198lApJ. . .245 . .650M The AstrophysicalJournal,245:650-670,1981April15 © 1981.TheAmericanAstronomicalSociety.Allrightsreserved.PrintedinU.S.A. These binariesaredefinedtobestarswhichhaveboth between theinnerandouterLagrangianzero-velocity components surroundedbyacommonenvelopelying formation, structure,andevolutionofcontactbinaries. later areusuallycalledWUrsaeMajorisstars,although marized byEggen(1961,1967),Binnendijk(1965,1970) equipotential surfaces.SystemsofspectraltypeFOand in theliterature,ithasbecomedesirabletosummarize and Ruciñski(1974).Sincenewerdatatheoriesexist W UMastarscomefromtheapplicationoflightcurve the hottercontactbinariesareverysimilar. theoretical predictions.Mostofthenewdataon these resultsandtocompareobservablequantitieswith synthesis techniquestothefittingofmodelsobserva- corrected colorsfortheprimarycomponentsofWUMa tions. Thesedataaretabulatedin§II.Densitiesand systems arederivedin§III.Amethodofclassifyingthe Theories offormationarediscussedin§VII,andtheo- § V,andspecificangularmomentaareobtainedinVI. Masses andluminositiesofWUMastarsareinferredin angular momentaofcontactbinariesisappliedin§IV. ries ofstructurein§VIII. Adetailedevolutionary importance ofmagneticbraking bystellarwindsis model isdevelopedin§IX, andtheoreticalgridsare compared withthedataderived fromobservation.The Much attentioninrecentyearshasbeengiventothe Observational dataonthesesystemshavebeensum- © American Astronomical Society • Provided by theNASA Astrophysics Data System A-type systemsareshowntobeevolved,havinglowerdensitiesandangularmomentathanthe W-type systems.Anewclassofcontactbinaryisidentified:the00Aquilaesystems,members minimum periods,inferredmasses,luminosities,andspecificangularmomentaarecomputed.The which haveevolvedintocontact. contact binarybehavior. fission model.Alternativeformationtheoriesarediscussed.Neitherthethermalrelaxationsoscilla- which isshowntobeeffectiveonashortertimescale.Magneticbrakingalso well withobservationsexceptthattheevolvedA-typesystemshavelostmoreangularmomentum tions theorynorthecontactdiscontinuityofbinarystructurecompletelydescribes important inotherkindsofbinariescontainingacooltidallycoupledcomponent. than predictedbygravitationalradiationalone.Thisisexplainedstellarwindmagneticbraking, Subject headings:stars:binaries—WUrsaeMajoris Data on37WUrsaeMajorissystemshavebeencollected.Densities,correctedprimarycolors, The specificangularmomentumofW-typesystemsisabouttwicethatpredictedbyRoxburgh’s Evolutionary gridsbasedonthecontactconditionhavebeencomputed,andareshowntoagree I. INTRODUCTION Palomar Observatory,CaliforniaInstituteofTechnology Received 1980May27;acceptedOctober17 CONTACT BINARYSTARS Stefan W.Mochnacki ABSTRACT 650 zero-velocity surfaces.Heusedadirectnumerical photosphere liesbetweentheinnerandouterLagrangian tact binaries,withacommonconvectiveenvelopewhose method basedontheRochegeometrytosynthesize b), Lucy(1973),WilsonandDevinney Hutchings andHill(1973),Whelan,Worden, theoretical lightcurves.MochnackiandDoughty(1972a, discussed in§X.Asummaryoftheconclusionswith common envelopetoanumberofsystems.Mauder Mochnacki (1973)fitteddetailedmodelsbasedonLucy’s (1972) andRuciñski(1973)usedFouriertechniquesto some discussionispresentedin§XI. more simplyclassifyalargernumberofsystemsinterms of thecommonenvelopemodel.Manymoreauthors, now existsbasedonmodelsmorerealisticthanthe especially Twigg(1976,1979)andWilson(1978),have have beenpresentedrecentlybyBinnendijk(1977)and since contributedtothissubject,sothatabodyofdata tions foundbyfittingRoche-type modelstolightcurves Russell-Merrill method.Excellentreviewsofthissubject tial, or“fill-out”betweenthe inner andouterLagrangian agree wellbetweendifferentauthors. Thesurfacepoten- Ruciñski (1978). Lucy (1968û,b)showedthatWUMastarsarecon- In general,thephotometric mass ratiosandinclina- II. DATAONWURSAEMAJORISSTARS 198lApJ. . .245 . .650M it isprobablynotwelldeterminediflefttobefittedby ity darkeningwhichshouldexistincontactbinaries,and surfaces, isalsofairlyconsistentlydetermined.Unfor- least squares.Similarargumentsapplytolimbdarken- tunately, thereislittleconsensusonthedegreeofgrav- ing. Thedetailedphotosphericphysicsusedbyindivid- ual workersstronglyaffectstheapparenttemperature differences foundbetweencomponents,andtoalesser degree thefill-outofenvelope. have thedeeperminimumcorrespondingtoatransitof for WUMastars.W-typesystemshavelightcurveswith the secondary,lessmassivecomponent;A-typesystems the deeperminimumcorrespondingtoanoccultationof component. Rucinski(1974)interpretsthisdefinitionas ponent ishotterthanpredictedbyLucy’s(1967)gravity- meaning thatintheW-typesystemssecondarycom- the secondaryinfrontofprimary,moremassive, velope. period onalogarithmicscale,togetherwithsystems darkening lawforanentirecommonconvectiveen- having reliablecolorsdeterminedbyEggen(1967).A pear tobemoreevolved(Wilson1978).Webbink(1977c) less than2days.Thesesystemsareincludedinthe few hotcontactsystemsarealsoshown.Table2lists eight contactsystemsofearlyspectraltypewithperiods interprets thedistinctionasbeingduetodifferent velopes. Mullan(1975)suggestsdifferentstarspotactivi- type thantheW-typesystems(Rucinski1974)andap- discussion forcomparisonwiththehotterWUMatype circulation patternsinhotandcoolconvectiveen- UMa starsandearly-typecontactbinariesbelongtotwo with sources.Thislistupdatesthecompilationof different sequences,andinfacthotcomponentswitha stars; itisdifficulttodeterminewhether“classical”W ties betweencomponents.ThedistinctionW hot andcoolcontactsystems maybesimilar(Webbink, (Lucy andWilson1979).Theevolutionaryhistoriesof radiative commonenvelopemaystillexchangeenergy there aresomepeculiarsystems. and Atypesystemsisnotalwayseasytomake, Roche geometry,butthedetailedphysicsdiffersfrom Rucinski (1974).Allthemodelswereobtainedusing photometry alone.Someofthespectroscopicmassratios mass ratiobecomesverydifficulttodeterminefrom mass ratiosarespectroscopic,sinceinsuchcasesthe are nottabulated.Forpartiallyeclipsingsystems,some author toauthor.Accordingly,temperaturedifferences nates isusedinthispaper(Mochnacki 1971;Mochnacki needed forthesesystems. are basedonpoorobservations;newobservations 19796, c). Binnendijk (1965)introducedaclassificationscheme Figure 1showsde-reddenedcolors(B—V)versus Generally, theA-typesystemsareofearlierspectral Data for37systemsarepresentedinTable1,together The Rochegeometrydefined incylindricalcoordi- © American Astronomical Society • Provided by theNASA Astrophysics Data System CONTACT BINARYSTARS 6G A istheseparationbetweencomponentcentersofmass; f— 2—F,whiletheWilsonandDevinney(1971)parame- where Gisthegravitationalconstant;911j,91tmass be seenwithsystemsoflargerqhavinglowerFexcept This diagramofnewerdatashowsthesameeffects of theprimaryandsecondarycomponent,respectively; noted byRucinski(1973,1974),namely,thattheW-type F forlargerq. systems haveFnear1.0andtheA-type geometry hasbeenfullydescribedmathematicallyby of thesystemisdefinedbyCandratioq—K/y{i, and Cisthenormalizedsurfacepotential.Thegeometry for thehotcontactsystems,whichappeartohavehigher somewhat largerfill-outfactors.Aroughcorrelationcan where C(q)^and1^F<2.,arethe definitions offill-outorover-contactparametersexistin Mochnacki andDoughty(1972a). assuming thateachcomponentactsasapointmass.The the literature.Foracommonenvelope,Idefine normalized potentialsforinnerandoutercontact,re- tial value, sphere isdefinedbyanequipotentialsurfacewithpoten- and Doughty1972a;Binnendijk1977).Thephoto- spectively. Rucinski’s(1973)parameter/isrelatedby ter ßisrelatedby 2 deduced withoutknowledgeoftheirabsolutedimen- immediately (Roberts1899;Kopal1959): sions. Knowingtheperiod,relativeradii,andmassratio, 2x the meandensitypj,pofeachcomponentfollows x2 where %(F,q)isthevolume of theithcomponentusing nents astheunitoflength,q isthemassratioWl/ÿJl the separationAofcenters ofmassthecompo- and Pistheperiodindays. 2 2l9 Figure 2showsthefill-outFversusmassratioq. The constantCisnotveryconvenient,andseveral The evolutionarystatusofeclipsingbinariescanbe III. DENSITIESANDCOLORSOFCONTACTSYSTEMS P2 = Pi = i 2%Cm 8 £cm \{F,q)(\+q)p ’ T(F,4)(l+4)^ (< 2 —G{$fl+$l)C/2A, (1) x1 0.0794 0.079 _ 3 (4b) (4a) 651 p) 198lApJ. . .245 . .650M Name VW Cep Star XY Leo 44 iBooBC TZ Boo CC Com TW Get ER Cep AM Leo YY Eri CW Cas HD 101799 AH Cnc AC Boo W UHa AB And SW Lac U Peg XY Boo FG Hya RW PsA RZ Com AU Ser TX Cnc AH Vir W Crv V566 Oph AK Her RZ Tau AW UMa Notes: UZ Leo ER Ori RR Cen £ CrA V502 Oph DK Cyg 00 Aql BU Vel © American Astronomical Society • Provided by theNASA Astrophysics Data System b) Spectroscopicallydeterminedmass ratio. a) ColorsfromEggen(1967)unless otherwisereferredto. d) Averageofparametersfromsame source. c) Colorinferredfromspectraltype. l 0.439 , 0.326 ' 0.326 1 0.471 f 0.439 r 0.471 Period 0.268 0.221 0.284 0.278 0.297 0.286 0.319 0.317 0.321 (days) 0.352 0.321 0.370 0.366 0.332 0.338 0.334 0.371 0.360 0.375 0.360 0.386 0.383 0.388 0.408 0.410 0.422 0.416 0.618 0.606 0.423 0.591 0.453 0.507 0.516 a c Color B-V 0.85: 0.86 1.24 0.63: 0.82 0.98 0.69 0.66 0.75 0.53 0.60 0.90 0.61 0.61 0.57 0.66 0.62 0.49 0.53 0.62 0.75 0.87 0.61 0.78 0.71 0.44 0.53 0.59 0.39 0.36 0.54 0.375 0.36 0.36 0.66 0.37 0.37 0.76 0.29 Data forWUrsaeMajorisStars Reddening E(B-V) 0.03 0.00 0.03 0.07 0.00 0.00 0.02 0.00 0.02 0.02 0.00 0.04 0.00 0.06 0.03 0.05 0.02 0.02 0.05 0.10 0.00 0.05 0.00 0.00 0.02 0.02 0.00 0.09 0.05 0.09 0.15: TABLE 1 b b b b b b b d Ratio 0.50 0.521 0.79 0.41 0.22 0.59: 0.53 0.87 0.145 0.59 0.40: 0.299 0.415 0.526 0.142 0.185 0.43 0.54 0.81 : 0.50: 0.300 0.670 0.62 0.813 0.78 0.42 0.238 0.372 0.233 0.113 0.079 0.757 0.249 0.180 0.072 0.34 0.33 Mass 0.271 0.251 0.824 652 q Potential 3.932 3.856 3.91: 3.994 3.77: 3.90: 3.91: 3.954 3.805 3.88 3.584 3.767 3.532 3.826 3.837 3.903 3.945 3.619 3.92: 3.89: 3.923 3.880 3.957 3.749 3.867 3.871 3.732 3.712 3.763 3.964 3.559 3.646 3.563 3.64 3.424 3.844 3.761 3.677 3.965 3.652 C Fill-out 1.034 1.235 1.0 1.0: 1.0: 1.15: 1.0: 1.0 1.373 1.2 1.5 1.454 1.799 1.550 1.072 1.217 1.0: 1.13 1.1 1.126 1.21 1.15: 1.342 1.254 1.075 1.127 1.25 1.101 1.545 1.320 1.5 1.055 1.957 1.4 1.745 1.1 1.55 1.35 1.060 1.607 F Inclination 90.0 68.0 67.0 76.0 75 88 77.8 81.8 84 88 83.2 85.8 86.0 85.2 68.4 86 84 63.1 67: 87.5 87.0 75 77.5 86.5 79.1 80 80.8 82.9 81.1 82.4 80 72.3 78.7 74 79.1 84.0 80.3 84.9 87.2 i References Source (15), (16) (1), (21) (12), (16) (14) (21) (7), (21) (18) (12) (12) (12) (30) (12) (21) (14) (21) (28) (21) (22) (26) (21) (23) (21) (24) (25) (25) (12) (14) (26) (25) (21) (21) (13) (21) (26) (16) (21) (14) (21) (5) (3) (8) 198lApJ. . .245 . .650M where systems,whoseprimaryisattheterminal-agemainsequence,wouldbeexpectedtohewithgivenmassratioq;suchsystems contact binarymodelswithinitialmassratio0.7.Thedashedlinesareforq=0.2.hatchedarearepresentstheregion have evolvedintocontact.ThesystemsTZBooandWCrvareeachindicatedbyafilledcirclewithcross. 1 forwhichEggen(1967)hadreliablyde-reddenedcolors.ThesolidUnesrepresenttheenvelopezeroageandterminalmainsequence Q Fig. 1.—De-reddenedcolor{B—V)versustheperiodofcontactbinarystars.TheopencirclesarethosesystemsnotappearinginTable 0 © American Astronomical Society • Provided by theNASA Astrophysics Data System a a a a a V701 Seo0.7620.070.311.003.728 1.566.827 VIOIO Oph..0.6610.18...0.4893.873 1.17685.111 V535 Ara0.6290.10...0.3613.879 1.0268219 V1073 Cyg..0.7860.10...0.243.763 1.1369.621 GK Cep0.4830.08...0.894.00:1.0:72.56 AU Pup1.1260.000.6443.652 1.7168110 BHCen 0.7920.150.350.973.889 1.206909 Twigg 1979.(22)Whelan,Mochnacki, andWorden1974.(23)Whelan,Worden,Mochnacki1973. (24)Whelan (18) Rucinski19766;Rucinski,Whelan,andWorden1977.(19)Schöffel 1979.(20)TapiaandWhelan1975.(21) SvCen 1.6590.060.270.843.537 1.908417 et al.1979.(25)LucyandWilson 1979. (26)WilsonandDevinney1973.(27)Leung1977. (28)Winkler Doughty 1972a.(14)Mochnackiand19726.(15)Rucinski 1973.(16)Ruciñski1974.(17)1976a. Schneider 1977.(10)Leungand1978.(11)Wilson 1977.(12)Lucy1973.(13)Mochnackiand 1977. (4)Eggen1967.(5)Hoffman1978.(6)HutchingsandHill1973. (7)Knipe1971.(8)Leung1976.(9)and 1977. (29)WoodwardandWilson 1977. (30)Wordenetal.1978. a Source ReferencesforTables1and2.—(1)Berthier1975.(2)Binnendijk 1970.(3)Burchi,Milano,andRusso Colorinferredfromspectraltype. Name (days)B—VE(B—V)qCFiReferences Star PeriodColorReddeningRatioPotentialFill-outInchnationSource Data forHotContactBinarieswithPeriod<2Days Mass TABLE 2 653 198lApJ. . .245 . .650M 654 same meaningasinFig.1. listed inTables1and2usingthecylindricalcoordinate presented inTables3and4respectively.Adouble methods ofMochnackiandDoughty(1972û),are (1978) hasnotedtheimportanceofusingvolumesrather tested byintegratingthevolumesofspheres.Wilson tor wasperformed,toanaccuracyofbetterthan1% Simpson’s ruleintegrationofthecylindricalradiusvec- ble. Iassumethatsuchacomparisoncanbemadeby than sideradiiforstructuralmodelcomputations. primary’s internalluminositywhichistransferredtothe ing thetemperaturetoincludefractionof keeping thevolumeofprimaryconstantandcorrect- quence andevolutionarymodelsforsinglestarsispossi- temperature index,acomparisonwiththemainse- has thesecondaryderivingmostofitsluminosityby is transferredtothesecondary(Mochnacki1971;Moses secondary. Lucy’sconvectivecommonenvelopemodel where L,aretheapparent(radiative)luminositiesof b). Uptoathirdoftheenergygeneratedbyprimary “sideways convection”fromtheprimary(Lucy1968a, the primaryandsecondary,respectively.Iassumethat quantity Uwhichisthetransferredcomponentof the energygenerationrateofeachcomponentis energy radiatedfromthesurfaceofprimary, governed byanaverageruleformainsequencestars, secondary’s luminosityexpressedasafractionofthe J0rgensen (1970,hereafterCJJ): derived fromthemodelsof Copeland,Jensen,and 1974). FollowingMochnacki(1971),onecandefinea x2 Fig. 2.—Fill-outfactorFversusmassratioq.Symbolshave Volumes ^(F^q)werecomputedforthesystems By plottingthedensitypjofprimaryagainsta © American Astronomical Society • Provided by theNASA Astrophysics Data System 4 L (internal)oc9JÊ. (6) L —/^(internal) 2 MOCHNACKI (5) are Assuming thattheeffectivetemperaturesofcompo- nents areequal(toafirstapproximation),wehave where Sthesurfaceareasofprimaryand largely onthemassratioqandslightlyfill-outF. secondary components,respectively.Numericalcompu- tations byMochnacki(1971)showthatUdepends by constant radiusweretheenergytransfershutoffisgiven 2 given by rected colorindex(B—V)isshowninFigure3.Values is theempiricalzero-agemainsequence(ZAMS)mass- of (B—V)wereobtainedbyinterpolatingthevalues density relationbyusingthetheoreticalmass-luminosity radius relationofLacy(1977),transformedtoacolor- temperature calibrationstabulatedbyCJJ.Alsoshown relation ofCJJwhichLacyfoundtoagreewellwith observations. ZAMS, withsomeexceptions.Theseexceptions,suchas (1978). TheW-typesystemsaregenerallyclosertothe systems arelessdensethanzero-agemainsequence F, fromTable3intotheMorton-AdamsandBlaauw information asthecolor-perioddiagram(Fig.1)but momentum isconsidered. stars, inagreementwiththeinferredresultsofWilson with theeffectsofdifferentmassratiosandfill-outs 00 Aquilae,willbecomeverysignificantwhenangular where 9^,,Wlarethemasses ofthecomponents,R nuclear evolutionintheprimary,whereasFigure1, removed. Figure3isolatestheevidenceofinternalor x x and Raretheireffectiveradii, kRandare their radiiofgyration,and Q istheorbitalfrequency. standard color-perioddiagram,doesnot. momentum ofabinarysystemrotatingsynchronously and uniformlyis 2 x 2 x2 The increaseintheprimary’seffectivetemperatureat The “corrected”temperatureToftheprimaryis x The meandensitypoftheprimaryversuscor- It isclearfromFigure3thattheprimariesofA-type The density-colordiagram(Fig.3)containsthesame x Following Webbink(1976a),thetotalangular J= IV. ANGULARMOMENTUMOFCONTACTBINARIES 2 mwiA m+ x2 x2 4 U=(S/S-q^)(l +,(7) 2} log 7y=7^+A7^.(9) Alog T=^log(l+U).(8) e (2 + MkR x2 (10) 198lApJ. . .245 . .650M VW Cep CC Com YY Eri TW Get XY Leo Star Name AB And CW Cas TZ Boo ER Cep 441 BooBC RZ Com W UHa FG Hya^ SW Lac 00 Aq1 AK Her AH Vir AH Cnc AC Boo UZ Leo AU Ser RR Cen e CrA BU Vel AW UMa“j RZ Tau V566 Oph W Crv U Peg V502 Oph TX Cnc XY Boo AM Leo ER Ori HD101799 DK CygI RW PsA American Astronomical Society •Provided bythe NASA Astrophysics Data System 0.444 0.455 0.438 0.460 0.471 0.568 0.442 0.462 0.437 0.515 0.401 0.444 0.581 0.427 0.456 0.580 0.402 0.507 0.534 0.45: 0.466 0.554 0.548 0.515 0.503 0.424 0.426 0.439 0.407 0.610 0.409 0.520 0.553 0.492 0.473 0.482 0.622 0.405 0.500 0.526 0.342 0.350 0.303 0.305 0.323 0.361 0.263 0.250 0.257 0.346 0.359 0.308 0.403 0.325 0.225 0.302 0.368 0.267 0.33: 0.301 0.327 0.262 0.207 0.335 0.277 0.315 0.381 0.356 0.296 0.209 0.360 0.356 0.370 0.273 0.284 0.321 0.368 0.306 0.310 0.337 g cm 2.69 0.78 2.00 0.83 1.34 1.47 1.73 2.03 1.78 1.07 1.33 1.26 1.28 0.25 0.37 0.62 0.90 1.25 0.26 0.63 0.63 0.79 1.22 0.23 0.38 0.40 0.88 0.92 0.98 0.61 0.64 1.05: 0.51 0.94 0.68 0.94 0.46 1.10 0.89 1.21 Properties ofWUrsaeMajorisStarsComputedfromtheDatainTable1 g cm 2.51 3.31 1.91 2.26 2.07 2.60 1.58 1.30 1.89 2.23 1.25 1.19 1.41 0.66 1.69 1.55 0.48 0.51 0.81 0.97 0.79 0.28 0.43 0.90 0.72 1.33: 1.29 1.05 1.02 1.07 0.64 0.71 1.00 1.13 1.18 1.09 1.06 1.38 1.25 1.31 -3 4150 4553 5330 5853 5100 5548 5150 5648 5600 6150 5920 6246 4870 5221 5400 5630 6250 6814 5070 5559 5950 6195 5950 6191 5670 6224 5670 6226 5900 6267 6600 7236: 5950 6375 7050 7279 7650 8134 6250 6613 5380 5859 6450 6961 6450: 6987: 5500 5892 5220: 5704: 7250 7729 7350 7702 5900 6359 7250 7428 5950 6523 5830 6213 7250 7419 6650 6970 6250 6803 7050 7470 5920 6338 5400 5752 7700 8215 7700 8289 eff °K 0.171 days 0.169 0.197 0.241 0.189 0.244 0.080 0.274 0.272 0.327 0.216 0.264 0.048 0.048 0.264 0.058 0.497 0.151 0.177 0.27: 0.216 0.124 0.125 0.026 0.403 0.236 0.256 0.223 0.023 0.126 0.380 0.351 0.367 0.080 0.335 0.229 0.179 0.228 0.155 0.352 P o TABLE 3 M(TAMS) ZAMS)M^ipr)M^Pr) t 2118 0.87 0.98 1.05 1.05 1.16 1.16 0.97 0.96 1.18 1.27 1.37 1.23 1.14 1.23 1.38: 1.11 1.39 1.70 1.61 1.77 1.60 1.26 1.13 1.32 1.28 1.21 1.27 1.60 1.15 1.42 1.29 1.39 1.48 1.14 1.14 1.32 1.74 1.73 1.38 (0) TAMSZAMScms'x10" 1.06 1.35 1.56 1.51 1.49 1.35 1.29 1.67 1.78 1.31 1.31 1.67 1.48 1.63 1.48 2.25 1.92: 2.31 1.89 2.19 2.12 1.73 1.58 1.85 1.80 1.53 1.70 1.95 1.70 1.74 2.21 1.90 1.60 1.81 1.90 1.56 1.79 2.31 2.30 6.6 5.4 5.4 5.1 5.8 4.7 4.5 5.1 4.0 4.2 4.5 5.0 4.2 4.5 4.2 2.4 3.6: 2.1 2.1 4.8 2.0 3.9 4.4 4.5 4.0 4.4 4.1 4.9 2.6 3.7 3.6 3.4 3.1 3.4 3.8 3.8 2.6 2.3 2.3 6.5 5.2 5.2 5.6 4.5 4.3 4.9 4.3 4.8 4.0 4.0 4.8 3.8 4.3 4.0 2.2 3.4: 1.8 1.9 1.9 4.6 4.2 3.7 4.2 4.3 2.4 3.4 2.8 4.7 2.4 3.5 3.1 3.8 3.1 3.6 3.6 3.9 2.1 2.1 0.84 0.94 0.71 0.99 1.14 1.19 0.58 1.16 0.58 1.25 1.40 1.14 1.16 0.94 1.22 1.32 0.79 1.45 1.32 0.89 1.12 1.80 0.97 0.78 0.97 0.58 0.58 1.16 1.39 1.44 1.53 1.22 1.67 1.22 1.52 1.45 1.14 1.45 1.35 0.96 0.84 1.11 1.11 1.35 1.40 0.73 0.73 1.39 1.67 1.50 1.39 1.37 1.47 1.65 1.14 0.97 1.73 1.35 1.58 2.21 0.97 0.71 1.50 0.71 1.12 1.53 1.22 1.39 1.83 1.65 1.77 1.85 1.19 1.72 1.42 2.06 1.62 1.75 A? W? Type W w W w w w W w w W: A A A A W A A A W A? A W W A 198lApJ. . .245 . .650M 2 656 MOCHNACKIVol.245 Rewriting andsubstitutingKepler’slaw, where themassratioqisgivenby^/Wlj, ing onthesystemconfiguration.Webbink(1976a)takes k —k=0.10andusestheRocheinnercontactlobe total mass,andf(q)isadimensionlessfunctiondepend- approximation (Kopal1959). 2 1
ß w <* \ [ Mi-m)1/3 ] 2 6\j
-1
f(n) dfi (30) PRIMARY MASS (Solar Masses) Fig. 8.— Structural exponents a and \ versus primary mass. where /(/x) is given by Webbink (1976a) These constants are defined in eqs. (28) and (34), and have been estimated from the models of Iben (1967a, ¿>). The dashed lines f(fi)=n(\ —/i)+0.0572|Lt—0.0705/i(l —/i)1/3 show the chosen extrapolations below one solar mass, for which nuclear evolution is comparatively slow. +0.0214(1-/x)2/3, (31) 1.50, 2.25, and 3.0 interpolated linearly for inter- mediate values of the primary’s mass. It is assumed to and hence be constant for ^ 1.0 307 0- Figure 8 shows a as a df( ix) function of primary mass. = 1.0572 — 2/1—0.0705(1 -/i)l/3 Again, following Webbink (1979a), the evolution of /xc. is assumed to follow —0.0143(1—/i)~i/3+0.0235 /t(l -/i)“2/3. dhifi c s (28) ~dT i • (32)
Assuming y = 1 = constant, Iben’s Population I models The rate of loss of angular momentum due to gravita- give a=0.81X10-10 yr-1 and 5 = 3.5. tional radiation, din J/dt, is given by the usual general It must be noted that these calculations ignore the relativistic quadrupole formula, changes in the primary’s structure caused by rapid rota- tion and the energy transfer from primary to secondary. 3 Rotation generally increases the volume of a star, de- dhxJ _ 32G ättVO-M) , . creases its luminosity, and increases its lifetime. On the dt 5c5 ^4 • (33) other hand, energy transfer should tend to decrease the volume of the primary component in a contact system. It should be noted that this equation has been ques- These effects combined together are relatively unim- tioned by some authors (e.g., Cooperstock and Hobill portant unless the rotation is nonuniform (Whelan 1972). 1980). For mass ratios close to 1.0, or very small, the energy Each evolutionary track was computed by assuming transfer is small, and Whelan’s results may not be initial values for q and 907, and integrating equation (30), applicable. The rotating single star models of Papa- with appropriate substitutions, using a Runge-Kutta integration routine. A metallicity of Z=0.02 was as- loizou and Whelan (1973) suggest a maximum over- r estimate of about 20% in the density for <7=1.0 and sumed, and A =0.71 at the start of each integration in about 30% for <7<0.1 if one uses the nonrotating mod- the choice of the various constants and exponents for els. Any such estimates, however, are highly dependent the approximating formulae. on details such as mixing lengths. The mean density of The luminosity at any point on the evolutionary track FG Hya in particular may be lower than predicted by was determined by using the relation neglecting rotation. b) Evolution with Angular Momentum Loss = (M> The total angular momentum is obtained by substitut- ing equations (25) and (26) into equation (11) so that The exponent \ was obtained from Iben’s models,
3+ 2 and is also plotted in Figure 8. The zero age luminosity (?aK ^o/ (/tK^ was (29) L(9D7i)zams obtainedr by interpolation among the g—A(l—/i)1/3 CJJ models for Z=0.02, A =0.70. The luminosity of the
© American Astronomical Society • Provided by the NASA Astrophysics Data System 198lApJ. . .245 . .650M mass Webbink (1979û). ratios of0.70downto0.15.Systemswithinitialmass masses Wlbetween1.0and3.0 bined luminosityandthevolumeradiiwereusedto ratios qabove0.72wereunstable,inagreementwith evolution ofthesecondary’scoretakesplace.Thecom- No. 2,1981 secondary wassimilarlyobtained,assumingthatno compute theoreticalmeancolors. pendicularly totheZAMSlocus.Thepopulationof systems evolveessentiallyalongtheZAMSrelationfor ary gridsforinitialmassratiosq=0.2,0.7.Low-mass the initialmassratio.High-masssystemsevolveper- color-period diagraminFigure1iswellcoveredbythis T band inFigures1and9correspondstosystemswith evolutionary scheme,withtheexceptionofsystemssuch 0 masses qare0.7{solidlines),0.2 {dashed lines).ComparewithobservationsinFig.1. primaries ontheterminal-agemainsequence,withq=0.6 as OOAgi,WCrv,RWPsA,andAUSer.Theshaded (bottom ofband)and0.8(topband).Moreevolved with largerq.Initiallydetachedsystemswhichhave would heinornearthisband.Thesystemswhichdo evolved intocontactwithoutalargemassratioreversal systems willhetotherightandbelowthisband,even near thisbandallhavequitelargemassratios,low 0 Q A gridofevolutionarymodelswascomputedfortotal Figure 9isthecolor-perioddiagramwithevolution- Fig. 9.—Evolutionarytracksinthe color-perioddiagram.Themasses,andvariouselapsedtimesineons sincezeroage,areshown.Initial © American Astronomical Society • Provided by theNASA Astrophysics Data System c) ComparisonofTheorywithObservation CONTACT BINARYSTARS ratio q=0.2.Theenvelopeofthetrackswasshownin density pjversus(B—V)forinitialmassratioq$=0.7. large initialmassratio.Theonlypossiblyunevolved while otherssuchasAKHerlieclosertothetrackfor Figure 12showsthetheoreticaltracksforinitiaimass Hya lieclosertothetracksforlowinitialmassratio, Figure 3.CertainevolvedA-typesystemssuchasFG low massratiosystemsmaybeduetoobservational mass ratioisTZBoo,butotherwisealltheA-type system withrelativelyhighmeandensityandverysmall primary densitiesandhighangularmomenta.Iconclude expect aboutasmanyunevolvedsystemsoflowmass effects (van’tVeer1978),butneverthelessonewould systems appeartobeevolved,withdensitiesmuchlower than expectedforagezero.Thelackofunevolvedcool figurations. that thesesystemsevolvedfrominitiallydetachedcon- minimum periodslongerthanzero-agemainsequence shown againstminimumperiodPinFigure10.Again, have hadextremelylowmassratiosaszero-agesystems, the systemsOOAgi,WCrv,RWPsA,andAUSerhave 0 u systems withmassratiog=1.0,whilemostoftheA-type or havelostmoreangularmomentumthanpredictedby tionary modelpredicts.TheA-typesystemsmusteither systems haveshorterminimumperiodsthantheevolu- the presenttheory. 0 Figure 11showsthetheoreticaltracksofmeanprimary Theoretical correctedprimarycolors(B—V)are x 663 198lApJ. . .245 . .650M stars inFig.4. elapsed timeineonsshown.Compare withobservedstarsinFig.3. Fig. 10.—Correctedprimarycolorversusminimumperiodforthesameevolutionarymodelsshownin9.Comparewithobserved Fig. 12.—Sameas11,butfor initialmassratio#=0.2. F. 11..—Theoreticaltracksof mean primarydensityversuscorrectedcolor,forstarting massratioq-0.7.Massesand 0 IG Q © American Astronomical Society • Provided by theNASA Astrophysics Data System MINIMUM PERIOD(days) 198lApJ. . .245 . .650M have largermassratios. with lowqstronglysuggeststhatyoungWUMastars ratio asevolvedones.Thelackofunevolvedsystems plausible mechanismsofangularmomentumlossresult- ratios ofsomeA-typesystemsarenotnecessarilyevi- ing insmallermassratios.Stellarwindmagneticbraking dence forlowinitialmassratiosbecausethereareother is aparticularlyefficientprocess,andwillbeshownin loss. § Xtobeasufficientmechanismforangularmomentum Whelan (1975)forthecontactbinaryeCrA,isthat contact. Afurtherpossibility,exploredbyTapiaand systems, suchas00Agi,haveprobablyevolvedinto contact fromsemidetachedsystemsinwhichthesec- some oftheextremeA-typesystemshaveevolvedinto velope phasemaybepossibleforclosesystems,since binary evolutioniswellknownfromtheexampleofAS momentum islostduringthesemidetachedstageof ondary isthemoreevolvedcomponent.Thatangular Webbink (\911a)hasshownthatsecondariesofless especially ofshort-periodnoncontacteclipsingbinaries, rapid accretionofmatter.Furtherobservationalstudies, A-type systemshaveevolvedintocontact,thentheir Eri (Refsdal,Roth,andWeigert1974).Iftheextreme than 0.69ftmayshrinkratherexpandduring luminosity, sincethetheoreticalevolutionaryH-Rdia- are necessarytosortouttheevolutionarypathsleading inferred empiricalH-Rdiagramintheupperpartof required todeterminewhichcomponentisthemore tems areprobablyattheinitialstageofmassexchange, to theformationofcontactbinaries.The00Aqlsys- hand, dositalittlehigherthanthemodelpredicts. secondaries cannotbegeneratinganunusualamountof period distributionhistogramofcontactbinarysystems evolved. arrested bycomingintocontact.Furtherstudiesare gram inthelowerpartofFigure6agreeswellwith Figure 6.TheOOAquilae-typeobjects,ontheother has beensuggestedbyLucy(1976)aspossibleevidence present model,lowmassratioA-typesystemsalsocan been detachedsystems.Withthepossibleexceptionof have periodslongerthan0.45dayswithouteverhaving for theOOAqlclassofbinary,but,accordingto for evolutionintocontact.Thiscanbeshowntotrue which mayhaveevolvedascontact binariesandothers early-type systemssuchasV701Sco(WilsonandLeung of whichhaveevolvedinto contact. Webbink(19766, 0 “tail” thereforeconsistsof evolved systems,someof 1977) andBHCen(LeungSchneider1977),Lucy’s 1977ö, b,19796,c)hasmodeled casessimilartothese. The unexpectedlylowangularmomentaandmass We haveseenabovethatcertainhighmassratio Mass ratioreversalwithoutenteringacommonen- The existenceofa“tail”towardlongerperiodsinthe © American Astronomical Society • Provided by theNASA Astrophysics Data System d) EvolutionintoContact CONTACT BINARYSTARS binaries. Solar-typestellarwindscanremoveasignifi- that predictedbygeneralrelativityhasaninteresting cant amountofangularmomentumfromrotatingstars solution applicableaswelltostarswhicharenotcontact ing inallkindsofclosebinaries,andhisscenariofor (e.g., Schatzman1962;Brandt1966;Mestel1968; Roberts 1974).Huang(1966)describedmathematically be directlycomparedwithobservations.Refsdal,Roth, contact binariesisverysimilartotheevolutionary the effectsofangularmomentumlossbymagneticbrak- make anyquantitativetimescaleestimateswhichcould magnetic brakingasthemechanismforangular scheme developedinthispaper.However,hedidnot momentum lossindetachedandsemidetachedsystems, and Weigert(1974)Eggleton(1976)havesuggested The magneticfieldoftheSuncanbedescribedbestasa estimate ofitseffect. stars, butineachcasewithnoaprioriquantitative and van’tVeer(1979)hasdonethesameforWUMa pressive observationalevidenceforthisoveralldescrip- spiral pattern(Parker1958;WeberandDavis1967). the coronaalongopenfieldslinesdirectedoutwardina netic equatorialplane(PneumanandKopp1971).Im- rotating obliquedipolewithacurrentsheetinthemag- wind streamsoriginatinginactiveregionsandflowing The fieldinthesestreamscanaccountforasignificant outward throughcoronalholesalongopenfieldlines. are largeirregularitiesinthefieldcausedbyhigh-speed senberg (1978)andbyVillanteetal.(1979).Therealso tion hasbeenobtainedbySmith,Tsurutani,andRo- poloidal magneticfieldBequaltoabout1-2gauss et al.1977).Whicheverviewpointisused,“floppyhat” Wilcox 1978).TheradialcomponentBofthemagnetic or “spikyball,”onecanconcludethattheSunhasa fraction oftheinterplanetarymagneticfield(Levine averaged overtheentirephotosophere(Svalgaardand field atlargedistancesfromtheSunisgivenby where Risthephotosphericradius.Thelatitudedepen- below, whichapplytotheequatorialplane. dence ofthefieldwillbeneglectedforcalculations p proposed byMullan(1975)forWUMastarsonthe r basis ofasimpledynamotheory,leadingtoactivity ous convection.Poloidalfieldsof30-50gausshavebeen thought tobeassociatedwithrapidrotationandvigor- what distinguishesthecooler W-typesystemsfromthe istence ofspotsonWUMa starshasbeenproposed hotter lessmagneticallyactive A-typesystems.Theex- similar toorgreaterthanontheSun.Mullansuggests that theresultinggreaterspot activityontheprimaryis 0 The problemofangularmomentumlossinexcess In thecaseofSun,chargedparticlesescapefrom Surface magneticfieldsinlatetypestarsareusually X. STELLARWINDSANDEVOLUTIONOFBINARIES 2 B =(R/r),(35) rp0 665 198lApJ. . .245 . .650M W UMaitselftobecoveredbyspots. many times(e.g.,Binnendijk1970).Newconfirmation for thishypothesishasbeenobtainedbyEaton,Wu, tions. Theyfindabout20%oftheprimarycomponent and Rucinski(1980)usingsatelliteultravioletobserva- 666 W UMastars(Dupree,Hartmann,andPreston1979) indicate activecoronaeandchromospheres.Thissug- in WUMastars,analogoustobutmoreintensethan gests enhancedsolar-typeactivity,andonecansafety assume theexistenceofmagneticfieldsandstellarwinds the Sun. 1979) andofstrongultravioletemissionlinesfrom one assumesanextrapolationofSkumanich’s(1972) and Dumey’s(1972)evidenceforBocfíinrotating in slowlyrotatingsolar-typestarsandWUMastars. B ~40-100gaussforWUMaprimaries. solar-type stars.ScalingupfromtheSun,onegetsfields The formerareslowmagneticrotators(SMR),inwhich higher outwardvelocities(BelcherandMacGregor1976). magnetic accelerationisdominant,producingmuch fast magneticrotators(FMR),suchasWUMastars,the the thermalenergyinputtowindisdominant.In velocity atinfinity,Bistheaveragepolidalfieldover binary natureofthesystemasfarflowiscon- velocity, and9D?isthemasslossrate.Ineglect where Visthemagneticallyacceleratedoutwardflow the stellarsurfaceofradiusR,ßisangular is asafeassumptiononevolutionarytimescalesfor component inaWUMasystem.Completecouplingof cerned andtakeR=tobetheradiusofprimary rewrite equation(8)ofBelcherandMacGregor(1976) radial velocity(arathercrudeassumption),onecan p lobes (DeCampliandBahúnas1979). p convective componentswhichfillmostoftheirRoche the spinandorbitalangularmomentaisassumed.This where theoutwardvelocityexceedslocalAlfvén to give For asphericallysymmetricdensity distribution,Weber speed, isgivenby that forfastmagneticrotators,theAlfvénradius>, p and Davis(1967)showedthat thebrakingtimescaler M 0 0X A B The discoveriesofX-rayemission(Cruddaceetal Even highermeanpoloidalfieldsmaybeobtainedif There isafundamentaldifferencebetweensolarwinds Assuming sphericalsymmetryofthewinddensityand Belcher andMacGregor(1976)havefurthershown © American Astronomical Society • Provided by theNASA Astrophysics Data System V =\ r=1/2 M A (3/2)V/Sl. (37) a) ASimpleTheory M sôî ,1/3 MOCHNACKI (36) 4 9-12 5 10 _13- where Jisthetotalangularmomentumand/ is givenby one finds, torque. Combiningequations(36),(37),(38),and(14), where isthetotalmassand/(F,q)givenby equation (12).Ifoneassumesthat where aisstellarpoloidaldynamoconstant,then after somemanipulation, phase. Thisfollowsfromtheusualestimatethatabout requiring thatmoststarsgothroughacontactbinary evolution, onecanconcludethatthebrakingtimescale out.) SincetheA-typesystemsshowevidenceofnuclear than about5X10“timesthenucleartimescalewithout First, onecannotallowthebrakingtimescaletobeless cannot bemuchshorterthanthenucleartimescale. author thanksananonymousrefereeforpointingthis braking component’sradiustothebinaryseparationhas Conversely, themagneticbrakingtimescalehastobe scale iftheWsystemsaretoevolveintoA-typesystems. shorter thanthegravitationalradiationbrakingtime loss ratehasonlyaninversecuberooteffect,whilethe have shorterbrakingtimes.Themagnitudeofthemass contact systems,andsystemsofsmallmasswillalso scale willobviouslybeshortestforcontactorover- a strongeffectuponthebrakingtimescale.The magnetic fieldhasa—4/3power. data fromTable3,/(F,#)~0.25,3ft,~1.17 1/2000 ofallobservedstarsareWUMastars.(The p is thenabout(2-4.5)X10 yearsforülft^lO, is about4X10gaussseconds. Thebrakingtimescalet Assuming thattheSunhas23^ ~1gauss,thevalueofa 8.4 X10cm,onefinds, 103ft yr,respectively. Thepoloidalfieldinthis b p o Some simplelimitsonmagneticbrakingcanbeplaced. Equations (39)and(41)showthattheratioof Case I:AtypicalW-typesystem,TXCancri.—Taking 2 28_1/3 2sl/3 ' \47TÏÏÎ/ Tß- T(TXCnc)~8X103)ia/). (42) _/Gai\ s U) T=-///=3//(20r¿TO), (38) fl h) ApplicationofTheory B=ai p 2 Gmai Rm x 4 V*. 1/3 2/3 Vol. 245 (39) (40) (41) 198lApJ. . .245 . .650M 12-5 9 913- 9 9 10 10 9 10 9 10 9 For 99?=10~9^oyr>a,=4X10gaussseconds, No. 2,1981 braking shouldbethedominantinfluenceonevolu- have T~2X10years.Thusstellarwindmagnetic one getsr~lX10years;if9ft~10~9P?yr,we /(F,<7)~0.14, R/A~0.51,•äft~l.;äft,and£,-7.4 r ~(5—11)X10years. case isabout70-80gauss.Afieldhalfofthatgives of TXCncisintherange2-11X10years,whichless tion ofalow-massW-typesystemsuchasCCCom. about 4X10years. than itspresentgravitationalradiationtimescaleof ^,-0.7^, F,-5X10cm,sothat Using datafromTable3,/(F,<7)=0.22,RA4~0.455, since ithasamid-Kspectraltype,andanextrapolation from theSunofSkumanich’slaw,B—aÜ,with same a,isprobablyunjustified.Ifthepoloidalfield could belessthan10years stronger, thelifetimeofCCComasaW-typesystem / ß ßo x10 5 o 1/ Taking thesamevaluesofaandTO,onegets p p For thesamevaluesofaand9F,wehaver~(2-4)X X10 cm,thebrakingtimescaleis If Upishalved,thent~(1-2)X10years.Thebraking nuclear evolutionandsinceitsmassratioisquitelarge, OO Aqlhaslowmeandensityindicatingadvanced 0.40, TO^O.ÇTOo,Ä,~9X10cm,onegets its probableunevolvedanalog,CCCom. time scaleisthereforeevenshorterinFGHyathan fairly recently. the possibilityisreinforcedthatitcameintocontact p 10 years.Halvingagivesr~(5-4)XSince mass ratiosystemisknowntohavelostangular pfi momentum sinceitsrapidphaseofmasstransfer (Refsdal, Roth,andWeigert1974). Dimensionsarefrom losing angularmomentumas arapidmagneticrotator, R=2.2 .Assumingthat thesubgiantsecondaryis b Popper (1973):9ft,=1.99ft,9 ft =0.29ft,A=10.6F pÄ 2q 0 2o0 The magneticfieldinCCComisnotwellguessed, It isfarilysafetoconcludethatthebrakingtimescale Case II:Alow-massW-typesystem,CCComae,— Case HI:ACoolA-typesystem,FGHydrae.—With Case IV:OOAquilae—Wiihf(F,q)~0.26,R,/A~ Case V:Semidetachedbinary,ASEridani.—Thislow © American Astronomical Society • Provided by theNASA Astrophysics Data System 28l/3 281/3 281/3 T(CCCom)~3.5X10Wa/)~. (43) t(00 Aql)~6.6X10(3fca/)“.(45) s T(FGHya)~1.3X10afta/) .(44) b B 8 t~(3.5-7)X 10years. b CONTACT BINARYSTARS 2 8 2 9 and that/(#)—#/(l+#)=0.086,then quired orderofmagnitude. onds, wehaver~4X10years,whichisofthere- lobe, F~0.45F,sothat whence A—1.18F.IfthecoolsecondaryfillsitsRoche typical parameters:period=4hours,9^j=—0.4, is thesameforUGeminorium-typestarsasSun The quantity\dJ/dM\isjustthespecificangular wind magneticbrakingincataclysmicbinariesisobvi- is tenuousatbest.However,theimportanceofstellar (49) iseasilysatisfied,andthemasslossratetermin equal toQr.Forefficientmagneticbraking,condition momentum transportrateLofWeberandDavis(1967), seconds, wehaver~10years.Theassumptionthata equation (48)isnegligible.Theresultsofthispaper ous fromequation(47)foranysensiblevaluesofïïiïand initially detachedsystemevolvesintocontact,substan- V UMa systems.Ontheotherhand,itispossiblethatifan suggest that|d\nM/dt|<0.011J/dtformostW been neglected.Onecaneasilyshowthatallowingfor increase itsminimumperiod.Suchamechanismmay fl have causedtheunusuallylongminimumperiodsof tial masslosswithoutefficientmagneticbrakingmay minimum periodvariesas g 0 the lossofbothangularmomentumandmass, OO Aquilae-typesystems. 20 plain mostoftheangularmomentum lossinWUMa cially importantnotonlyduringtheformationofcon- The conditionthatPdecreaseisthen much oftheirlifetime.Not only canstellarwindsex- tact binaries(Huang1966;Mestel1968),butalsoduring on thefurtherevolutionof systems containingacool stars, buttheycanalsohave a verysignificantinfluence fip 0 _lo-15 12-5 If 9ft~lO9ftyranda,=4X10gausssec- Assuming 9fc~10“9^0yrand=4X10gauss Case VI:Cataclysmicbinary.—Iassumethefollowing The effectofmasslossontheminimumperiodhas 0/ These calculationsshowthatmagneticbrakingiscru- 2841/3 r(cataclysmic)^3X109fea,) .(47) Ä/ 2841/3 T(ASEri)~7X10aña,)“. (46) B; dlnP_ dlnJdlnM 0 35 dt ' c) Discussion dM 3AT dJ ^J_ > 667 (48) (49) 198lApJ. . .245 . .650M include inthecomputationofevolutionarygrids.A been consideredbySiscoeandHeinemann(1974). pertinent tomagneticfields,coronaeandwinds.Some ment ofwindsincontactandotherbinaryconfigura- of thetheoreticalproblemsbinarystarwindshave self-consistent three-dimensionalhydromagnetictreat- 668 tions isneeded,togetherwithmoreobservationaldata Webbink’s conceptsofclosebinaryevolution,butthat W UrsaeMajorisstarsareingeneralagreementwith initial massratio<7~0.7. were probablyformedascontactbinariesoffairlyhigh three identifiablesubclassesofcontactbinaries: systems presentlyincontact.Theseprocessesgiveriseto there areatleasttwodifferentprocessesthatresultin losing muchangularmomentumatpresent.Sincethey contact binariesorwhichhaveevolvedinturnfroma sities closetothezero-agemainsequence.Thesesystems to theW-typesystemswhoseprimarieshavemeanden- by gravitationalradiationhasbecomeunimportant now havesmallmassratios,angularmomentumloss A orWtypesystemsintheclassificationschemeof existed ascontactsystemsatagezero.OOAquilaeisthe density havetoomuchangularmomentumto dicted bygravitationalradiation,andthishasbeen Wilson (1979).Masslossmay havebeendrastic. They couldbecalled“B-typesystems,”afterLucyand most extremecaseknown.Suchobjectscanbeeither semidetached configurationcorrespondtotheA-type probably implieslittlestarspotactivity(Mullan1975). The magneticbrakingeffectshouldbelessinthese (Webbink 1976a).Theregularityoftheirlightcurves ondary ortheprimaryismoreevolvedcomponent. Binnendijk (1970),anditisunknownwhetherthesec- shorter timescale,withoutdrasticlossofmass. shown tobeduestellarwindmagneticbrakingona systems havelostmoreangularmomentumthanpre- systems oflowmeandensityandmassratio.These systems, justasitisinearlyFandhottersinglemain- variables. Alow-massRSCVnbinarycanalsoevolve sequence stars(Kraft1969). into contacttoformasystemsuchas00Aql. degenerate systemssuchastheUGemcataclysmic Efficient magneticbrakingofRSCVnandsemide- tidally coupledcomponentwithoutacommonenvelope. tached systemsmayultimatelyleadtoveryshortperiod 0 clearer whenmoreisknown abouttheshort-period detached orsemidetachedsystems. Mostofthebinaries The brakingtheoryappliedhereisstilltoocrudeto This paperhasshownthattheobservationaldatafor a) “Classical”little-evolvedWUMastarscorrespond The hotterA-typeWUMasystemsshouldnotbe c) Evolvedsystemsoflargemassratioandlowmean h) EvolvedWUMastarswhichhavealwaysbeen These presentlyvaguesubclasses willbecomemuch © American Astronomical Society • Provided by theNASA Astrophysics Data System XL SUMMARYANDCONCLUSIONS MOCHNACKI 9108 The resultsofthispapershowthataccretingcoresrather development, assummarizedbyLucyandRicco(1979). than homologouspolytropesshouldbeusedinfissionor binary formationproblem. ing hasbeensuggested(Huang1966;Mestel1968),and mentation atanearlystagefollowedbymagneticbrak- Roxburgh’s (1966)fissiontheorybasedonformationof fragmentation models.Theangularmomentaofrela- Wilson areshowntobeevolvedsystemswithpeculiari- tively unevolvedWUMabinariesaretoohighfor a radiativecoreinrotatingHayashiprotostar.Frag- The innercontactconditionasdefinedbyWebbink resolved. Theso-calledB-typesystemsofLucyand The primariesofcontactbinariesresemblesinglestars why contactbinariesprefertheinnerLagrangiansurface. (1976a) hasprovedtoberemarkablyconsistentwiththe should beconsideredinamoremodemtreatmentofthe observations, andthereforeanynewtheorymustshow ties andnotdetachedcounterpartsofW-typesystems. prediction ofcontactbinarybehavior. of thesamemassonceluminositytransferiscorrected lar windbrakingofafastmagneticrotator.Thetime predicted bygravitationalradiationisexplainedstel- nor thecontactdiscontinuitytheoryoffersacomplete for. Neitherthethermalrelaxationoscillationstheory with periodsbetween0.45and0.60daysareratherfaint perature indicatorunaffectedbyinterstellarreddeningis light-curve andline-profileanalyses.Anaccuratetem- may explaintheoriginsofevolvedcontactbinaries. braking timescalesareunlikelyunlessthefields needed. TheworkofEggen(1967)isstillthemost of theirevolutionarystatusandabsolutedimensions scale ofthiseffectinWUMastarsisestimatedtobe ing. SuchaneffortwasbegunbyRucinski(1976c). extensive photometricsurveyofWUMastars,buta tems canbeexpectedtoevolveintocontact.Knowledge and requirelargetelescopesfortheirstudy.Thesesys- will placestringentlimitsontheeffectsofmagnetic about 10-10years,longerthantheyearsorless give bettermeasuresoftemperaturesandlineblanket- braking. (ItiscuriousthatthepresentroughdataonER suggested byvan’tVeer(1979).Muchshortermagnetic spectrophotometric surveyatmoderateresolutionshould stars inoldopenclusters,suchasNGC188andM67, stronger. DetailedobservationalstudiesoftheWUMa deduced forWUMastarsinthefield.) Cep andAUCncindicatehighermeandensitiesthan momentum lossinotherkinds ofbinariescontaininga large fractionofitsRochelobe. 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