198lApJ. . .248. .27 9P © 1981.TheAmericanAstronomicalSociety.Allrightsreserved.PrintedinU.S.A. The AstrophysicalJournal,248:279-290,1981August15 We nowknowthatX-rayemissionfromstarsisthe have forthefirsttimedemonstratedpervasivenessof between X-rayemissionandbolometricluminosity. which haveamoresharplypeakedluminosityfunction. norm andthatalmostallstars,withthepossibleexcep- the coronalphenomenoninstars(Vaianaetal.1981). observed; therangewithineachspectraltypeistypically time, Vaianaetal(1981)notedthatwithineachspectral tion ofverylatetypegiantsandsupergiants(Ayresetal type abroadrangeofX-rayluminositylevelswas two tothreeordersofmagnitude,exceptforFstars, 1981), havebeendetectedasX-raysources.Atthesame Standards. 2 4 3 l X-ray observationsfromtheEinsteinObservatory For earlytypestarsthereisevidenceofacorrelation A1so OsservatorioAstronómicodi Palermo,Italy. StaffMember,QuantumPhysics Division, NationalBureauof GuestObserverwiththeEinstein Observatory. Also OsservatorioAstrofísicodiArcetri,Firenze,Italy. © American Astronomical Society • Provided by theNASA Astrophysics Data System 7 19±05 2 luminosities, andprojectedrotationalvelocitiesvsin/forstarsofvariousspectraltypes bolometric luminosity.Theproportionalityconstantis(1.4±0.3)X10~andindependentof behavior observed.Earlytypestars(03-A5)haveX-rayluminositieswhichareproportionalto luminosity classesobservedbytheEinsteinObservatory.Therearetwoclearlydefinedpatternsof luminosity class.Incontrast,latetypestars(GtoM)haveX-rayluminositiesstronglydependenton X-ray luminosityonrotation. intermediate, havingX-rayluminositiessubstantiallyhigherthanwouldbepredictedonthebasisof rotation rate[L~(vsin/)-']andindependentofbolometricluminosity;thisrelationforlate relation/^ ~QbetweentheX-raysurfacefluxandstellarangularvelocity.Fstarsasaclassare type starsisagainfoundtobeindependentofluminosityclass.Thisdependenceequivalenta dependence. ThelocationofRSCVnstarsasaclassisdiscussedwithrespecttothedependence the earlytypestarL-relation,butsubstantiallylowerthanexpectedfromlatevelocity Subject headings:stars:coronae—rotation—X-rays:sources x xbol RELATIONS AMONGSTELLARX-RAYEMISSIONOBSERVEDFROMEINSTEIN, We havedeterminedthecorrelationbetweenobservedstellarX-rayluminosities,bolometric I. INTRODUCTION STELLAR ROTATIONANDBOLOMETRICLUMINOSITY 12 R. Pallavicini,L.Golub,Rosner,andG.S.Vaiana Received 1980December9;accepted1981February12 Laboratory forAtmosphericandSpacePhysics Harvard-Smithsoniaii CenterforAstrophysics Joint InstituteforLaboratoryAstrophysics 3,4 J. L.Linsky 3 ABSTRACT T. Ayres AND 279 68 had nearlythesamecolor,relationshipisequivalent X-ray toV-bandluminosityratioforasampleofsix early O-typestars;sinceallofthestarsinthissample Hamden etal(1979)reportedtheconstancyof ratio. LongandWhite(1980)reportedastrongcorrela- to onehavingaconstantX-raybolometricluminosity tion betweenX-rayandbolometricluminositiesfora that itextendsfrom04throughA9using35starstotal, ranging from10“to10“ofL. sample of16starsrangingfrom04throughB9,withL of gravityatfixedT*. and isindependentofluminosityclass,i.e., spectral typesforwhichtheaboveruleholds,finding chromospheric andcoronalemissioninlatetypestars, there areseverallinesofevidence,bothobservational factor (Vaiana19806;Linsky 1980).Forinstance,early and theoretical,whichsuggestrotationasaprominent statistical workonCanemission (Wilson1966;Kraft bol x 1967a; Skumanich1972)has shownthatthelevelof Among variousparameterswhichmayberelevantfor In thefollowing,wewilldeterminerangeof 198lApJ. . .248. .27 9P 1 for mechanismscoronalformation. classes, andfinally,in§IV we discusstheimplications for starsofdifferentspectral typesandluminosity the data;in§IIIwediscuss resultsofthecorrelation on rotationalvelocities.Inthenextsectionwepresent tions fromtheEinsteinObservatoryandpublisheddata throughout theH-RdiagrambyusingX-rayobserva- with surfaceturbulenceinducedbyrotationalinstabili- possibly throughtheinteractionofprimordialfields ship betweenstellarX-rayemissionandrotation used fortheheatingofstellarcoronae(Thomas1981), portant asasourceofnonthermalenergywhichmaybe ties (Vaianaetal.1981). Lamers 1981).Moregenerally,rotationmaybeim- stellar windgeneration(Conti1978;Cassinelli1979; gravity duetorapidrotationalsoaffectsmasslossesand role insuchphenomenaasBestars(Slettebak1976), X-ray emissionofearlytypestars.Itcertainlyplaysa and inotherstarsforwhichthereductionofeffective ter (Vaiana1980a,b,c;Rosner1980;Linsky1980). rotation shouldbeexpectedtoanimportantparame- related tomagneticfieldsasitisfortheSun,then level ofchromosphericandcoronalemissioninstarsis netic fieldsarecommontoalllatetypestarsandifthe rotation andconvection(see,forexample,Tassoul1978, Parker 1979).Ifconvectionanddynamo-generatedmag- which inturnareconsideredtobecontinuouslygener- ated byadynamoactioninvolvingtheinteractionof (Zwaan 1977),arelargelydeterminedbymagneticfields, and Rosner1978)aswellchromosphericemission solar analogy.Inthecase,coronalemission(Vaiana further supportedbytheoreticalargumentsandthe may beprincipallyduetorotation(BoppandFekel exist thattheso-calledBYDrasyndromeindMestars L forthreeslowlyrotatinglatetypestars,buthisdata are includedinourpresentstudy.Finally,indications (Walter, Charles,andBowyer1980;Walter 280 chromospheric andcoronalemissionofRSCVnstars binary systems,whichareforcedtosynchronismby tidal interaction,mayberesponsiblefortheenhanced 1977; BoppandEspenak1977). (Ayres andLinsky1980).Enhancedrotationinclose to thedifferentrotationrateoftwocomponents emission betweentheprimaryandsecondarystarsof spectroscopic binaryaAurhasbeeninterpretedasdue strong differenceinchromosphericandtransitionregion 1981). Johnson(1981)findsnotrendinrotationversus as coronalemission(Vaianaetal.1981).Further,the than averagechromospheric(Linksyetal1979),aswell This isfurthersupportedbythemoredetailedfinding such as7TUMaandEQVir,appeartohavestronger that somewell-known,young,fast-rotatingsinglestars, chromospheric emissionisrelatedtorotationandage. x It isourpurposeinthispapertoexploretherelation- It ispossiblethatrotationmayalsobeimportantfor The observationalindicationsmentionedaboveare © American Astronomical Society • Provided by theNASA Astrophysics Data System PALLAVICINI ETAL. ing from1929.Bemaccaand Perinottousedaselected who alsoconsideredpapers published previously,start- from paperspublished1949(Slettebak1949)to angle withrespecttothelineofsight)havebeenderived equatorial velocityandiistherotationaxisinclination catalogs onlyforpurposesofcomparison. have preferredtoassignarotationalvelocity—when 1969 enterintothecompilation byUesugiandFukuda, ities havebeenpublished(UesugiandFukuda1970; ture andacriticalanalysisofthedata.Wehaveused after completinganewsearchofalltherelevantlitera- available-— toeachofourX-raystellarsourcesonly Bemacca andPerinotto1970,1971;1973),we luminosity referstotheindividualcomponentsin 1979. Allthepaperspublished duringtheperiod1949- between thetwocomponents.Formultiplesystemsre- system andnoambiguityispresent. solved bytheHighResolutionImager(HRI),X-ray limit. Forbinarysystemsformedbystarsofsimilar have treatedthetotalX-rayluminosityasanupper spectral types,thetotalX-rayfluxhasbeensplitequally considered bothcomponents(whenpossible),butwe in thechannelboundaries. from thesystem.Whenambiguityispresent,wehave observed X-rayluminosityreferstothetotalemission order of~20%duetogainvariationsanduncertainties optical identificationandotherrelevantdatacanbe data reductiontechniqueshavebeenfullydescribedby Einstein Observatory(HEAO2).Theinstrumentand Walter andBowyer(1981).Mostofthedatahavebeen surements areestimatedtohaveuncertaintiesofthe (1980). TheX-rayluminositiesderivedfromIPCmea- found inVaianaetal.(1981)andLongWhite Giacconi etal.(1979).DetailsonX-raysourcelocation, a position-sensitiveX-raydetectoratthefocusof obtained withtheImagingProportionalCounter(IPC), by recent,asyetunpublished,datafromtheCfAsurvey, son, wehavealsousedresultsforRSCVnstarsfrom Guest ObserverJ.Cassinelli.Forpurposesofcompari- as wellunpublisheddatakindlyprovidedtousby the guestobserverprogramsofAyresandLinsky, Columbia groupsurvey(LongandWhite1980),from additional publisheddataonearlytypestarsfromthe Einstein Observatory.Mostofthedataarefrom and collaborators(Vaianaetal.1981),supplementedby Center forAstrophysics(CfA)stellarsurveyprogram Projected rotationalvelocitiesvsini(whereisthe Although extensivecatalogsofstellarrotationalveloc- For visualbinarysystemsnotresolvedbytheIPC, The X-raydatausedinthispaperareallfromthe a) X-rayObservations b) RotationalData II. THEDATA Vol. 248 198lApJ. . .248. .27 9P _1 5 No. 1,1981RELATIONBETWEENROTATIONANDLUMINOSITY281 number ofpaperspublishedduringtheperiod1949- , Slettebak’sscaleisnotdefinedandwehaveassumedas 50) werepublishedafter1970. tained withdifferentdispersionsandareof 1969. Aboutone-halfofthepapersweused(morethan racy andtoreducethemthesamescale.Asastan- quality, wehavemadeanefforttoestimatetheiraccu- km sbytheclassicpapersSlettebak(1949,1954, dard, wehaveadoptedthescaleestablishedatvsin/>20 respect tothisscale,themorerecentdataofSlettebaket al. (1975)shouldbeincreasedby~5%forAandFstars t> sin150kms“^DatafromBuscombe(1969)canbe Ebbets (1977)forOstarsmustbeincreasedby~30%at placed onthesamescalebyreducingthem—45% and ~15%forBstars,whilethedatabyConti 1955, 1956,1963;SlettebakandHoward1955).With (see alsoBuscombeandStoeckley1975).Similarcorrec- tions havebeenmadewhenevernecessary. the basisofHyadesandComaclusterdata.Withrespect standard thescaleestablishedbyKraft(1965,1967a)on to thatscale,themorerecent,accuratedataby Smith (1976,1978,1979),andDominy(1979), techniques appeartobehigherbyupafactorof2, and GrayMartin(1979),basedonFourier and acorrectionmustbemadetoensureinternalcon- widths givenbyHuang(1953)usinghisinterpolation sistency. has beenattributedtoHuang’sdata,giventheuncer- reliable spectroscopicdeterminationofvsiniisavail- formula andayfactorof1.25.Lowweight,however, tainty oftheyvalue.FordMestarsforwhichno termined fromthephotometricperiod,attributedto able, equatorialrotationalvelocitiesvhavebeende- been assignedasameasureofthereliability measurement wasavailable,aweightedaverageofthe spot rotation(Kron1952;BoppandFekel1977). different (corrected)valueshasbeencomputedand adopted asthevsinivalue;aprobableerrorhasalso upper limitonvsinihasbeenassigned. to thedispersionofspectrographused),onlyan adopted value.Forstarswithnarrowlines(withrespect lever arminvsiniwhichwehaveourdata(afactorof>20,see established bytheolderbutmoreextensivedataset.Thelarge and reliablerotationalvelocitiesareavailable;for—20% eq velocity scale. not changeinasubstantiveway,even withafactorof2changein emission onrotationallowustoformulateconclusionswhichwill Figs. 5and7)theobservedstrongdependenceofX-ray preprint fromD.Soderblom(Soderblom 1981)containingnew rotation measurementsforsolar-type stars.Therearefivestarsin -1 Since rotationaldatafromdifferentsourceswereob- 6 5 6 For lowerrotationalvelocities(vsin/<20kms) Rotational datahavebeendeterminedfromline For allstarsforwhichmorethanonerotational © American Astronomical Society • Provided by theNASA Astrophysics Data System We havefound69starsforwhichX-rayluminosities Wehavechosentoadjustallmeasurementsthescale After thispaperwasacceptedfor publication,wereceiveda _1 -1 limits. Ourdatasamplecontains33main-sequencestars, of thesestars,however,thevsinivaluesareonlyupper 3 Walter andBowyer(1981).Thenamesofstarsused, tral typesobservedbytheEinsteinsurvey.Inconjunc- tion withtheabovesample,wehaveincludedin figures therelativelocationsofRSCVnstarsfrom their spectraltypes,thevaluesofL,andosin/, 10 subgiants,14giants,and12supergiantsofallspec- and referencesareallgiveninTable1. xbol L andprojectedrotationalvelocityvsiniforallstars Although thereisageneraltendencyoftheX-ray of ourdatasampleisshowninFigure1.Different luminosity toincreaseforincreasingvaluesofvsin/,the symbols areusedtoindicatedifferentluminosityclasses. plot appearstobeessentiallyascatterdiagram,espe- cially forrotationalvelocitiesvsin/>50kms(i.e., rotational velocities(osin/<50kms,i.e.,mostly mostly starsofspectraltypesearlierthan—F).Atlower _1 v sin/.Note,however,thatthereisasharplydefined to increasewithvsin/appearsmorepronouncedif x boundary extendsfromlowluminosity,rotation,to boundary acrosswhichessentiallynostarsappear.This stars ofspectraltypelaterthan—F),thetendencyL* high luminosity,rotation.Theboundaryroughly allowance ismadeforthenumerousupperlimitson between X-rayluminosityandprojectedequatorialrota- tional velocitybysubdividingthedatasampleinto follows alawoftheformL*oc(t)sin/). will beimmediatelyapparentthatrotationisnotan gether starsofallspectraltypesandluminosityclasses; important factorindeterminingtheX-rayemissionlevel relation holdsthroughouttheentireH-Rdiagram.It there isnoapriorireasontoassumethatsingle subgroups ofsimilarspectraltype.Figure1mixesto- of earlytypestars,andthesewillbediscussedsep- luminosity orrotationinlaterspectraltypesandto closely todeterminewhetherthereexistdependencieson ble. arately. Wethenexaminetheindividualsubclassesmore determine theextenttowhichrelationsareapplica- permit anadequateaccountingforprojectioneffectsin observed scatter.First,thequantityvsin/doesnot the X-axisinourplotsdueonlytostatisticaldistri- a smalldatasample.Therewillthusbespreadalong his listwhichwehadincludedinthe table;forfourofthesethere is nosignificantdifferencebetween ouradoptedvsin/andthat quoted bySoderblom.Inthecase ofiPer,anupperlimit new determinationhasbeenadded toFigure7. 15 kmsisnowgivenbySoderblom as3.5±0.7kmsthis A plotshowingtherelationshipofX-rayluminosity In thefollowingwewillexaminerelationship We notethatseveralcausesmaycontributetoan a) Overview III. RESULTS 198lApJ. . .248. .27 9P 20 , 24 , 22 , 21 , 29 28 27 26 25 23 40 34 32 31 30 11 . 10 . 47 46 45 44 43 42 41 36 35 33 14 . 13 . 12 . 49 48 38 37 17 . 16 . 15 . 39 19 18 . 50 51 2 . 6 . 4 . No. 5 . 3 . 9 . 7 . 8 . 1 . © American Astronomical Society • Provided by theNASA Astrophysics Data System 1 2 1 2 1 2 0 OríC 0 OriA H Col a Vir(Spica) X Car HD 93205 fOph HD 93250 £ Per 8 Per ß CenA r Ori 8 OriA t Ori HD 93403 e Ori a Cam 67 Oph HD 93129A a Lyr iß Per a Lup f OriA ? Pup 29 CMa p Leo K Ori a CMa (Algol) (Vega) a CVn eSgr a Oph 8Cyg y Gem a CVn (Sirius) 9Sgr a Hyi a Car 46 Tau (Canopus) HR 4574 ß Com a CenA a Tri 0 Cyg p Psc vr UMa HD 8774 HD 108102 HR 1436 í Per v Col Vir Star 07 V 09.5 V B2 rv 09.5 V 03 V 03 V Bl IV 09.5 V ( +B3p) 09 III 07.5 III B5 III 05 Illf B5 III B1 III AO V BO. 5le BO la 03 If 09.511 A1V 09.5 la B5Ib B1 lab A5III AO IV (+KIV+A5) B8V B2 09.7 lb 04 If 07 la A9V B9IV B9.5 V 05 FOV B9.5III (or A9III) F7 V F3 V FOV FO lb F7 IV F8V F4V F4V F5 V F2V G2V GOV G4V F6 rv GOV Sp Summary ofDataforStarsUsedinThisWork 1 Adopted* vsini -1 (kms) 210±20 285 ±25 370 ±30 240 ±30 130±10 200 ±20 160±20 115±20 165±15 210±30 150±20 105 ±25 120 ±20 140± 10 150±20 120±20 150± 15 150±20 175±45 130± 10 145 ±20 4.5 ±1.5 70 ±20 30± 10 85±15 25±5 60± 10 60± 10 90± 15 80 ±10 80± 10 30± 10 60±5 60 ±10 80 ±10 20±5 35± 10 35± 10 90± 15 35± 10 17±5 15±5 10±5 <10 <20 <15 <15 7±2 3±1 3±1 8±3 (L vs.vsin/) x TABLE 1 b Notes for 48 48 48 3.30.41 3.19.26.30.43.48 48 3,7,41,42 3.30.36.41 3.9.14.15.26 3,9,27 3,9,27 1.9.15.32.48 1,9, 15,32,48 3.7.15.26.42 3,4,24,25,41,47 3,4,28,34,59 3.30.36.41 3.9.48 9.26.35.48 9.48 3.9.42 10,36,52 1.9.19.18.21.26 3.4.25.41 3,4,23,24,25 3,4,12,15,29 3.4.24.31.37.41 1.9.15.26.41.48 1.9.48 3,6,12,15 37 3.5.8.25.41 1.7.41 3.41 3 38 40,54,58 3,6,8 6.8.16.20 38 3,6,8,20,22,38 3 3.20 5,6,8,16,20 3.5.6.8.41 3,6,8,16,20,22 1.3.9.27.48 1.9.48 17 17 16,20,22,54 v sini 41.43.48.52 32,48 44.46.47.53 39,41 41.54 22.54 log L x 32.2 33.0 31.3 31.1 33.0 30.3 30.0 31.0 32.0 33.3 29.2 32.4 30.2 33.6 32.5 30.7 31.8 32.3 31.3 29.0 27.6 26.9 29.6 31.9 32.2 31.1 29.8 29.1 29.2 30.7 32.7 32.4 32.2 29.0 28.6 27.9 29.0 29.9 28.9 29.1 29.2 30.0 29.2 28.4 28.7 28.7 28.3 27.1 29.1 27.6 29.5 l°g L h 38.6 38.4 37.6 38.3 39.6 40.2 38.8 37.0 39.5 37.9 38.5 39.8 39.0 39.2 36.6 38.1 39.1 39.2 38.1 39.2 39.4 38.8 35.4 35.0 35.9 39.7 37.4 39.5 39.4 35.8 35.7 36.4 35.2 35.8 34.5 34.5 34.5 34.7 37.3 34.0 34.0 34.0 34.2 34.2 33.6 34.7 34.5 34.0 33.6 33.6 34.0 c Notes forL v (a) (a) (a) (b,c) (a) (b) (b) (a) (b) (a) (a) (b) (b,c) (a,l) (a) (a) (b) (a,l) 0,q) (a,l) (a,l,q) (b) 0,q) (a) (a) (a,d) (l,q) (b) (b) (a) (a,r) (a,e) (a,e) (b) (a) (a) (a) (a) (a) (a) (a) (a) (a) (a) (a) (a,m) (v) (a,m) (a) (a) (a) 198lApJ. . .248. .27 9P X-ray variabilityinlatetypestars,resultingabroad- bution instellarorientations.Second,theremaybe X-ray luminosityvariesbyslightlymorethanoneorder cycle (Kreplin1970;Kreplinetal.1977),withflaring of magnitudeintheIPCX-raypassbandduringasolar ening ofthedistributionparalleltoY-axis.Thesolar obvious correlationbetween X-ray luminosityandequa- type starsofspectral03toB5(andtypes ods. torial rotationalvelocity,either fortheentiresampleof cate differentluminosityclasses. Wedonotfindany B8-A5, tobediscussedlater). Differentsymbolsindi- activity contributinganotherfactorof2forshortperi- Figure 2showsaplotofLversusvsiniforearly x 12 © American Astronomical Society • Provided by theNASA Astrophysics Data System Wilson andSkumanich1964.(17)Kraft1965.(18)Kochetal.1965(19)WallersteinWolff(20)1966.(21) Herbig andSpalding1955.(7)SlettebakHoward(8)(9)1956.(10)Struveetal.1958.(11) Danziger andFaber1972.(39)Dworestsky1974.(40)BoesgaardHagen(41)Slettebaketal.1975.(42)DayWarner et al.1970.(33)Gershberg(34)Hill1971.(35)BaschekandScholtz(36)Watson1972.(37)Levato(38) Rosendhal 1970.(28)vandenHeuvel(29)Preston(30)LevatoandMalaroda(31)GearyAbt(32) Struve andZebergs1959.(12)Slettebaketal.1961.(13)Meadows(14)AbtHunter1962.(15)1963).(16) Slettebak 1966.(22)Kraft1967ö.(23)19676.(24)Deutsch1967.(25)Palmeretal.1968.(26)Buscombe1969.(27) luminosity splitequallybetweentheAandBcomponents,(g)vderivedfromsettingeclipseperiodequaltophotometricperiod. X-ray emissionlikelytooriginatefromtheK-component.(e)LreferstotalaandCVn.(/)Total and Ebbets1977.(49)BoppFekel(50)Andersonetal.(51)PopperUlrich(52)HutchingsStoeckley J. Cassinelli.(m)ProgramofGuestObserverL.Linsky.(n)H.M.Johnson,(o) (h) vderivedfromphotometricperiod.(/)Lreferstothetotalfluxsystem,G5IV+Mstars,(j)X-rayemission Observer K.Zwaan.(p)Johnson1981.(q)Cassinellietal.(r)ProgramofGuestA.Fabian,(s)MeweandZwann attributed tothesecondary,(k)cderivedfromorbitalperiodassumingsynchronousrotation.(/)ProgramofGuestObserver 1975. (43)BuscombeandStoeckley(44)Smith1976.(45)Hall(46)Deeming1977.(47)Milliardetal.(48)Conti 1979. (58)Smith(59)Rucinsky(60)AyresandLinsky1980. 1977. (53)Kuruczetal.(54)Smith1978.(55)GrayandMartin1979.(56)Dominy(57)VogtFekel 1981. (0Ayresetal.(m)Walter1980.(t?)CfAunpublished. eq x cqx eq 1 60.. .24UMaG2IV 54 ....70OphAKOV 53 ....EQVirK5V 52 ....eEriK2V 63.. .aAurG5III+ 62.. .fiHerAG5IV+ 61.. .TjBooGOIV 58.. .YYGemMlVe 57.. .61CygBK7V 56.. .61CygAK5V 55 ....70OphBK5V 59 ....YZCMiM4.5Ve 64.. .ßLepG5III 68 ....fAndKlIMII 67.. .«SerK2III 66 ....¿GemK0III 65 ....r¡DräG8III b 69 ....ZHerKOIV a c No. StarSp(kms~)vsini^ogLlogLforL* xbol Notes forvsini.—(1)Slettebak1949.(2)Kron1952.(3)Huang1953.(4)1954.(5)OkeandGreenstein(6) For anexplanationoftherelativeweightsgiventovarioussourcesandvelocityscalesadopted,seetext(§IIb). Notes forL:(a)Vaianaetal.1981.(6)LongandWhite1980.(c)Fortheprimarystar,(d)Rotationrateofprimary,but x b) EarlyTypeStars(O-B) (Capella) GOIII RELATION BETWEENROTATIONANDLUMINOSITY (2 Mstars) 3bc Adopted vsin/Notesfor 40±5 2,11,49 30 ±106,60 10 ±249,50 33±5 45,51 35±5 5,6,45,51 11 ±25,6 (sec.) TABLE 1—Continued <15 6 <25 6,8 <25 15 <25 15 <15 6,8 <15 3,5,6,8,16,20 <15 6 2±1 6,15,57 2=tl 6,15,54 5±1 33,49 2± 16,55,56 2± 16,55,56 bined effectsofthedependenceLonbolometric increasing rotationalvelocities;webelieve,however,that luminosity (seelaterinthissection)andofthestatistical may haveX-rayluminositiesdifferentbymorethan especially trueformain-sequencestarsandgiants(which early typestarsorwithineachluminosityclass.Thisis dependence ofrotationalvelocitiesoneffectivetempera- this isaselectioneffectandsimplyduetothecom- some tendencyoftheX-rayluminositytoincreasewith tional velocities).Onlysupergiants,takenalone,show three ordersofmagnitudeforstarscomparablerota- ture forearlytypesupergiants(see,e.g.,Rosendhal 1970). x L. ThisisshowninFigure 3,whereLisplottedasa tween Landvsiniforearly typestarsiscontrastedby a strongdependenceofL on bolometricluminosity bol x x x The apparentabsenceofany clearcorrelationbe- 27.2 32.1(a,n,p,Q 27.2 32.5(a,n,p,f) 28.1 32.5(a,n,p,f) 28.1 33.2(a,n,p,f) 29.4 32.3(a) 28.3 33.1(a,n,p) 28.5 30.6(v,h) 29.6 32.2(a,g) 27.6 34.0(a,i) 28.0 34.4(a) 29.2 36.1(a) 30.0 34.5(a,o,s) 27.8 35.2(t) 27.9 35.2(a) 30.3 35.8(a,j) 29.9 34.6(u) 27.8 35.2(a) 30.3 34.0(a,k) 283 198lApJ. . .248. .27 9P 7 1 7 284 line profiles(Slettebak1956;Rosendhal1970).Macro- line. Thereisnoindicationofsystematicdifferences pears wellcorrelatedwithL,andabestfitrela- detected bytheEinsteinObservatory.Differentsymbolsindicatedifferentluminosityclasses.TheX-rayluminositiesarefrompublished rotational velocitiesofearlytypestars(especiallyO the well-knownuncertaintiesondeterminationof between differentluminosityclasses.Asimilardepen- from avarietyofpublishedsources;valuesusedintheplotareweightedaveragesavailablemeasurements,allreducedto the with respecttorotationathighereffectivetemperatures by anumberofauthorsonthebasissparserdata tionship givesapproximatelyL^\0~witha function ofLforthesamestarsusedinFigure2(plus Slettebak-Kraft scale.Noticethatatlowrotationrates,onlyupperlimitsofvsiniareavailableformanystars. surveys byVaianaetal.(1981)andLongWhite(1980),othersourcesasindicatedinthenotestoTable1.Therotationaldata are turbulence isthoughttobecomeincreasinglyimportant turbulence androtationfromtheobservedbroadened stars), owingtothedifficultiesofseparatingmacro- dence ofX-rayluminosityonbolometricfor scatter oftheorderafactor3aboutdiebestfit additional B8-A5starstobediscussedlater),^ap- early type(OandB)starshadpreviouslybeensuggested Cassinelli a/.1981). (Hamden etal1979;LongandWhite1980; symbols) andofspectraltypesB8-A5(filledsymbols).Differentsymbolsindicatedifferentluminosityclasses.Thehorizontalbars X-ray emissionislikelytooriginatefromtheKOIVcomponent,ratherthanB8Vprimary. velocities forbothgroupsofstars03-B5andB8-A5separately.ThepeculiarsystemAlgolmaynotbelongtothesamesubsetstars,since and luminosities(Ebbets1979). IflinebroadeninginO the probableerrorsonadoptedvaluesofvsini.NoticethatthereisnoobviouscorrelationbetweenX-rayluminositésandrotational data. bol xbol bol 10 ~;thequotederrorsare1s.d., basedonthedispersionin 7 The conclusionsabovemaybesomewhataffectedby Fig. 1.—ScatterdiagramofX-rayluminositiesvs.projectedrotationalvelocitiesforstarsvariousspectraltypesandluminosityclasses Fig. 2.—ScatterdiagramofX-rayluminositiesvs.projectedrotationalvelocitiesvsiniforstarsspectraltypes03
198Lapj. . .248. .27 9P the Astrophysical Journal, 248:279-290
