars quotedblright comma Astrophys period J period comma 3 1 1 comma 1 97 endash 2 1 3 comma \ hspace ∗{\ f i l l } [ 2 ] \quad Alpar ,M . A . , Cheng , A . F . , Ruderman ,M . A . , and Shaham , J . , ‘‘ Anew class of radio open parenthesisof Neutron 1 986 Stars closing : Timing parenthesis Noise of period Pulsars .. ”4 ,periodAstrophys 3 . J . , 3 1 1 , 1 97 – 2 1 3 , ( 1 986 ) . 4 . 3 $\ l e f t . p u l s a r s \ begin { a l i g n e d } &’’ \\ open square[ 4 ] bracket Anderson 4 closing , S . B square . , Gorham bracket , P .. . W Anderson . , Kulkarni comma , S S. R period . , Prince B period , T . Acomma . , and Gorham Wolszczan comma , A . P , period W period comma &, \end{ a l i g n e d }\ right . $ Kulkarni“ Discovery comma S period R period comma Prince comma T period A period comma and Wolszczan comma A period comma .. quotedblleft Discovery of two radio pulsars in the globular cluster M 1 5 ” , Nature , 346 , 42 – 44 , ( 1 990 ) . 3 . 1 . 3 \ centerline { Nature , 300 , 728 −− 730 , ( 1 982 ) . \quad 2 . 6 , \quad 2 . 6 , \quad 2 . 6 . 2 } of two radio[ 5 ] pulsars Andersson in the globular, N . , cluster Jones M , 15 D quotedblright . I . , Kokkotas comma , Nature K . D . comma , and 346 Stergioulas comma 42 , endash N . , 44 “ comma open parenthesis 1 990 closingr− Mode parenthesis runaway period and 3 period 1 period 3 \ hspace ∗{\ f i l l } [ 3 ] \quad Alpar ,M . A . , Nandkumar , R . , and Pines , D . , \quad ‘‘ Vortex Creep and the Internal Temperature open square bracketrapidly rotating5 closing neutron square bracketstars ” , ..Astrophys Andersson . J comma . Lett . .., N534 period, L 75 comma – L 78 .. , Jones( 2000 comma ) . .. D period I period comma .. KokkotasADS :commahttp : .. K / period / adsabs D period.h commav ard .. . and edu Stergioulas / abs / comma2000 A .. p N J period . . . comma 534 ..L quotedblleft. . 7 5 A r. hyphen 2 . 2 Mode runaway and \ centerline { of Neutron Starsa−r : Timing Noise of Pulsars ’’ , Astrophys . J . , 3 1 1 , 1 97 −− 213 ,(1986) . \quad 4 . 3 } rapidly rotating[ 6 ] neutron Arzoumanian stars quotedblright , Z . , Chernoff comma , D . F Astrophys . , and Cordes period , J period. M . , Lett “ The period Velocity comma Distribution 534 comma of L 75 endash L 78 comma open parenthesisIsolated 2000 closing parenthesis period \ hspace ∗{\ f i l l } [ 4 ] \quad Anderson , S . B . , Gorham , P .W. , Kulkarni , S . R . , Prince , T . A . , and Wolszczan , A . , \quad ‘‘ Discovery ADS : http : slash slashRadio adsabs Pulsars period ” h , subAstrophys a-r v ard . J period . , 568 edu,slash 289 – abs 301 slash , ( 2002 2000 ) .A p 2 J period period period 534 L period period 7 5 A period .. 2 period[ 7 ] 2 Arzoumanian , Z . , Cordes , J . M . , and Wasserman , I . , “ Pulsar Spin Evolution , \ centerline { of two radio pulsars in the globular cluster M1 5 ’’ , Nature , 346 , 42 −− 44 ,(1990).3.1.3 } openKinematics square bracket , 6 closing square bracket .. Arzoumanian comma Z period comma Chernoff comma D period F period comma and Cordes commaand the J period Birthrate M period of Neutron comma Star .. quotedblleftBinaries ” , Astrophys The Velocity . J Distribution . , 520 , 696 of – Isolated 705 , ( 1 999 ) . 3 . 4 . 1 \ hspace ∗{\ f i l l } [ 5 ] \quad Andersson , \quad N., \quad Jones , \quad D.I., \quad Kokkotas , \quad K.D., \quad and Stergioulas , \quad N., \quad ‘‘ Radio Pulsars[ 8 ] Arzoumanianquotedblright , comma Z . , Astrophys Fruchter period , A .J S period . , and comma Taylor 568 , comma J . 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URL ( cited on 23 May ADS : .. http : slash slash ad s abs period h sub a-r v ard period edu slash a bs slash 1 9 94 ApJ period period period 422 period period 67\ hspace 1 A period∗{\ f .. i l4 l period} [ 8 3 ] \quad Arzoumanian , \quad Z., \quad Fruchter , \quad A.S., \quad and Taylor , \quad J.H., \quad ‘‘ Orbital Variability in the Eclipsing 2008) : open square bracket 1 0 closing square bracket .. ASTRON comma quotedblleft The European Pulsar Timing Array quotedblright comma \ centerline { Pulsar BinaryPSRB $ 1 957 + 20 $ ’’ , Astrophys . J . Lett . , 426 , L85 −− L88 , (1994) . \quad 4 } projectht homepage t p : / period / w w URL w . open at parenthesis nf . c s cited ir o on . 24 au June / r e s earch / pul s a − r/ psrcat / . 2 . 2 2008 closing parenthesis : 00 \ hspace ∗{\[ 1 3f ]i l l Australia} [ 9 ] \ Telescopequad Arzoumanian National Facility , Z , “ . ATNF , Nice Pulsar ,DGroup . J .project , Taylorhomepage , J . . URL H . ( ,cited and Thorsett , S . 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R. comma D ., Astron45 Kramer, 3447 . comma – Soc 3468 . , M ( , 1 period 368 992 ) , comma . 283 4 .−− 7 Camilo . 1292 comma ,(2006).2.11.2,2.11.3, F period comma and Freire comma P period C \quad 2 , \quad 4 00 period C period comma .. quotedblleft The Parkes High hyphen Latitude pulsar [ 50 ] \[quad 5 1 ]Caldwell California Institute , R . R of . Technology , and Allen , “ Laser , B Interferometric . , \quad Gravitational‘‘ Cosmological Wave Observatory constraints on cosmic − string gravitational ra − survey quotedblright comma Mon period Not period R period Astron period Soc period comma 368 comma 283, endash 292 comma open diation ’’ , Phys . Rev . D , 45 , 3447 −− 3468 , ( 1 992 ) . \quad 4 . 7 . 1 parenthesisproject 2006 homepage closing parenthesis . URL ( cited period on 29 2 period January 1 1 2005 period ) : 2 comma 2 period 1 1 period 3 comma .. 2 comma .. 4 open square bracket 50h closing t tp : square / / bracket w w w .. . 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California Institute of Technology comma quotedblleft Laser Interferometric Gravitational Wave CaseWalker 1 quotedblright , M . A . Case, and 2 Bailes comma , M . , eds . , Pulsars : Problems and Progress ( IA U Colloquium 1 60 ) , \ centerline {http://www. l igo .caltech.edu. \quad 3 . 4 } projectProceedings homepage of period the 1 60 URL th Colloquium open parenthesis of the cited IAU on , held 29 January at the Research 2005 closing Centre parenthesis for Theoretical : Astrophysics h t, tp University : slash slash of Sydney w w w ,period Australia l igo , period 8 – 1 2 c January al t e ch 1 period996 , ASP e du Conference period .. 3 Series period , vol4 . 1 5 , pp . 539 – 540 [ 52 ] \quad Camilo , F . , A Search for Millis econd Pulsars , Ph . D . Thesis , ( Princeton University , Princeton , open, ( square Astronomical bracket Society 52 closing of the square Pacific bracket , San .. Francisco Camilo comma , U . S .F A period . , 1 996 comma ) . 2 A . 7 Search for Millis econd Pulsars comma Ph period D U.S.A. ,1995). \quad 4 period Thesis[ 54 comma ] Camilo open , parenthesis F . , “ Deep Princeton Searches forUniversity Young Pulsars comma ” Princeton , in Bailes comma , M . , Nice , D . J . , and Thorsett U period, S . E S . period , eds . A , Radio period Pulsars comma : 1 In 995 Celebration closing parenthesis of the Contributions period .. 4 of Andrew Lyne , Dick Manchester and \ hspace ∗{\ f i l l } [ 53 ] \quad Camilo , F . , \quad ‘‘ Intermediate − Mass Binary Pulsars : a New Class of Objects openJoe square Taylor bracket – a Festschrift 53 closing Honoring square bracket Their .. 60 Camilo th Birthdays comma, F ASP period Conference comma .. Series quotedblleft , vol . 302 Intermediate , p . 1 45 hyphen , ( Mass Binary Pulsars $?$ ’’ , in Johnston ,S . , : a NewAstronomical Class of Objects Society ? quotedblright of the Pacific comma , San Francisco in Johnston , U comma . S . A . S , period 2003 ) comma . 2 . 1 1 . 5 Walker[ comma 55 ]M Camilo period , FA .period , Foster comma , R . and S . Bailes , and comma Wolszczan M period , A . , comma “ High eds - period precision comma timing Pulsars of PSR : Problems J and Progress open Walker , M . A . , and Bailes , M . , eds . , Pulsars : Problems and Progress ( IA U Colloquium 1 60 ) , parenthesis1713 IA + 747 U Colloquium : Shapiro delay 1 60 ” closing , Astrophys parenthesis . J . Lett comma . , 437 , L 39 – L 42 , ( 1 994 ) . 4 Proceedings of the 1 60 th Colloquium of the IAU , held at the Research Centre for Theoretical Proceedings[ 56 ] of theCamilo 1 60 , th F .Colloquium , Lorimer , of D the . R IAU . , Freire comma , P held . C . at C the . , Lyne Research , A . Centre G . , and for ManchesterTheoretical , R . N . , Astrophysics , University of Sydney , Australia , 8 −− 1 2 January 1 996 , ASP Conference Series , Astrophysics“ Observations comma of University 20 millisecond of Sydney pulsars comma in 47 Tucanae Australia at comma 20 centimeters 8 endash ” 1 , 2 JanuaryAstrophys 1 996 . comma J . , ASP535 Conference, Series comma vol . 15 , pp . 539 −− 540 , ( Astronomical Society of the Pacific , San Francisco , U . S . A . , 1 996 ) . 2 . 7 vol period975 – 990 1 5 , comma ( 2000 pp) . period2 . 1 1 539 . 4 ,endash 3 . 1 . 540 3 , comma 3 . 1 .open 3 , parenthesis 3 . 2 . 3 Astronomical Society of the Pacific comma San Francisco comma U period S[period 57 ] Camilo A period , F comma . , Lyne 1 ,996 A . closing G . , Manchester parenthesis , Rperiod . N .2 , Bell period , J 7 . F . , Stairs , I . H . , D ’ Amico , N . , [ 54 ] \quad Camilo , F . , ‘‘ Deep Searches for Young Pulsars ’’ , in Bailes ,M . , Nice , D . J . , and Thorsett , S . E . , openKaspi square , V bracket . M . , 54 Possenti closing , square A . , bracket Crawford .. Camilo , F . comma , and F McKay period , comma N . P . quotedblleft F . , “ Discovery Deep Searches of five binary for Young Pulsars quotedblright commaeds . in , Bailes Radio comma Pulsars00 M period : In comma Celebration Nice comma of D period the Contributions J period comma and of Thorsett Andrew comma Lyne S , period Dick E Manchester period comma andeds Joeradio period Taylorpulsars comma−− RadioAstrophysa PulsarsFestschrift . : J In . CelebrationLett Honoring . , 548 of, the L Their 1 Contributions 87 – 60 L 1 th 9 1 Birthdays, of ( 200Andrew 1 ) . Lyne 2 , . ASP7 comma , 2 Conference . 1Dick 1 . 2Manchester , 4 Series , vol . 302 , p . 1 45 ,, ( Astronomical Society of the Pacific , San Francisco , U . S . A . , 2003 ) . \quad 2 . 1 1 . 5 and Joe[ 58Taylor ] Camilo endash , a F Festschrift . , Nice , D Honoring . J . , and Their Taylor 60 th , J Birthdays . 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Astron comma . 424 Soc comma . , 42364 endash, 1 44 0 1 comma 1 – 1 0 open 14 , parenthesis ( 2005 ) 2003 closing parenthesis M., \quad and Markwardt , \quad C.B., \quad ‘ ‘ Nuclear − powered millisecond pulsars and the maximum spin period. 2 Related period 2 online comma version .. 5 ( cited on 1 2 July 2008 ) : frequency of neutron stars ’’ , Nature , 424 , 42 −− 44 ,(2003) .2.2 , \quad 5 openh square t t pbracket : / 67/ arX closing i v square . o bracket r g / .. Champion ab s / ast comma r o .. - D ph period / 0 5 J period1 6 0 comma8 . 2 .. .quotedblleft 1 1 . 5 Latest timing results for PSR J 1 829[ 70 plus ] 2456 Champion quotedblright , D . J . comma , Ransom .. personal , S . M . communication , Lazarus , P . , comma Camilo , F . , Bassa , C . , Kaspi , V . M . [ 67 ] \quad Champion , \quad D.J., \quad ‘‘ Latest timing results for PSRJ $ 1 829 + 2456 $ open, Nice parenthesis , D . J .2005 , Freire closing , P .parenthesis C . C . , Stairs period , I .. . 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M . , Weis − system. quotedblright , Venkataraman comma , A . Mon , and period Vlemmings Not period , W . , “ An Eccentric Binary Millisecond Pulsar in the Galactic berg , J . , and Taylor , J . H . , ‘‘ PSRJ $ 1 829 + 2456 : $ a new relativistic binary system ’’ ,Mon . Not . R periodPlane Astron” , Science period, 805 Soc period, ( 2008 comma ) . Related 350 comma online version L 6 1 endash ( citedL on 65 28 comma October open 2008 parenthesis ) : 2004 closing parenthesis period .. 2 R . Astron . Soc . , 350 , L6 1 −− L65 , ( 2004 ) . \quad 2 . 1 1 . 3 , \quad 3 period 1 1 periodh t t 3 p comma : / /.. 3arXi v . org / abs / 805 . 2396 .2.9,2.11.2, 4.6, 5, 3 open square[ 71 ] bracket Chandler 69 closing , A . Msquare . , Pulsar bracket Searches .. Champion : From comma Radio D period to Gamma J period - Rays comma, Ph McLaughlin . D . Thesis comma , ( M period A period comma [ 69 ] \quad Champion , D . J . , McLaughlin ,M . A . , and Lorimer , D . R . , \quad ‘‘ A survey for pulsars in EGRET and LorimerCalifornia comma Institute D period of Technology R period comma , Pasadena .. quotedblleft , U . S . A A . survey , 2003 )for . pulsars 3 . 1 . in 3 EGRET error boxes ’’ , \quad Mon . Not . \quad R. \quad Astron . \quad Soc . , \quad 364 , \quad 1 0 1 1 −− 1 0 14 , \quad ( 2005 ) . Related online version error boxes[ 72 ] quotedblright Chatterjeecomma , S . , .. Mon Vlemmings period , Not W period . H ... T .R , period Brisken .. Astron , Wperiod . F . , .. Lazio Soc period , T .comma J . W .. 364 comma .. 1 0 1 1 ( cited on 1 2 July 2008 ) : endash. 1 , 0 14 Cordes comma , .. J open . M parenthesis . , Goss , 2005 W . closing M . , parenthesis Thorsett , period S . E Related . , Fomalont online , version E . B . , Lyne , A . 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J . , Lazarus comma[ 73 ] P Chaurasiaperiod comma , H .Camilo K . , and comma Bailes F period , M . , comma “ On Bassa the Eccentricities comma C period and Merger comma Rates Kaspi of comma Double V period M period comma Freire ,P . C . C . , Stairs , I . H . , van Leeuwen , J . , Stappers ,B .W. , Cordes , J .M. , Hessels , J .W. T . , Nice commaNeutron D period Star Binaries J period and comma the Creation of ‘ Double Supernovae ’ ” , Astrophys . J . , 632 , 1 54 Lorimer , D . R . , Arzoumanian , Z . , Backer , D . C . , Bhat , N . D . R . , Chatterjee , S . , Cognard , I . , Freire– 1 comma 59 , ( 2005 P period ) . Related C period online C period version comma ( cited Stairs on 1 comma2 July 2008 I period ) : H period comma van Leeuwen comma J period comma Stappers Deneva , J . S . , Faucher − Gigu $ \grave{e} $ re , C . − A. , Gaensler ,B.M. ,Han , J . 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URL pul( cited hyphen on 1 9 March 2001 ) : ht t p :sars / / quotedblright w w w . c comma olora Nuovo do . Cimento e du / geography B comma 10 / 1 g comma craft 1 / 27 n comma ote s open/ gp parenthesis s / gp s 1 988 closingf . parenthesis htm l . period 4 . 1 .. 4 period [ 92 ] \quad Damour , T . , and Taylor , J . H . , \quad ‘ ‘ Strong − field tests of relativistic gravity and binary 5 [ 94 ] Davis , M . M . , Taylor , J . H . , Weisberg , J . M . , and Backer , D . C . , “ High - precision $\ l e f t . p u l s a r s \ begin { a l i g n e d } &’’ \\ opentiming square obser bracket - 92 closing square bracket .. Damour comma T period comma and Taylor comma J period H period comma .. quotedblleft &, \end{ a l i g n e d }\ right . $ Strong hyphenvations field tests of the of millisecondrelativistic gravity pulsar PSR and binary 1937 + Case 21 ” 1, Nature quotedblright, 315 Case, 547 2 – comma 550 , ( 1 985 ) . 4 Phys . Rev . D , 45 , 1 840 −− 1868 , ( 1992 ) . \quad 4 . 4 Phys period[ 95 ] Rev Detweiler period D , S comma . L . , 45 “ comma Pulsar 1 timing 840 endash measurements 1 868 comma and the open search parenthesis for gravitational 1 992 closing waves parenthesis ” , As period .. 4 period 4 open- square trophys bracket . J . , 93234 closing, 1 1 square 0 – 1 1 bracket 4 , ( 1 979.. Dana ) . comma 4 . 7 , P period4 . 7 . H1 period comma quotedblleft The Global Positioning SystemRow \ hspace ∗{\ f i l l } [ 93 ] \quad Dana , P . H . , ‘‘ The Global Positioning $\ l e f t . System\ begin { array }{ c} ’’ \\ 1 quotedblright[ 96 ] Row Dewey 2 comma , R . J System . , and homepage Cordes , J comma . M . , “ Department Monte Carlo of simulations Geography of comma radio pulsars and their progen , \end{ array } p r o j e c t \ right .$ homepage , Department of Geography , University- itors ” of , ColoradoAstrophys at . 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C . , \quad ‘ ‘ High − precision timing obser − openRadio square Astronomy bracket 95 Observatory closing square , Green bracket Bank .. , Detweiler West Virginia comma , June S period 6 – 8 L , 1 period 984 , NRAOcomma Workshop .. quotedblleft , vol Pulsar. 8 timing measurements and the, searchpp . 234 for – gravitational 240 , ( National waves Radio quotedblright Astronomy comma Observatory As hyphen , Green Bank , \ centerline { vations of the millisecond pulsar PSR $ 1 937 + 2 1 $ ’’ , Nature , 315 , 547 −− 550 , ( 1 985 ) . \quad 4 } trophys period J period comma 234 commaU 1 .1 S 0 .endash A . , 1 1 984 1 4 ) comma . 3 . 1 open . 1 parenthesis 1 979 closing parenthesis period .. 4 period 7 comma .. 4 period[ 7 99 period ] Downs 1 , G . S . , and Reichley , P . E . , “ JPL pulsar timing observations . I I . Geocentric [ 95 ] \quad Detweiler , S . 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\noindent http : //www. l i vi ngrev i ews . org/ lrr − 2008 − 8 BinaryBinary and and Millisecond Millisecond Pulsars Pulsars .... 69 69 \noindenthline Binary and Millisecond Pulsars \ h f i l l 69 open square bracket 1 1 5 closing square bracket .. Freire comma P period C period C period comma Kramer comma M period comma and Lyne\ [ \ commar u l e {3em A period}{0.4 G pt period}\ ] comma .. quotedblleft Determination of the orbital parameters of binary[ 1 1 pulsars 5 ] Freire quotedblright , P . C . C comma . , Kramer Mon , Mperiod . , and Not Lyne period , A . R G period . , “ DeterminationAstron period of Soc the period orbital comma parameters 322 comma 885 comma open parenthesisof binary 200 1 pulsars closing ” parenthesis , Mon . Not period . R . Related Astron online. Soc . version, 322 open, 885 parenthesis , ( 200 1 ) cited . Related online version ( cited \noindenton 1on 2 1July 2[ July 2008 12008 1 closing 5 ) ] : \ parenthesisquad Freire : ,P . C . 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Hobbs comma G period comma quotedblleft Pulsars, and Gravitational Wave Detection supernova explosion on the Dynamics of a binary st ar of an Arbitrary orbital $\ l e f t .Eccentricity \ begin { a l i g n e d } & quotedblright. , 267 comma, 322 –open 333 parenthesis , ( 1 983 ) . 2005 2 . 6 closing parenthesis period URL open parenthesis cited on 22 January ’’ \\ 2005[ 1 closing 43 ] parenthesis Hobbs , G . : , “ Pulsars and Gravitational Wave Detection ” , ( 2005 ) . URL ( cited on 22 January &,ht tp : slash\end slash{ a l i g ar n e Xiv d }\ periodright org. $ slash abs slash astr o hyphen ph slash 4 1 2 1 5 3 period .. 4 period 7 period 3 comma .. 4 period 8 Astrophys . J . , 267 , 322 −− 333 , (1983) . 2 . 6 open square bracket 1 44 closing square bracket .... Hobbs2005) comma : G period comma Lorimer comma D period R period comma Lyne comma A period G period comma and Kramer comma M period comma .... quotedblleft A statistical study of 233 pulsar ht tp : / / ar Xiv . org / abs / astr o - ph / 4 1 2 1 5 3 . 4 . 7 . 3 , 4 . 8 \noindentproper motions[ 1quotedblright 43 ] \ h f i l lcommaHobbs Mon , periodG . , Not ‘‘ period Pulsars R period and Astron Gravitational period Soc period Wave comma Detection 360 comma ’’ 974 , ( endash 2005 992 ) . comma URL ( cited on 22 January [ 1 44 ] Hobbs , G . , Lorimer , D . R . , Lyne , A . G . , and Kramer , M . , “ A statistical study of 233 pulsar open parenthesis 2005 closing parenthesis period 2 period 1 0 comma 2 period 1 0 proper motions ” , Mon . Not . R . Astron . Soc . , 360 , 974 – 992 , ( 2005 ) . 2 . 1 0 , 2 . 1 0 \ [open 2005 square ) bracket : \ ] 1 45 closing square bracket .. Hobbs comma G period B period comma Faulkner comma A period comma Stairs comma [ 1 45 ] Hobbs , G . B . , Faulkner , A . , Stairs , I . H . , Camilo , F . , Manchester , R . N . , Lyne , A . G I period H period comma Camilo comma F period comma Manchester comma R period N period comma Lyne comma A period G period . , Kramer , M . , D ’ Amico , N . , Kaspi , V . M . , Possenti , A . , McLaughlin , M . A . , Lorimer , D . R . comma Kramer comma , Burgay , M . , \ centerlineM period comma{ ht tp D quoteright : / / ar Amico Xiv comma . org N / period abs /comma astr Kaspi o − commaph / 4 V 1period 2 1 M 5 period 3 . \ commaquad 4 Possenti . 7 . comma 3 , \ Aquad period4 comma . 8 } Joshi , B . C . , and Crawford , F . , “ The Parkes multibeam pulsar survey : IV . Discovery of 1 76 McLaughlin comma M period A period comma Lorimer comma D period R period comma Burgay comma M period comma pulsars and parameters for 248 previously known pulsars ” , Mon . Not . R . Astron . Soc . , 352 , 1 439 – \noindentJoshi comma[ 1 B 44period ] \ Ch period f i l l Hobbs comma and ,G Crawford . , Lorimer comma F,D period . R comma . , Lyne .. quotedblleft ,A . G The . Parkes , and multibeam Kramer ,M. pulsar survey , \ h f : i .. l l IV‘‘ A statistical study of 233 pulsar 1 472 , ( 2004 ) . 2 . 1 1 . 2 , 2 , 4 period Discovery of 1 76 [ 1 46 ] Hobbs , G . B . , Lyne , A . G . , Kramer , M . , Martin , C . E . , and Jordan , C . , “ Long - Term \ centerlinepulsars and{ parametersproper motions for 248 previously ’’ , Mon known . Not pulsars . R quotedblright . Astron comma . Soc Mon . , period 360 , Not 974 period−− 992 R period ,(2005) Astron period .2.10 Soc period ,2.10 } Timing comma 352 comma Observations of 374 Pulsars ” , Mon . Not . R . Astron . Soc . , 353 , 1 3 1 1 – 1 344 , ( 2004 ) . 2 3 \noindent1 439 endash[ 1 1 472 45 comma ] \quad openHobbs parenthesis ,G .2004 B .closing , Faulkner parenthesis ,A period . , .. Stairs2 period 1 , 1 I period . H 2 . comma , Camilo .. 2 comma , F . .. ,4 Manchester , R . N . , Lyne ,A . G . , Kramer , [ 1 47 ] Hogan , C . J . , and Rees , M . J . , “ Gravitational interactions of cosmic strings ” , Nature , 3 M.open ,D square ’ Amico bracket ,N 1 46 . closing , Kaspi square ,V bracket .M. .... , Hobbs Possenti comma ,A G period . , McLaughlin B period comma ,M. Lyne A comma . , Lorimer A period G ,D period . R comma . , Burgay ,M. , 1 1 , 1 9 – 1 1 4 , ( 1 984 ) . 4 . 7 . 1 Kramer comma M period comma Martin comma C period E period comma and Jordan comma C period comma .... quotedblleft Long hyphen [ 1 48 ] Hotan , A . W . , Bailes , M . , and Ord , S . M . , “ Geodetic Precession in PSR J 1 14 1 – 6545 ” , TermJoshi Timing , B . C . , and Crawford , F . , \quad ‘‘ The Parkes multibeam pulsar survey : \quad IV . Discovery of 1 76 Astro - phys . J . , 624 , 906 – 9 1 3 , ( 2005 ) . 2 . 1 1 . 2 pulsarsObservations and of parameters 374 Pulsars quotedblright for 248 previously comma Mon known period Not pulsars period ’’R period , Mon Astron . Not period . R Soc . Astron period comma . Soc 353 . comma , 352 1 , 3 1 1 [ 1 49 ] Hulse , R . A . , “ The discovery of the binary pulsar ” , Rev . Mod . Phys . , 66 , 699 – 7 1 0 , ( 1 endash1 439 1−− 344 comma1 472 open , ( parenthesis 2004 ) . 2004\quad closing2 . parenthesis 1 1 . 2 period , \quad .. 2 32 , \quad 4 994 ) . 4 . 5 open square bracket 1 47 closing square bracket .. Hogan comma C period J period comma and Rees comma M period J period comma .. [ 1 50 ] Hulse , R . A . , and Taylor , J . H . , “ Discovery of a pulsar in a binary system ” , Astrophys quotedblleft\noindent Gravitational[ 1 46 ] \ interactionsh f i l l Hobbs of cosmic ,G strings . B . quotedblright , Lyne ,A comma . G .Nature , Kramer comma ,M. 3 1 1 comma , Martin ,C . E . , and Jordan ,C . , \ h f i l l ‘ ‘ Long − Term Timing . J . Lett . , 195 , L 5 1 – L 53 , ( 1 975 ) . 2 . 6 . 1 , 3 . 1 . 3 , 4 . 5 1 9 endash 1 1 4 comma open parenthesis 1 984 closing parenthesis period .. 4 period 7 period 1 [ 1 5 1 ] Hunt , G . C . , “ The rate of change of period of the pulsars ” , Mon . Not . R . Astron . Soc . , \ centerlineopen square{ bracketObservations 1 48 closing of square 374 Pulsars bracket .. ’’ Hotan , Mon comma . Not A period . R .W Astron period comma . Soc Bailes . , comma353 , M1 3period 1 1 comma−− 1 344 and Ord , ( 2004 ) . \quad 2 3 } 153 , 1 1 9 – 1 3 1 , ( 1 971 ) . 4 . 2 comma S period M period comma quotedblleft Geodetic Precession in PSR J 1 14 1 endash 6545 quotedblright comma Astro hyphen \noindent [ 1 47 ] \quad Hogan ,C . J . , and Rees ,M. J . , \00quad ‘‘ Gravitational interactions of cosmic strings ’’ , Nature , 3 1 1 , phys[ 1 period 52 ] J IASF period , comma “ AGILE 624 : comma Astro 906 - rivelatore endash 9 Gamma 1 3 comma a Immagini open parenthesisLEggero 2005project closinghomepage parenthesis . URL period .. 2 period 1 1 period 2 , 1open 9 −− square114 bracket ,(1984) 1 49 closing . square\quad bracket4 . 7 .... . 1 Hulse comma R period A period comma quotedblleft The discovery of the binary ( cited on 24 June 2008 ) : pulsar quotedblright comma Rev period Mod period Phys period comma 66 comma 699 endash 7 1 0 comma open parenthesis 1 994 closing \noindent [ 1 48 ] ht\quad tp :Hotan / / agile , A .W.. r m ,. Bailes iasf . ,M cnr . . , it and / Ord. 2 . 1 , 1 S . 5 . M . , ‘‘ Geodetic Precession in PSR J 1 14 1 −− 6545 ’’ , Astro − parenthesis period .... 4 period 5 00 physopen[ 1. square 53 J ] . bracket, INFN 624 , 1 “, 50 The 906 closing Virgo−− square913P roject bracket , (2005)project .. Hulsehomepage comma . \quad R . URLperiod2 . ( 1 citedA 1 period . on 2 29 comma January and 2005 Taylor ) : comma .. J period H period comma , .. quotedblleft Discovery of a pulsar in a binary system quotedblright comma .. Astrophys period .. J period h t t p : / / w w w . v ir go . i n fn . i t . 3 . 4 \noindentLett period[ comma 1 49195 ] \ commah f i l l LHulse 5 1 endash , R L . 53 A comma . , ‘‘ open The parenthesis discovery 1 975 of closing the binary parenthesis pulsar period 2’’ period , Rev 6 period . Mod 1 comma . Phys .. . , 66 , 699 −− 710 ,(1994) . \ h f i l l 4 . 5 [ 1 54 ] International SKA Project Office , “ The Square Kilometre Array ” , project homepage . URL ( 3 period 1 period 3 comma .. 4 period 5 cited on 23 January 2005 ) : \noindentopen square[ bracket 1 50 ] 1 5\quad 1 closingHulse square , bracket R . A .. . Hunt , and comma Taylor G period , \ Cquad periodJ.H., comma quotedblleft\quad The‘‘ Discovery rate of change of of a period pulsar of the in a binary system ’’ , \quad Astrophys . \quad J. ht tp : / / w w w . s kate l e s cop e . org . 1, 2.11.7, 4.7.3 pulsarsLett quotedblright . , 195 ,L51 comma−− MonL53,(1975).2.6.1, period Not period R period Astron period\ Socquad period3 . comma 1 . 3 153 , comma\quad 4 . 5 [ 1 55 ] Jacoby , B . A . , Recycled Pulsars , Ph . D . Thesis , ( Calfornia Institute of Technology , Pasadena 1 1 9 endash 1 3 1 comma open parenthesis 1 971 closing parenthesis period .. 4 period 2 , U . S . A . , 2004 ) . Related online version ( cited on 27 October 2008 ) : \noindentopen square[bracket 1 5 1 1 ] 52\quad closingHunt square , bracket G . C .. . IASF , ‘‘ comma The rate .. quotedblleft of change AGILE of : period .. Astro of hyphen the rivelatore pulsars Gamma ’’ , Mon a Immagini . Not . R . Astron . Soc . , 153 , ht t p : / / r e sol v er . calte ch . edu / Cal t e c hE T D : e td - 0 1 272005 - 0 1 50 1 2 . 4 LEggeroRow1 1 9 −− 1131 quotedblright ,(1971) Row 2 comma . \quad LEggero4 . homepage 2 period URL [ 1 56 ] Jacoby , B . A . , Bailes , M . , Ord , S . M . , Knight , H . S . , and Hotan , A . W . , “ open parenthesis cited on 24 June 2008 closing parenthesis : Discovery of Five Recycled Pulsars in a High Galactic Latitude Survey ” , Astrophys . J . , 656 , 408 – 41 3 \noindentht tp : slash[ slash1 52 agile ] \quad periodIASF, r m period\quad iasf period‘ ‘ AGILE cnr period : \ itquad slashAstro period 2− periodrivelatore 1 1 period Gamma 5 a Immagini $\ l e f t . LEggero\ begin { array }{ c} ’’ \\ , ( 2007 ) . Related online version ( cited on 1 2 July 2008 ) : , \openend{ squarearray bracket} p r o j e 1 c 53 t \ closingright .$ square homepage bracket .. INFN. URL comma quotedblleft The Virgo ProjectRow 1 quotedblright Row 2 comma Project ht t p : / / ar X i v . or g / abs / astr o - p h / 0 609 4 48 . 2.1 1.3,2, 4 homepage( cited period on 24 URL June open 2008 parenthesis ) : cited on 29 January 2005 closing parenthesis : h t t p : slash slash w w w period v ir go period i n fn period i t period .. 3 period 4 \ centerlineopen square{ brackethttp 1 : 54 // closing agile square . rm. bracket iasf .. International . cnr . SKA it / Project . 2 . Office 11 comma . 5 } .. quotedblleft The Square Kilometre Array quotedblright comma project homepage period URL Living Reviews in Relativity \noindentopen parenthesis[ 1 53 cited ] \ onquad 23 JanuaryhtINFN tp :2005 , / ‘‘ / closing The w w Virgo parenthesis w . l $\ il : evi f t ngrev. P r o j i e c e t \ wbegin s .{ orgarray / lrr}{ c} - 2008’’ \\ - 8 , \end{ array } p r o j e c t \ right . $ homepageht tp : slash . URL slash ( w cited w w period on 29 s kate January l e s cop 2005 e period ) :org period .. 1 comma .. 2 period 1 1 period 7 comma .. 4 period 7 period 3 open square bracket 1 55 closing square bracket .. Jacoby comma B period A period comma Recycled Pulsars comma Ph period D period Thesis\ centerline comma open{http://www.virgo. parenthesis Calfornia Institute of Technology infn. comma it. Pasadena\quad comma3 . 4 } U period S period A period comma 2004 closing parenthesis period Related online version open parenthesis cited on 27 October 2008 closing parenthesis\noindent : [ 1 54 ] \quad International SKA Project Office , \quad ‘‘ The Square Kilometre Array ’’ , project homepage . URL (ht cited t p : slash on 23 slash January r e sol v er2005 period ) calte: ch period edu slash Cal t e c hE T D : e td hyphen 0 1 272005 hyphen 0 1 50 1 2 period .. 4 open square bracket 1 56 closing square bracket .. Jacoby comma B period A period comma Bailes comma .. M period comma .. 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A parenthesis . , 2004 2007 ) .closing Related parenthesis online period version ( cited on 27 October 2008 ) : Related online version open parenthesis cited on 1 2 July 2008 closing parenthesis : \ centerlineht t p : slash{ ht slash t ar p X : i //v period r e or sol g slash v abser slash . calte astr o ch hyphen . edu/Cal p h slash 0 609 t e 4 48chETD: period .. 2 period e td 1− ..0 1 period1 272005 3 comma− 0 2 1 comma 50 1 2 . \quad 4 } .. 4 \noindenthline [ 1 56 ] \quad Jacoby , B . A . , Bailes , \quad M., \quad Ord ,S .M. , Knight ,H. S . , \quad and Hotan , \quad A.W., \quad ‘‘ Discovery of Five RecycledLiving Reviews Pulsars in Relativity in a High Galactic Latitude Survey ’’ , Astrophys . J . , 656 , 408 −− 413 , ( 2007 ) . Relatedht tp : slash online slash wversion w .. w period ( cited l i vi onngrev 1 i 2 e wJuly s period 2008 org ) slash : lrr hyphen 2008 hyphen 8 \ centerline { ht tp : //arXi v . org/abs/ astr o − ph/0609448 . \quad 2 . 1 \quad 1 . 3 , 2 , \quad 4 }

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Kluzniak comma W period comma Ruderman comma M period comma Shaham comma J\ [ period\ r u l comma e {3em}{ and0.4 Tavani pt }\ comma] M period comma .. quotedblleft Nature and evolution of the eclipsing[ 1 92 millisecond ] Kluzniak binary , W . , pulsar Ruderman PSR , 1 M 957 . , Shaham plus 20 , quotedblright J . , and Tavani comma , M . Nature, “ Nature comma and 334 evolution comma of 225 the endash 227 comma open parenthesiseclipsing 1 988 millisecond closing parenthesis binary pulsar period PSR 2 period 1957 + 8 20 ” , Nature , 334 , 225 – 227 , ( 1 988 ) . 2 . 8 \noindentopen[ 1 square 93 ][ bracket 1 Knight 92 ] 1 ,\ 93 Hquad .closing S .Kluzniak , Bailes square , bracketM ,W . , Manchester ... Knight, Ruderman ,comma R . N , H. M, period and . Ord, S Shaham period , S . 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Related online version ( cited on 1 2 h t t p : slash slash arX i v period o r .. g slash .. ab s slash astr o hyphen ph slash 0 6 0 8 1 5 5 period .. 2 period 1 1 period 6 \ [Julyh t 2008 t p : / ) / arX : \ i] v . o r g / ab s / astr o - ph / 0 6 0 8 1 5 5 . 2 . 1 1 . 6 open square bracket 1 94 closing square bracket .. Kolonko comma M period comma Gil comma J period comma00 and Maciesiak comma K period[ comma 1 94 ] .. Kolonko quotedblleft , M . On , Gil the , J pulse . , and hyphen Maciesiak width , K statistics . , “ On in the radio pulse Case - width 1 quotedblright statistics in Case radio 2pulsars comma , Astron period Astrophys period comma 428 comma 943 endash 95 1 comma open parenthesis 2005 closing parenthesis period .. 2 period 3 Astron . Astrophys . , 428 , 943 – 95 1 , ( 2005 ) . 2 . 3 \ centerlineopen square{ brackethttp://arXiv.or 1 95 closing square bracket .. Kondratiev\quad g comma/ \quad V periodab s I / period a s t r comma o − ph/0608155. Lorimer comma D period R\ periodquad comma2 . 1 1 . 6 } [ 1 95 ] Kondratiev , V . I . , Lorimer , D . R . , McLaughlin , M . A . , and Ransom , S . M . , “ A pulsar McLaughlin comma M period A period comma and Ransom comma S period M period comma .. quotedblleft A pulsar census of census of the lo cal group ” , Astrophys . J . , in preparation . 2 . 1 1 . 6 \noindentthe lo cal group[ 1 94 quotedblright ] \quad commaKolonko Astrophys ,M. period , Gil J period, J . comma , and in Maciesiak preparation period , K . .. , 2\ periodquad 1‘‘ 1 period On the 6 pulse − width statistics in radio [ 1 96 ] Kopeikin , S . M . , “ Binary pulsars as detectors of ultralow - frequency gravitational waves ” $\ lopen e f t . square p u l s a bracket r s \ begin 1 96{ closinga l i g n e square d } &’’ bracket\\ .. Kopeikin comma .. S period M period comma .. quotedblleft Binary pulsars as detectors , Phys . Rev . D , 56 , 4455 – 4469 , ( 1 997 ) . 4 . 7 . 1 of&, ultralow\ hyphenend{ a frequencyl i g n e d }\ gravitationalright . $ waves quotedblright comma [ 1 97 ] Kozai , Y . , “ Secular perturbations of asteroids with high inclination and eccentricity ” , Astron . AstronPhys period . Astrophys Rev period . D , comma 428 , 56 943 comma−− 4455951 endash , ( 2005 4469 comma ) . \quad open parenthesis2 . 3 1 997 closing parenthesis period .. 4 period 7 J. , 67 , 59 1 – 598 , ( 1 962 ) . period 1 ADS : h tt p : / / ad s a bs . h ar v a r d . e d u / ab s / 1 9 6 2 A J . . . . . 6 7 . . 5 9 1 K . 2 . 9 \noindentopen square[ bracket 1 95 ] 1 97\quad closingKondratiev square bracket , .. V Kozai . I comma . , Lorimer Y period , comma D . R quotedblleft . , McLaughlin Secular perturbations ,M . A . of , asteroids and Ransom with high , S . M . , \quad ‘‘ A pulsar census of [ 1 98 ] Kramer , M . , Backer , D . C . , Cordes , J . M . , Lazio , T . J . W . , Stappers , B . W . , and inclinationthe lo andcal eccentricity group ’’ quotedblright , Astrophys comma . J Astron . , in period preparation . \quad 2 . 1 1 . 6 Johnston , S . , “ Strong - field tests of gravity using pulsars and black holes ” , New Astron . Rev . , 48 , J period comma 67 comma 59 1 endash 598 comma open parenthesis 1 962 closing parenthesis period 993 – 1 2 , ( 2004 ) . 4 . 7 . 3 , 3 1 \noindentADS : h tt[ p 1: slash 96 ] slash\quad .. adKopeikin s a bs period , h\ arquad v .. aS.M., r d period e\ dquad u slash‘‘ ab Binary s slash 19 pulsars .. 6 2 A J as period detectors period period of ultralow period period− 6frequency gravitational waves ’’ , [ 1 99 ] Kramer , M . , Bell , J . F . , Manchester , R . N . , Lyne , A . G . , Camilo , F . , Stairs , I . H . , D 7Phys period . period Rev 5 . 9 D 1 K , period 56 , ..4455 2 period−− 4469 9 , ( 1 997 ) . \quad 4 . 7 . 1 ’ Amico , N . , Kaspi , V . M . , Hobbs , G . , Morris , D . J . , Crawford , F . , Possenti , A . , Joshi , B . C . open square bracket 1 98 closing square bracket .. Kramer comma M period comma Backer comma D period C period comma Cordes , McLaughlin , M . A . , Lorimer , D . R . , and Faulkner , A . J . , “ The Parkes Multibeam Pulsar Survey - comma\noindent J period[ 1M 97period ] \ commaquad LazioKozai comma , Y T. period , ‘‘ J Secular period W perturbations period comma Stappers of asteroids comma B period with W high period inclination comma and Johnston and eccentricity ’’ , Astron . III . Young pulsars and the discovery and timing of 200 pulsars ” , Mon . Not . R . Astron . Soc . , 342 , commaJ . , S 67period , 59 comma 1 −− 598 , ( 1 962 ) . 1 299 – 1 324 , ( 2003 ) . 2 . 4 , 2 . 1 1 . 2 , 2 . 1 1 . 5 quotedblleft Strong hyphen field tests of gravity using pulsars and black holes quotedblright comma New Astron period Rev period comma [ 200 ] Kramer , M . , and Stairs , I . H . , “ The Double Pulsar ” , Annu . Rev . Astron . 48\ centerline comma 993 endash{ADS: 1 2h comma tt p : // \quad adsabs . harv \quad ard.edu/abs/19 \quad 62AJ.....67..591K. \quad 2 . 9 } Astrophys . , 46 , 541 – 572 , ( 2008 ) . open parenthesis 2004 closing parenthesis period .. 4 period 7 period 3 comma .. 3 1 ADS : http : / / ad s abs .h v ard . edu / a bs / 2008 AR A & A . . 46 . . 5 4 1 K . 4 . 8 \noindentopen square[ bracket1 98 ] 1\ 99quad closingKramer squarea−r ,M. bracket , .. Backer Kramer comma ,D . MC period . , Cordes comma Bell, J comma .M. J , period Lazio F period , T . comma J .W. Manchester , Stappers , B .W. , and Johnston , S . , [ 201 ] Kramer , M . , Stairs , I . H . , Manchester , R . N . , McLaughlin , M . A . , Lyne , A . G . , Ferdman comma‘ ‘ Strong R period− Nfield period tests comma of Lyne gravity comma A using period pulsars G period commaand black Camilo holes comma ’’ F period , New comma Astron Stairs . Rev comma . , I period 48 , 993H period−− 1 2 , , R . 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A Multibeam . , Lorimer Pulsar Survey , D . hyphen R . , III and period Faulkner Young , A . J . , ‘‘ The Parkes Multibeam Pulsar Survey − I I I . Young 2008) : pulsarspulsars and and the the discovery discovery and timing and of timing200 pulsars of quotedblright 200 pulsars comma ’’ Mon , Mon period . Not Not period . R . R Astron period Astron . Soc period . , Soc 342 period , 1 comma 299 −− 1 324 , ( 2003 ) . \quad 2 . 4 , \quad 2.11.2,2.11.5 342 commaht 1 299 tp endash : / / arXi v . org / abs / astr o - ph / 60941 7 . 4.4, 4.5, 4.5,3 1 324[ 202 comma ] Kramer open parenthesis , M . , 2003 Xilouris closing , parenthesis K . M . , period Camilo .. , 2 period F . , 4 Nice comma , D.. 2. J period . , Backer 1 1 period , D 2comma . C . 2 period 1 1 period 5 \noindentopen, square Lorimer[bracket 200 , ] D 200\ .quad R closing . , DoroshenkoKramer square , bracket ,\ Oquad . V ...M., , LangeKramer ,\ Cquad comma . , andand .. Sallmen M Stairs period , S comma. , I “ . Profile .. 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Rep period comma 442 comma .. 1 9 endash 1 65 comma .. open parenthesis 2007 closing parenthesis period Related online version open parenthesisJuly2008) :cited on 1 2 \noindentJuly 2008 closing[ 206 parenthesis ] \quad Lattimer : , \quad J.M., \quad and Prakash , \quad M., \quad ‘‘ Neutron star observations : \quad Prognosis for equation of state constraintsh t t p : / / ’’ ar , Xi\quad v .Phys org / . abs\quad / asRep tro - . p , h 442 / 6 , 1\ 2quad 4 40 1.2.2, 9 −− 1 4.5, 65 , \quad 4.6 ( 2007 ) . Related online version ( cited on 1 2 h t t[ 207p : slash ] Lawson slash ar , K Xi . v D period . , Mayer org , slash C . J abs . , Osborne slash as tro , J .hyphen L . , and p h Parkinson slash 6 1 ,2 M 4 40 . L period . , “ 2 Variations period 2 comma in the .. 4 period 5 comma .. 4 period 6 \ [JulySpectral 2008 Index of ) the Galactic: \ ] Radio Continuum Emission in the Northern Hemisphere ” , Mon . Not . R . openAstron square . 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G period commaPopulation Konacki Synthesis comma ” M, Astrophys period comma . Space and Phys So suppress-l . Rev . , tysi9 , n-acute 1 – 1 78 ski , ( comma 1 996 ) T. Related period comma online version quotedblleft Arecibo tim hyphen ing and single hyphen pulse observations of eighteen pulsars quotedblright comma Astrophys period J period comma 600 comma 905 endash \ centerline( cited on{ADS 1 2 July : h 2008 ttp ) : / / adsabs . h $ a−r$ vard. edu/abs/1991ApJ. . . 379 . . 359L. \quad 2 . 8 } 9 1h 3 t comma t p : open / / parenthesis xr ay . sai2004 . closing m su parenthesis . r u / period∼ my s t er y / ar t i c l e s / r e view / . 3 . 5 ADS : h .. t tp : slash slash a d s a .. b s .. period h .. a r v a .. r d period edu slash a b s slash 2 0 4 .. Ap J period period period 6 0 0 \noindent[ 2 1 2[ ] 209 LOFAR ] \quad , “ TheLewandowski Low Frequency ,W Array . ” , , project Wolszczan homepage , A . . URL , Feiler ( cited on , 24 G June . , 2008 Konacki ) : , M . , and So \ l t y s i period period 905 L period .. 4h t t p : / / w w w . lof ar . org . 2 . 1 1 . 7 $ \openacute square{n} bracket$ ski 2 1,T 0 closing . , ‘‘square Arecibo bracket tim .. Li− comma X period comma .. quotedblleft Formation of Mildly Recycled Low hyphen ing and[ 2 1 3 single ] Lo ¨−hmerpulse , O . observations, Kramer , M . , Driebe of eighteen , T . , Jessner pulsars , A . , ’’Mitra , Astrophys, D . , and Lyne . J , A . . ,G 600 . , “ , 905 −− 913 , (2004) . Mass BinaryThe parallax Pulsars , from mass Intermediate and age of the hyphen PSR J Mass 2 1 45 - 750 binary system ” , Astron . 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J . , 564 , 930 −− 934 , ( 2002 ) . \quad 2 . 7 Population[ 2 1 5 ] Synthesis Lommen quotedblright , A . N . , Kipphorn comma Astrophys , R . A . period , NiceSpace , D . J Phys . , Splaver period , Rev E . period M . , Stairs comma , I 9 . comma H . , and 1 endash 1 78 comma open parenthesis 1 996 closing parenthesis period Related online version \noindentBacker[ , D 2 . 1 C 1 . , ] “ The\ h f Parallaxi l l Lipunov and Proper , V Motion . M . of , PSR Postnov J 30 + , 451 K ” . , AAstrophys . , and . Prokhorov J . , 642 ,M, . E . , \ h f i l l ‘‘ The Scenario Machine : \ h f i l l Binary Star open1 parenthesis0 1 2 – 1 0 1 cited 7 , ( on 2006 1 2 ) July . Related 2008 closing online version parenthesis ( cited : on 1 2 July 2008 ) : h t t p : slash slashh ttp xr ay : period / / arXi sai period v . morg su / period a bs r / u as slash tro thicksim - p h /.. my60 1s t 52 er 1 y slash. 4 ar . 2t i c l e s slash r e view slash period .. 3 periodPopulation 5 Synthesis ’’ , Astrophys . Space Phys . Rev . , 9 , 1 −− 1 78 , ( 1 996 ) . Related online version ( cited[ 2 1 on6 ] 1 Lommen 2 July , 2008 A . N .) , Zepka: , A . F . , Backer , D . C . , McLaughlin , M . A . , Cordes , J . M . , openArzoumanian square bracket , Z 2. , 1 and 2 closing Xilouris square , K . bracket M . , “.. New LOFAR Pulsars comma from quotedblleft an Arecibo DriftThe Low Scan Frequency Search ” , ArrayAstrophys quotedblright comma project homepage period URL open parenthesis cited on 24 June 2008 closing parenthesis : \ centerline.J. {,http://xray.545 , 1 7 – 1 0 14 , ( 200 1 ) sai . 2 .msu.ru $/ \sim $ \quad myst ery/art i c l es/review/. \quad 3 . 5 } h t[ t 2p 1 : slash7 ]slash Lorimer w w , Dw period. R . , lof “ ar Pulsar period statistics org period – I .. I . 2 The period lo cal 1 .. low 1 period - mass 7 binary pulsar population ” , openMon square . Not bracket . R . 2 Astron 1 3 closing . 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B hyphen . , and 2008 Freirehyphen 8 , P . C . C . , \ h f i l l ‘‘ The Arecibo 430 MHz Intermediate Galactic \ hspace ∗{\ f i l l } Latitude Survey : \quad Discovery of Nine Radio Pulsars ’’ , \quad Astrophys . \quad J . , 594 , \quad 943 −− 95 1 , \quad ( 2003 ) .

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\noindent [ 280 ] \ h f i l l Navarro , J . , de Bruyn ,A .G. , Frail ,D . A . , Kulkarni , S . R . , and Lyne ,A .G. , \ h f i l l ‘‘ A very luminous

\ centerline { binary millisecond pulsar ’’ , Astrophys . J . Lett . , 455 , L 55 −− L58 , (1995) . }

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\noindent [ 281 ] \ h f i l l Ng , C . − Y . , and Romani ,R .W. , \ h f i l l ‘‘ Birth Kick Distributions and the Spin − Kick Correlation of

\ hspace ∗{\ f i l l }Young Pulsars ’’ , Astrophys . J . , 660 , 1 357 −− 1 374 , ( 2007 ) . Related online version ( cited on 1 2

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Ryba comma M period F period comma and Taylor comma J period H period comma .. quotedblleft High Precision Timing of Millisecond Pulsars period II period Astrometry comma \noindentOrbital Evolutionhttp comma : //www. and Eclipses l of i PSR vi 1 ngrev 957 plus 20 i ewsquotedblright . org/ comma lrr Astrophys− 2008 period− 8 J period comma 380 comma 557 endash 563 comma open parenthesis 1 99 1 closing parenthesis period .. 4 period 3 hline Living Reviews in Relativity ht tp : slash slash w w w period l i vi ngre v i e w s period or g slash lrr hyphen 2008 hyphen 8 BinaryBinary and and Millisecond Millisecond Pulsars Pulsars .... 85 85 \noindenthline Binary and Millisecond Pulsars \ h f i l l 85 open square bracket 329 closing square bracket .. 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V closing . and, “ Opportunities parenthesis Parallax period forof detecting PSR .. 4 periodJ 437 ultralong 2−− 471 gravitational 5 ’’ , waves Astrophys ” , Sov . . Astron J . Lett . , 22 ., , 478 , L 95 −− L 98 , (open 1 997 square ) . bracket\quad 3304 .closing 2 square bracket36 – 38.... , (Sazhin 1 978 comma) . 4 . M 7 period V period comma quotedblleft Opportunities for detecting ultralong[ 331 gravitational ] Scheuer , waves P . A quotedblright . G . , “ Amplitude comma variations Sov period ofAstron pulsed radio period sources comma ” 22 , Nature comma, 2 18 , 920 – 922 , \noindent36 endash[ 38 330 comma ] \ openh f i parenthesisl l Sazhin 1 978, M closing .( V 1 968 . parenthesis , ) . ‘‘ 3 Opportunities . 1 period . 2 .. 4 period for 7 detecting ultralong gravitational waves ’’ , Sov . Astron . , 22 , open[ 332 square ] Segelstein bracket ,331 D . closing J . , Rawley square , bracketL . A . , .... Stinebring Scheuer , comma D . R . ...., Fruchter P period , A A . S period . , and G Taylor period , commaJ . H . , .... “ quotedblleft Amplitude variations\ centerlineNew of pulsed{36 radio−− 38 sources , ( quotedblright 1 978 ) . \ commaquad ....4 . Nature 7 } comma .... 2 18 comma .... 920 endash 922 comma open parenthesismillisecond 1 968 closing pulsar parenthesis in a binary period system .. ”3 ,periodNature 1 period, 322 2, 7 1 4 – 7 1 7 , ( 1 986 ) . 4 00 \noindentopen square[bracket 331 ] 332\ h f closing i l l Scheuer square bracket , \ h f .... i l l SegelsteinP.A.G., comma ....\ h D f iperiod l l ‘‘ J Amplitude period comma variations .... Rawley comma of pulsed .... Lperiod radio A sources ’’ , \ h f i l l Nature , \ h f i l l 2 18 , \ h f i l l 920 −− 922 , [ 333 ] Seiradakis , J . H . , and Wielebinski , R . , “ Morphology and characteristics of radio pulsars period comma .... Stinebring comma .... D period R period comma .... Fruchter comma .... 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\noindent [ 372 ] \ h f i l l Thorsett , S . E . , and Dewey ,R . J . , \ h f i l l ‘‘ Pulsar Timing Limits on Very Low Frequency Stochastic

\ centerline { Gravitational Radiation ’’ , Phys . Rev . D , 53 , 3468 , ( 1 996 ) . \quad 4 . 7 . 1 }

\noindent [ 373 ] \ h f i l l Toscano , \ h f i l l M., \ h f i l l Sandhu , \ h f i l l J.S., \ h f i l l B a i l e s , \ h f i l l M., \ h f i l l Manchester , \ h f i l l R.N., \ h f i l l Britton , \ h f i l l M. C . , Kulkarni , \ h f i l l S.R.,

\ hspace ∗{\ f i l l }Anderson , S . B . , and Stappers , B .W. , \quad ‘‘ Millisecond pulsar velo cities ’’ , Mon . Not . R . Astron .

\ centerline {Soc . , 307 , 925 −− 933 , ( 1 999 ) . \quad 4 . 2 , 2 , \quad 4 }

\ [ \ r u l e {3em}{0.4 pt }\ ]

\ hspace ∗{\ f i l l } Living Reviews in Relativity

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