1955ApJ. . .121. . .71C 1 found tolie,asagroup,veryneartheirmaximumsize.Anevolutionarymechanismisproposed,relating Those withmasslimitlessthan1Owereclassifiedasdefinitelyabnormalsubgiants.Thesestars of thecomponents.Thismassratioisdirectlyrelatedtosizezero-velocitysurfacepassing luminosities ofthesubgiantsecondariesdependnotonlyontheirmassesandradiibutmassratio listed 82eclipsingvariablesforwhichspectroscopicdeterminationsofthevelocity-curve the advanced“biologicalage”ofthesestarstofactthattheyfillinnerzero-velocitysurface. From thephotometricradiiofsecondariesitwaspossibletoobtainanupperlimittheirmasses. paper. TheworkofParenagohasrecentlybeenreviewedanddiscussedbyStruve in closebinarysystems,asexemplifiedbyeclipsingsystemswithAlgol-typelight-curves. through theinnerLagrangianpointofsystem,whichsetsanupperlimittosizestar. of theAlgoltypehasbeenstudiedinlightaresultbyStruve(1953),showingstatisticallythat ponents ofthebinarysystem. of theprimarycomponentaloneareavailable.Fromtheseheselected54systemsthat profitable fieldofstudyforclarifyingthisdistinction.P.Parenago(1950)hasrecently corresponding totheobservedspectraltype,Parengowasable,fromspectroscopic The remaining53allhavemain-sequenceprimariesandformthesubjectmatterofthis also possessadequatephotometricdata.Oneofthesesystemshasasupergiantprimary. is theAcomponentofvisualbinaryfHerculis.Eclipsingbinariesarethereforea the firstclasscontainingallsinglestars,whereasmembersofsecondoccuronly secondary dependsnotonlyonitsmassandradiusbutalsotheratioofcom- Such systemsmightalsoincludethefirstornormaltypeofsubgiant,whoseprototype which passesthroughtheinnerLagrangianpointL\.Weshallrefertothisas masses ofthesecondariesare,onaverage,belowsolarmass,whiletheirradiiare and photometricdata,tocomputedirectlythemassradiusofsecondary,aswell The questionarises,then,astowhetherinsome casesthesecondarycomponent(as- a binarysystemislimitedbythedimensionsofzero-velocitysurfacesurroundingit, considerably largerthanthesun’sradius.Nowsizeofastarwhichismember as thedistancebetweencomponents.Asurveyofhislistshowsatoncethat zero-velocity surface.Itsdimensionsarealwayssmallerforthelessmassivecomponent. Gould (1954).Struve(1953)hasshownstatisticallythattheluminosityofasubgiant abscissa wasr(thephotometricradiusofthesecondary), andtheordinateratio sumed tobethelessmassive)fillsthisinnersurface, asillustratedschematicallyin surface, acommonenvelopecannotexist,andonemusttake theinnersurfaceasthatofswollenstar. Figure l. the secondLagrangianpoint,Lj,asincaseofßLyrae. However,ifonlyonestarfillstheinner 2 1 © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem A recentpaperbyParenago(1950)onthesubgiantcomponentsof“single-line”eclipsingbinarysystems By choosingthemassofprimaryineachcaseasaveragemain-sequencevalue It hasoftenbeensuggestedthatsubgiantstarsfallintotwophysicallydistinctclasses, The starsofParenago’slistwerethereforeplotted on adiagram(Fig.2)forwhichthe Inthecaseofcontactbinaries,limitingsizeisgivenby thezero-velocitysurfacepassingthrough ON THESUBGIANTCOMPONENTSOFECLIPSING Berkeley AstronomicalDepartment,UniversityofCalifornia II. THEGROUPOPABNORMALSUBGIANTS BINARY SYSTEMS Received June22,1954 J. A.Crawford I. INTRODUCTION ABSTRACT 71 1955ApJ. . .121. . .71C is knownfromobservation (theinclinationoftheorbitisobtainedfrom photometric guess astothemassofprimary.However, massfunction, data). Sincethesecondary cannotliebelowthecurve,wecan,byplacingit onthecurve gests thatmanyofthesubgiantcomponentsdofill theinnersurface. and, inaddition,atendencyforthesubgiantstocluster quitenearthecurve.Thissug- as somesubgiantsabovethecurvewouldceasetobeclassifiedabnormal.Itshould cant separationbetweenthemain-sequencesecondaries andthesubgiantsecondaries dication would,forinstance,beaccentuatedifwehadusedWood’s(1950)limitingcurve, below) maytend,ontheaverage,tooversteplimitingboundary(perhapsbecauseof emphasized thataquantitativedescriptionofthese systemsisnotintendedinthispaper. the effectsofdynamicalequilibriummatterlyingnearboundary).Thisin- Li, forthecasep=0.25.Sectioninzz-plane.Axisofrotation(throughcentergravity)shownas limiting curvewasdrawn,givingalowerlimitto¡jlforgivenTodefinethiscurve, broken line.Thesizeoftheprimarystarisdrawnarbitrarily. primary andontheinclinationoforbit,becausedistortionfromsphericity.Second, of themasssecondarytosummasses.Onthissamediagramatheoretical per’s radiusforverysmallp.However,theexactlocationofcurveshouldnotbere- rough. ItcouldhavebeenimprovedbymakinguseoftheasymptoticbehaviorKui- from theprimary,andperpendiculartothesetwo.Form<0.2curvewassketched root ofthreeradiidefinedasthedistancefromcentersecondarytosurface, it wasnecessarytoascertainthatdimensionoftheinnersurfacewhichismeasuredas photometric radiusofthesecondaryalsodependstosomeextenton garded tooseriouslyforseveralreasons.First,thecurveisnotreallydefined,since the photometricradius.Forvaluesofpgreaterthan0.2,meanradiusinner surface asdefinedbyKuiper(1941,Table3c)wasused.Thiscorrespondstothecube and mostimportant,thedata(Fig.2)indicatethatabnormalsubgiants(seedefinition so astopassthroughthepoint/z=0,^0.Thetheoreticalcurveisthereforequite taken, respectively,paralleltotherotationaxis,alonginterstellaraxis(o;-axis)away 72 J.A.CRAWFORD © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem As wasmentionedearlier,thepositionofpoints inFigure2dependsonParenago’s The resultsofthiscomparisonareshowninFigure 2.Itappearsthatthereisasignifi- Fig. 1.—Schematicdiagramofthezero-velocitysurfacepassingthroughinnerLagrangianpoint 2 ml (SW1+2R2) 2 m9D?2, 1955ApJ. . .121. . .71C main-sequence secondariesareindicatedbycrosses.The18 dotsrepresentsubgiantsecondarieswhose upper masslimitislessthanIQ.Theopencirclesareother subgiants.Onesubdwarfisindicatedby semimajor axisoftheorbit),n,for53systems,with primary onthemainsequence.Thosewith a crossedcircle.Thefullcurveisthelimitingasdefined inthetext.Thedottedcurveisalimiting curve asdefinedsomewhatdifferentlybyF.B.Wood(1950). © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem Fig. 2.—Thequantitypisplottedagainstthephotometric radiusofthesecondary(inunits 1955ApJ. . .121. . .71C T its formationatagiven date bysomeunknownmechanism.Oneofthe stars will,in obtain alowerlimit¿iifor¡jlandanupperSftsmaxtoitsmass,givenbythefollow- ing expression: cy fortheprimariestolieaboveaveragemain sequence.Thisisanindicationthat be quitewronginsomecases.Thedataappeartoindicate thatthereisnomarkedtenden- less thanonesolarmass;18oftheseareclassifiedbyParenagoassubgiantsandin- This wasdoneforall53secondaries.Itfoundthat19starshadanuppermasslimit 74 these systemsarecomparativelyyoungoraverage membersofpopulationI. position, whereasthevaluesofMiarenot.The of9JîiinTable1maytherefore gested bytheirsubgiantcharacteristics,unlesstheyhadoriginallyaveryunusualchemi- evident thattheyclusternearerthecurvethandototalgroupofsubgiants. dicated inFigure2asblackdots(theremainingsecondaryislistedasubdwarf).It some uncertaintyastothepositionoftheoretical curve,itisnotpossibletoinferthat magnitude oftheprimaryataveragevalueformain-sequencestars.Theobserved small mass(<1O).Itisnotpossibletounderstandhowstarswithsuchcould the curve,thatistosay,fillinnerzero-velocitysurface.Onotherhand,these to notethatthemassesSDiiareextremelysensitive toanerrorinthetheoreticalcurve’s the primariestendtobesystematicallyunderluminous andundermassive.Itisessential metric correctionwithabsolutemagnitudeforagiven spectraltype).Ontheotherhand, luminosity ofthesecondary.Thetheoreticalcurveonwhichthisproceduredependsis, for theabsolutemagnitudeofprimaryandcouldproceed,asbefore,toobtain spectral type(Kuiper’sTables3and13wereused[1938],asthetypesarelisted for these18stars,themassofsecondaryisknown.Fromvaluethen velocity surfacewillbediscussed.First,however,awordshouldsaidaboutluminosi- which relatesthepeculiarpropeitiesofthesestarstofactthattheyfillinnerzero- cal compositionnotsharedbytheircompanions.Inthefollowingsectionahypothesis have hadenoughtimeinfivebillionyearstoreachtheadvancedstageofevolutionsug- stars werechosenbecausetheyformapeculiargroup,combiningsubgiantcharacterwith in theoldernotation),bolometricmagnitudeofprimarycanbeobtained.Bysub- and R2,bynotingthattheproducts/¿Ri/xRareconstantsdirectlyderivablefrom obtained. TheradiiofthetwostarsarethenobtainedfromParenago’svalues/jl,Ri, mate oftheluminositysecondary.However,onecandobetterthanthiswhen,as difference inmagnitudeandabolometriccorrectionarethenappliedtoobtainanesti- same algebraicsignastheincreaseinluminosity(neglectinganychangebolo- values listedbyParenago(main-sequenceaverages).Itwasfoundthat,exceptinone however, atpresentsomewhatcrude. mn instance, theincreaseofmassprimaryovermain-sequenceaveragehad Their masseswerealsoobtained.TheresultsaregiveninTable1.HereMiandM2 tracting thebolometriccorrection(Kuipei’sTable6)wethenobtainaconsistentvalue the observations.Assigningtoprimaryaneffectivetemperaturecorrespondingits ties. Parenagohasobtainedaverageluminositiesofsecondariesbyfixingtheabsolute 12 liebelowthemainsequenceinluminosity.Because ofthesmallnumberstarsand the absolutemagnitudesofcomponents;A99?iandAMiareincrementsover 13 ofthe18primarieshaveamasslowerthan main-sequence average,and,ofthese, 2 © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem Let usconsiderinageneral waytheevolutionofaclosebinarysystemsubsequent to It thereforeappearsjustifiabletosupposethatthese18secondariesactuallydolieon The absolutemagnitudesoftheprimarieswerecalculatedbyforegoingmethod. III. EVOLUTIONARYMECHANISM J. A.CRAWFORD 1955ApJ. . .121. . .71C general, bemoremassivethantheother.Thestarwill,frommass- point itwillacquireanunstabledepletedcore(SchönbergandChandrasekhar1942) begin tomoveveryrapidlytherightinH-Rdiagram(SandageandSchwarzschild luminosity relation,bemuchmoreluminousandwillevolverapidly.Atacertain continue untilthestarñllsinnerzero-velocitysurface.Thewillthen mass willeitherbecollectedbythecompanionorejectedfromsystemcen- rich inhydrogen;and,asmassislost,theratioofcontaineddepletedcore such asprominences,dominate.Themateriallost,lyingatthesurfaceofstar,willbe star cangraduallybecomelessmassivethanitscompanionandeventuallyluminous, Z Dra. of thestar.Asthisageincreases,expansionwillcontinue.Bymechanism trifugal force,probablydependingonwhetherornotfairlyviolentejectionmechanisms, to expandbutwillnotbeableholdonthemassthatpassesoutofsurface.This becoming thesecondarycomponent.Itshouldbenotedthatifstarlieswhollyinside TW Dra. to thetotalmassofstarwillincrease.Thisratioisameasure“biologicalage” from thesystem.Themainfeaturesof18stars—low massandsubgiantcharacter— ST Per. 1952), expandingitsradiusasitdoesso.Itisthenveryprobablethatthisexpansionwill Z Ori. TT Her.. W Del.. WW Cyg. T LMi. AK Her.. greater, sothatthereismore ofachanceobservingpeculiarsubgiantwhen ithaslost momentum isconservedinthesystem,i.e.,extent towhichmassisexchangedorlost decreases. Theexactmannerofthischangewilldepend ontheextenttowhichangular star. Thedimensionsofthesurfacewill,course, changeasthemassratiocontinuously accounted forbyremarkingthatthegreater fraction ofmassastarhaslostinthis or thesubgiantcomponentsofvisualbinarysystems. seem tobequalitativelyexplainedonthebasisof foregoingevolutionarymechanism. RW CrB. RS Cep.. portant questionwhichis difficulttodecideiswhetherornotmassexchanged between way, themorepeculiaritwillbecomeandgreater chanceitwillhaveofbeingso alter. Thereisthereforenopossibilityofthesurfaceitselfexpandingfasterthan classified. Inaddition,theamountoftimespent inthelower-massregionisprobably Conversely, oneshouldnotexpecttofindstarsof thistypeamongthesinglesubgiants RW Per. Y Leo.. RW Gem RZ Cas. considerable massandprobably becomethesecondarycomponentofitssystem. Anim- Y Psc. RT Per. the zero-velocitysurfacewithoutlosingmass,dimensionsofthiswillnot RZ Set. © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem The factthatthepeculiarstarsarefoundonlyamong thesecondariescanperhapsbe Star dF2 A3 A3 A5 A5 AO A8 A5 A2 B2 AO A3 A2 A6 B8 B6 B4 F8 Spi FO KO g GO K2 G5 G Sp 2 G-K 0.34 SUBGIANT COMPONENTS75 0.27 .58 .77 .62 .78 .68 .38 .29 .69 .23 .78 .21 .59 .13 .52 .32 .97 12.62 0.72 3.95 3.69 3.76 4.22 4.78 3.88 8.03 2.15 1.82 1.75 1.29 7.68 1.91 1.98 1.85 1.01 i?2 TABLE 1 4.10 0.92 3.02 0.49 0.82 3.44 0.70 0.69 3.36 7.02 1.49 1.51 1.20 1.34 1.12 Wh 43 52 24 +0.8 + 1.8 +2.1 + 1.3 +2.1 + 1.2 +1.2 +0.7 + 1.6 +2.0 +4.0 +0.1 +0.3 +2.0 +3.7 + 1.1 -1.6 -1.2 Mi +2.1 + 1.2 +0.9 +5.0 +1.4 -0.5 -0.5 -1.8 -2.6 -2.1 -2.5 -0.9 -0.4 -3.5 -1.1 -0.9 -5.8 -9.3 + 1.1 + 1.5 +0.1 + 1.0 + 1.7 +0.1 +0.6 + 1.7 +0.5 +0.4 +0.7 -1.3 + 1.3 -0.9 -0.9 -1.0 -1.3 -0.4 AMi +2.1 +4.3 +3.5 +4.7 +3.8 +5.6 +5.1 +2.0 +4.8 +4.1 +2.7 +4.7 +5.2 +4.2 +0.6 +5.5 + 1.6 +5.1 M 2 1955ApJ. . .121. . .71C íí, rich materialfromtheoutsideandthusbekeptrejuvenated.Theexistenceofsucha process mightenableonetoattributeagreateragesuchsystemthanisindicated by theearlyspectraltypeandmoderateluminosityofprimarystar. the components.Ifso,primarystarwouldconstantlyhavebeenreceivinghydrogen- finds thattheyareassociatedwiththesamephenomenon(fillingofinnerzero-veloci- 76 J.A.CRAWFORD investigation, andtoProfessorH.WeaverDr.K.Franklinforhelpfuldiscussions. Moulton, F.R.1914,CelestialMechanics(2ded.;NewYork:MacmillanCo.),p.281. to befound.InthisworkWooddiscussestheperiodfluctuationsofeclipsingbinariesand more detaileddiscussionofthemass-ejectionmechanismineclipsingbinarysystemsis ty surfacebythesecondarycomponent)asdescribedhere. Schönberg, M.,andChandrasekhar,S.1942,Ap.J.,96,161-172. Sandage, A.R.,andSchwarzschild,M.1952,Ap.J.,116,463-476. .1941,ibid.,93,133-177. Kuiper, G.P.1938,Ap.88,429-471. Parenago, P.1950,Astr.Zhur.,27,41-47. Struve, O.,andGould,N.1954,Pub.A.S.P.,66,No.388,28-31. Struve, O.1953,Lesprocessusnucléairesdanslesastres,Mêm.Soc.R.deLiège,4thSer.,14,236-253. Wood, F.B.1950,Ap.J.,112,196-206. © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem The writerdesirestoexpresshisthanksProfessorO.Struveforstimulatingthis In conclusion,wewishtociteanimportantpaperbyF.B.Wood(1950),inwhicha REFERENCES