1978ApJ. . .221. .175F The AstrophysicalJournal,221:175-185,1978April1 © 1978.TheAmericanAstronomicalSociety.Allrightsreserved.PrintedinU.S.A. the comparisonofstellarstructuremodelsagainst perature, chemicalcomposition,rotation,etc.—canbe Kl V+dM5e)providesanexcellentopportunityfor reliably determined.Thesepropertiesare(orcanbe) whosegrossproperties—mass,,tem- the widelyseparated,i.e.,noninteracting,double reliably establishedfortheAandBcomponentsof included inouranalysisbecauseofitsfaintnessand lack ofareliableorbit.Thebasicintentthispaperis component Proxima(seeHaischetal1977)cannotbe system. Unfortunately,thedistant,activedMe visual binarystarsintheHyadescluster(seeIben1967 similar topreviousunsuccessfulattemptsmodelthe diagram plusthestellarmasses,weseektodetermine and referencestherein).GiventwopointsonanH-R relevant totheevolutionarystatusofaCen;in§III Unlike theHyadescluster,aCenwillbeshownto priate fortheAandBcomponentstwovaluesof we describetheoreticalevolutionarysequencesappro- observational materialavailableintheliterature somewhat evolved. a consistentevolutionaryhistoryforthedoublestar. reanalysis oftheobservedabundances, basedonthe metallicity Z=0.02and0.04,areferencesolar equivalent measurementsof FrenchandPowell(1971), model (Z=0.02);in§IVwepresentapartial which provideaconsistency checkontheevolutionary in amoregeneralcontext. models ;finally,in§Vwediscuss andapplyourresults The nearbytriplesystemofaCentauri(G2V+ The paperisdividedasfollows:in§IIwediscuss © American Astronomical Society • Provided by theNASA Astrophysics Data System M©, (1.51,0.47[±4%])L,and(5800,5300[±100])K.Byconstructingconsistentevolutionary and temperaturesoftheABcomponentsaCentauriare,respectively,(1.11,0.92[±37J) models forthebinary,relativetoasolarfiducialsequence,wefindZ/Z~2,Y—7=—0.01, and asystemageof6billionyears.Apreviouscurve-of-growthanalysisbyFrenchPowell to theinterior,bulkofaccretionmusthaveoccurredinaverysmallnumbersignificant motions ofaCentauriandtheSun,impliesthatifaccretionmaterialfrominterstellar relation ATæ(3-5)AZforthegalacticenrichmentofheliumandmetals. medium hassubstantiallyalteredthemetallicityofsolarsurfaceconvectionzonewithrespect system isslightlymetal-richcomparedtotheSun.This,coupledwithnearlyidenticalgalactic supports theconjecturethatAandBcomponentshavesimilarcompositions, accumulations. OurresultsalsosuggestthattheSunandaCentauridonotobeyputative Subject headings:stars:abundances—evolutionindividualinteriors 0 aQ0 Astrometric dataandananalysisofavailablephotometrysuggestthatthemasses,, Center forAstrophysics,HarvardCollegeObservatoryandSmithsonianAstrophysical I. INTRODUCTION EVOLUTION OFTHEaCENTAURISYSTEM Brian P.FlanneryandThomasR.Ayres Received 1977July11;acceptedOctober12 ABSTRACT 175 II. PHYSICALPARAMETERSOFTHEaCENTAURISYSTEM reanalyze, availabledatainordertoderiveaccurate metric propertiesofthebinaryarequitereliable tures, andchemicalcompositionofaCen.Theastro- estimates forthestellarmasses,luminosities,tempera- because theyarebasedonawellobservedvisualorbit, the literature(e.g.,vandeKamp1958;Gasteyer available frommeasuredradialvelocityvariations. The massesoftheAandBcomponentsare1.11 on alargeparallax,andadditionalinformation very wellknown,thetotalandindividualmasses 0.92 M,respectively,andthebinarydistanceis Several orbitalsolutionsforthevisualbinaryexistin possible 1%errorinparallax,whiletheuncertainty Kamper andWesselink(1977),aslistedinTable1. should beaccuratetoabout37,correspondingthe of themassratioissomewhatsmaller,about2J, 1966); hereweadoptthevaluesrecentlyderivedby Parallax 0''746 ±0.008,1.34pc Semi majoraxis17''544,23.5AU Period 80.089years M/M, [Mq 1.11 ±0.04,0.920.03 (M +M)/M. 2.03 ±0.07 Mb/M. 0.828 ±0.007 1.34 pc.Becausetheperiodandsemimajoraxisare 0 0 0 a0b ab0 a In thissectionwediscuss,andinsomecases * KamperandWesselink1977. Astrometric PropertiesofaCentauri* a) AstrometricProperties TABLE 1 1978ApJ. . .221. .175F A long-wave RIJKLMN(Kron,Gascoigne,andWhite the standardUBV(Johnson1956;Cousinsand metrically inavarietyofbroad-bandsystemsincluding Lagerweij 1967;Eggen[seeThomasetal1973]),the and Branch1973),thesix-colorUViBGRI(Powell and French1970).Narrow-bandphotometricindices Ayres etal.1976]).Table2summarizesthephoto- are alsoavailable(Willstrop1965;Rodgers[see metric datatobediscussedinthissubsection. ponents canbeestimatedtosufficientaccuracy 1957 ;Thomas,Hyland,andRobinson1973Alexander 176 according tothefollowingidentity: with visual magnitudeV;hencetheexpressioninsquare that wecanconvertmeasuredsolarirradiances(e.g., The sumistakenovertheavailablephotometry.A brackets isadifferentialbolometriccorrection(B.C.). similar expressioncanbewrittenforL/L°,provided tudes. hand sideofequation(1),wemustdeterminethe absolute visualmagnitudesMoftheSun,aCenA, Labs andNeckel1970)intostellarabsolutemagni- magnitudes Vandmeasureddistances. and aCenB.Theseareobtainedfromapparent standard photometriccomparisonstandards(e.g., v Alpha CentauriAandBhavebeenmeasuredphoto- The relativeluminositiesoftheAandBcom- We havechosentoworkrelativetheapparent In ordertoevaluatetheleadingtermonright- However, theSunissome27magbrighterthan © American Astronomical Society • Provided by theNASA Astrophysics Data System i) TheApparentandAbsoluteVisualMagnitudesof b) Photometry,LuminositiesandColors a b s 6 f bd —26.760.65 0.87 4.811.00 Johnson 1966,asscaledto(B— F)©,(V—/)©.AlexanderandBranch1973(uncorrected). on Rodgers(seeAyresetal.1976) photometry.Thiswork,basedonWillstrop1965 From a CenB0.88°,0.91« a CenA-0.01°,+0.010.68°,0.69’ a bcd the Sun,a.CentauriA,andaB Notes.— Adoptedforthiswork. Thomasetal.1973.CousinsandLagerweij1967.This work,based * UsingunroundedvaluesforL , L. AB V[Terr,S(B.C)][r,S(B.C.)] M[S(B.C.)] eff v AA f ab f f ±0.03 (5770,0.0) (0.00) ±0.02 (5040,-0.20)(5320,-0.10) (-0.07) -0.01 0.690.874.35 1.51 ±47, ±0.02 (5630,-0.01) (5770,0.0) ±0.02(+0.01) a,cs 1.33 0.911.035.69 0.47 ±47 0 FLANNERY ANDAYRES Photometric Properties e e B— VV-IL/Lq 0.93 0.72 (L/Lb=3.18)* a (■) TABLE 2 0 aLyr aLyr the otherhand,absoluteirradianceofsolar a Lyr);thereforeVcannotbedetermineddirectly.On in thesameunits,correspondingtozero-pointof response functionintothesolarirradiancecurve by foldinganumericalrepresentationoftheF-filter apparent visualluminosityoftheSun,«^,indirectly spectrum attheEarthisknownveryaccurately(e.g., the stellarmagnitudescale(i.e.,V=0),wecan Labs andNeckel1970).Infact,wecanestimatethe (e.g., Labs1975).Ifwealsoknowtheabsoluteflux, apply thesyntheticF-filterresponsedescribedbyLabs flux units,weadopttheHayesandLatham(1975) convert intomagnitudestoobtainF©. the measuredapparentvisualmagnitudeofVega, monochromatic calibrationofVegaat5556Â,and as atransferstandard.Tocalibrate^inabsolute (1975) totheSchild,Peterson,andOke(1971)energy distribution. Finally,weconvert^to^using Blanco etal.1970).Inthisfashion,weobtain, 0 equally fromtheHayesandLathammonochromatic calibration andF. the stellarmagnitudescale,weobtain, tabulated byBeckers,Bridges,andGilliam(1976; which implies using thesolardistancemoduluscitedbyAllen(1973). Labs andNeckelcalibration),convertingto P«Lyr =+0-03±0.02mag(Johnsonetal.1966; for aCenAandBinTable2,gives, =0 aLyr We determinetheF=0absolutefluxusingVega The uncertaintyinthezero-pointabsolutefluxarises Applying theF-filterresponsetosolarirradiances Combining thesolarestimatewithvaluesofM 921 v ^ =3.63x10"±3%ergscm“s““ =0 M° =+4.81±0.03mag, v F =—26.76±0.03mag, 0 B V/V> -1.53±4%, L/L° -0.44±4%. V (at theEarth). Vol. 221 1978ApJ. . .221. .175F AB in ordertoestimatesyntheticB—Vcolorsforthe No. 1,1978 limitations inthedynamicrangeofstandardstellar which aredifficultforverybrightstarsowingto approach asacheckondirectmeasurementsoîB—F, interest inB—Varisesfromeffectivetemperature photometers (e.g.,CousinsandLagerweij1967).Our Sun, aCenA,andB.Weadoptthe“synthetic” particular, wewanttoknowwhetherthoB—Vcolors (7;)-color relationships(e.g.,Johnson1966).In of aCenAandBareindeedconsistentwithestimates broad-band photometry(e.g.,§IV). of (r,r)basedonothercolorindices(e.g., irradiance curve.TheVegaenergydistribution normalized BandVfiltersintothestellarspectral star byfoldingnumericalrepresentationsofthe is subjectedtoasimilarconvolutioninorder establish thezeropointofsyntheticB—Vscale ([5— F]=0.00;Johnsonetal1966;Blanco (1970; X<0.38,X^>0.70),andtheSchild, curves ofBeckersetal.(1976;0.38,T,andXfromthe valuestabulatedbyCox ratios arebyweight(seeCameron 1973).Radiative 0.16:0.11:0.73, andHe/e=3x10",whereall was specifiedbythestandardparametersX,7,Z, among H,He,C,N,and0basedonthe assumed tobepresentinequilibriumabundancewith and Flannery(1973).ThestandardEggletoncode ments ofFrenchandPowelltheevolutionary and massM. pheres discussedin§IVandshownFig.3.EvolutionarysequencesawayfromtheZAMSareplotted,withcrossesatintervals of the luminositiesderivedin§IIIandtemperaturesfromV—I(B-V)colorindices.Theheightofstippledregion and Stewart(1969)forZ= 0.02,0.04.Althoughour and Zimmerman(1975),wetreatconvectivemix- of onlyonedominantnuclearspecies.Hereweevaluate opacities areevaluatedby linearinterpolationin and theratiosZ/Z=0.75,C:N:0 the equationofstateasdescribedbyEggleton,Faulkner, Sun wereconstructedusingamodifiedversionof 0 CN0 Fig. 1.—Hertzsprung-RusselldiagramforaCenandtheSun.Squares(triangles)denotelocationofA,Bappropriateto Evolutionary modelsforaCenA,B,andthe © American Astronomical Society • Provided by theNASA Astrophysics Data System III. STELLAREVOLUTIONARYMODELS FLANNERY ANDAYRES L0G T ff e 9 two luminositiesandtemperaturesofaCen(seeSaio initial modelwemustspecifythemass,mixinglength the Sun.Calibrationofa,YforSunisachievedin length, andtwocompositionparametersbyfittingthe luminosities andtemperaturesatthesameage.In tion. Ourgoalistoconstructmodelsforbothcom- Although thetruesolarmetallicity isapparentlysome- the standardfashionbyevolvingsolarmodelfor mixing lengthforaCenA,Baresimilartothose models assumingthatboththeheliumabundanceand and Shibata1974),ourinitialapproachistoconstruct as describedabove). (as wellasthedistributionofreactingconstituents a, andtwoofthethreecompositionparametersX,Y,Z ponents ofaCensuchthattheysatisfytheobserved reasonable toassumethatstarsinabinaryformed effects ofrelativevariationsinmetallicity(Cox1976). tables shouldbeentirelyadequateforassessingthe what lower,weusedZ= 0.02 foroursolarmodel helium abundanceandmixing length,respectively. radius, L©andR©,whicharesensitiveprimarilytothe 4.7 x10yearstomatchtheactualluminosityand simultaneously andwiththesamechemicalcomposi- (primarily becauseopacity tableswereavailable). Having calibratedtheSun for Z=0.02,weregard opacities havechangedsince1969,theCoxandStewart Sun andthetheoreticalrepresentationofradiative Rather thanattempttodeterminetheage,mixing Even moresothanformembersofstarclusters,itis Vol. 221 No. 1, 1978 EVOLUTION OF a CEN SYSTEM 179 our models with Z = 0.04 as representing stars of square boxes, representing temperatures derived from twice solar metallicity. For the Sun, we find (a, Y) = V—I colors, are probably more reliable than the (1.33,0.256). By comparison, recent models of the triangles, which are based on B — F colors, because Sun with Z = 0.02 by Christensen-Dalsgaard and the latter are more susceptible to line blanketing Gough (1976) and Iben and Mahaify (1976) find effects. (a, Y) = (1.10, 0.245), (1.01, 0.236), respectively. Straightforward considerations of Christensen-Dalsgaard and Gough used the usual during main-sequence core hydrogen burning allow Eggleton code with conversion of one nuclear species, one to estimate the age of a Cen. The models determine hydrogen, and reaction rates evaluated in equilibrium both the slope ß of the (ZAMS) mass-luminosity from published rates of an older vintage than those relation, L oc Mß, and the rate of change in luminosity, used here. The Iben code is considerably different, d\ogL/dt, which, as indicated in Figure 2, is nearly especially in the treatment of the atmosphere, and in constant during the main-sequence phases. These evaluating opacities from a polynomial fit to published quantities, together with other properties of the models tables. Our model is somewhat different from other on the ZAMS and at 6 x 109 , are listed in models, but its intent is only to serve as a calibration Table 3. The observational results of the previous against which variations can be measured. section indicate that the ratios of mass and luminosity The evolutionary results are contained in a series of for a Cen A relative to B are 1.21 ± 0.01, and five sequences, one for the Sun and two for each com- 3.18 ± 0.1, respectively. Thus the observed slope of the ponent of a Cen with Z = 0.02, 0.04. Each series mass-luminosity law for a Cen is 6.1 ± 0.3, so that begins with a model high on the Hayashi track with a Cen A is approximately 30% brighter, relative to B, central temperatures so low that negligible nuclear than would be expected on the ZAMS, ß ^ 4.7. burning occurs. The contraction phase to the zero-age Evolution beyond the ZAMS readily accounts for the main sequence (ZAMS) required about 30-40 models enhanced ratio. In terms of coefficients tabulated in for each series, during which time the nuclear species Table 3 the age t can be expressed as begin to equilibrate. Only about 20 additional models were required to follow the evolution during core hydrogen burning to luminosities well above the , = log(LA/LB) - ß\og(MA/MB) observed luminosity of the star. Figure 1 plots the (d log Lj dt) A — (d\ogL/dt)B ’ ^ sequences in an H-R diagram, but for clarity the con- traction phases have been omitted. Tick marks which yields estimates of (4.1 ± 0.9) and (6.0 ± 1.1) x along each track represent intervals of 2 billion (109) 109 years for Z = 0.02 and 0.04, respectively. Thus, years. In the right-hand portion of the figure, two for consistent theoretical models, the observed ratios vectors indicate the displacement of ZAMS models of luminosity and mass lead one to predict an evolu- appropriate to a variation in Y of 0.02, and in mass tionary age for a Cen comparable with that of the Sun. of kM/M = 0.02. As discussed in the previous sec- Actual specification of the detailed properties of the tion, the shaded regions correspond to the “ observed” model requires that we compare the absolute values of positions of a Cen A, B, for which the luminosities stellar parameters, not just their relative variation. For relative to the Sun are known to about ± 4%, but the a fixed mass and metallicity, the absolute luminosity temperatures are less precisely determined. The of the theoretical model is a function only of age and

AGE (I09 years) Fig. 2—Luminosity variation with age for the models plotted in Fig. 1. The shaded region corresponds to intersection with the observed luminosity of « Cen A and B.

© American Astronomical Society • Provided by the NASA Astrophysics Data System 1978ApJ. . .221. .175F 9 180 FLANNERYANDAYRESVol.221 in Figure1,thevariationofZAMSluminosityis helium content;variationsofthemixinglengthpro- duce onlysmallchangesinluminosity.Asindicated approximately dlogL/dY=2.2,independentofmass logL(F,0 =logL(F,ZAMS)+(dlogL/dY)AY be expressedas 0.02, A=0.247,—0.003,whichimpliest for eachcomponentofaCen,inÀFandt.ForZ= or metallicity.Theluminosityasafunctionofagecan 4.4 billionyears,andAF=—0.05,i.e.,F0.206. we canuseequation(3)toproducetwoequations,one If wedefinethequantityA*=log(L/LMs),then that someevolutionmustoccurtoproducethenon- 0.04, A=0.230,0.098,whichresultsin¿ The nearcoincidenceinluminosityofaCenBandthe temperature logT=3.70by reducingato0.65.This with M/M=0.92,Z0.02, canbeshiftedfromits ture shift.Forexample,the modelofcomponentB from Figure1,themodelswithhighermetallicityare can accommodatethenecessaryevolutionwithoutan example, thediscussioninTrimble1975whichgives predicted primordialheliumabundance.(See,for modate modelsofsolarmetallicityrequiresahelium model luminositiescanbebelowtheobservedvalues lowered relativetoitssolarvalueinorderthatboth ZAMS luminosityratio,requiresthatFmustbe ZAMS modelsforZ=0.02,coupledwiththenecessity length parametercanalsoreadilyproducethetempera- § II)temperaturesofthestars.Thisisnotnecessarily also inbetteraccordwiththe“observed”(butsee abundance whichisevenslightlybelowtheminimum a compellingargument,sincevariationinthemixing- appreciable variationofheliumabundance.ForZ= nosity ofthemoremetalrichmodels(atsolarF) before evolutionarybrighteningoccurs.Toaccom- 360 Kshiftintemperatureoccurs whiletheluminosity ZAMS locationlog7^=3.73 witha=1.33,to 6.3 x10yearsandAF=—0.01.Asisapparent 0Yo ab obsZA ab e q F =0.229+0.094[plp]-)Theinitiallylowerlumi- c © American Astronomical Society • Provided by theNASA Astrophysics Data System 0.92 9.2(7)-0.3253.7340.0270.024"| 1.00 7.2(7)-0.1483.7520.0180.032 0.92.. 1.3(8)-0.4263.7100.0600.0m 1.11 6.5(7)0.0683.7760.004...f4.82 1.11.. 5.6(7)-0.0513.7530.0210.040[ 9_1 Ml MoAgelogL[LqTVMIMo(10yr)L/¿/log oonv + (dlogL/dt)t.(3) 4.8 (9)0.0043.7620.009 6.0(9) 0.3653.7820.0010.050J 6.0(9) -0.1803.7450.012...I 6.0 (9)0.1893.7630.011...J 6.0 (9)-0.3103.7210.053...I4.60 Stellar StructureModelsa=1.33,Y0.2556 TABLE 3 Z =0.02 Z =0.04 9 9 9 AB A 18 regarded asbeingthesameinaCenandSun, of themodeldecreasesonly2%(from0.47to0.46L). location ofthesysteminH-Rdiagramisquite Z =0.04models,coupledwiththeobservedenhance- good, andisconsistentwiththeenhancementof agreement ofthemetalrichmodelwithobserved However, totheextentthatmixinglengthcanbe the modelswithtime.Thesetracksarebasedon metals foraCenfoundbyFrenchandPowell. in anintersectionoftheobservedluminosityati~ each trackverticallybyAlogL=—0.11,andresult having asolarheliumabundance.Accordingtothe agreement inbothluminosityandtemperatureforthe produce anageof¿~6.3x10years.Thecombined requires onlyasmallshiftofAlogL=—0.02to 4.4 x10years.SatisfactoryagreementforZ=0.04 discussion ofthepreviousparagraph,achange chemical compositionsofaCenAandBareidentical, for aCenAandBusingmeasuredequivalentwidths essentially thesameinheliumcontentasSun. ment ofmetalsinaCen,suggeststhatthesystemis —which consistentlyreproduceagivenatomic we candeterminearangeofatmosphericmodels— of temperaturesensitiveCailines. on acceptablemetallicitiesandeffectivetemperatures 6 ±1x10yearsinage,twicesolarmetals,and AF =—0.05fortheZ0.02modelswouldshift designated byeffectivetemperaturepairs(T,r) compare (ref,7^®)asafunctionofthederived composition Zandaget.Ideally wewouldfindonly spectrum (e.g.,Fei,Cai)inbothstars.Wecanthen 0 the equivalentwidthsand evolutionarymodels. for (TeflA,T’eff).Thelatter dependonchemical abundance, say[Ca/H],withtheevolutionarytracks consistent withboththemodel atmospheresstudyof a smallregioninthe(T^fA T'efA-diagramwhichis eiieff f Figure 2illustratesthevariationinluminosityof In thissectionweestablishadditionalconstraints If wemakethereasonableassumptionthat IV. MODELATMOSPHERES d logL/dt 1978ApJ. . .221. .175F ,7 -2 2B A No. 1,1978 tion describedin§III.Therefore,weadoptthesimple The spectrumsynthesistestshereareenvisioned expedient ofscaledsolarphotospheremodels.The primarily asconsistencychecksonthesystemevolu- initial solarT(T¿)modelusedhereisthatproposed of atmosphericmodelsappropriatetoaCenAandB. recently byAllen(1976,ascommunicatedR.L. intensities. ThesolarT{r)relationisscaledtoa limb behaviorofopticalandinfraredcontinuum Kurucz; seealsoAvrett1977),basedonthecenter- hydrostatic equilibrium,solarabundancesforhelium, different effectivetemperatureaccordingtotheratio gravity andeffectivetemperatureconsideredhere(see, adequate overtherelativelynarrowrangeofsurface hydrogen andH".Thisapproachshouldbeentirely and theimportantelectrondonorsLTEforneutral 7eff*/^eff°- ToobtaindensitiesfromT*^),weassume e.g., CarbonandGingerich1969). to each7^*arebasedonthemeasuredstellarmasses bQQ 4.48-4.65 cms.Thesurfacegravitiescorresponding 4.37 cms“,andr=5000-5500Kwithlogg and thebolometricluminositiescitedin§II. weak lineequivalentwidthsforaCenAandBbased 100 K:r=5500-6000Kwithlogg4.22- mostly becausetheminorityspecieslinesarepartic- analysis here,werestrictourattentiontotheCai on moderatelyhighdispersionspectrograms.Inthe spectrum, partlyforcomputationalsimplicity,but ularly temperaturesensitive(I.P.=6.11eVversus 7.87 eVforFe). eff ions (e.g.,§IIabove).However,thecurrentlackof would utilizethespectraofseveralabundantatomsand high-dispersion profiledataanduncertaintiesconcern- ing nonthermalbroadeninginthephotospheresof eff To producesuchadiagram,wefirstconstructsets We constructedsixmodelsforeachstarinstepsof French andPowell(1971)havepublishedlistsof Of course,amorecompletesurveyofCenAandB © American Astronomical Society • Provided by theNASA Astrophysics Data System ä) AGridofModelAtmospheres b) Equivalent-WidthData(Cai) 4526.94. 4512.27. 6161.29. 5512.98. 5260.39. 6471.66. 6166.44. 6499.65. [Fe/H]. [Ca/H] t FrenchandPowell1971Table 3. Ï FrenchandPowell1971Table 2. * FrenchandPowell1971Appendix, A(Â) aB W° (mÀ)(mÂ) AaÁ 24 83 32 93 70 62 83 85 EVOLUTION OF«CENSYSTEM 106 26 43 87 81 82 81 89 TABLE 4 131 132 112 105 126 105 1 45 60 A K a a CenAandBargueagainstmorecomprehensive study here. equivalent widthscommontoaCenAandB.These the integratedsunlightAtlasofBeckers,Bridges,and corresponding solarequivalentwidthsobtainedfrom are giveninTable4,togetherwithestimatesofthe each linebyFrenchandPowellusingdifferential abundance ratios(logarithmicunits)establishedfor curves ofgrowth.ThefinalcolumnsTable4com- Gilliam (1976).AlsolistedinTable4arethe[Ca/Fe] line pairswiththevaluesobtainedbyFrenchand pare themean[Ca/Fe]ratiosforsampleofeight Powell fortheirentireaCenAandBCailists(34 reproduce themeasuredequivalentwidths,using Powell, arealsogiven. 30 lines,respectively).[Ca/H]ratiosrelativetothe (1977). Inallcases,adepth-independentclassical determined the[Ca/H]abundanceratiosrequiredto Sun, basedonthevaluesof[Fe/H]citedbyFrenchand was takenofthepotentialeffectenhancedmetallicity microturbulence of2kms“wasassumed.Noaccount LTE spectrumsynthesisapproachdescribedbyAyres the electrondensity.Hencecomputedequivalent because theopticaldepthscalesofCailinesand the electrondonorabundances.Theinferred[Ca/H] widths shouldberelativelyunaffectedbychangesin on theatmosphericstructureofgridmodels, increasing modeleffectivetemperatureforbothaCenA ratios werefoundtoincreasesystematicallywith H" backgroundcontinuumbothdependlinearlyon ionization ofneutralcalcium. widths comparisonareillustratedinFigure3.The and Baswouldbeexpectedaccordingtotheenhanced large openparallelogramrepresentstheenvelopeof line pairsofthespectrumsample.(Aparticular (re, Teff®)trajectoriesdeterminedfortheindividual values whichreproducethemeasuredequivalentwidth “trajectory” representsthelocusof(T,T*) pair ()T,W*)ofagivenCailineinCenAandB ff eiief a French andPowell(1971)listeightpairsofCai For eachCailinepairandatmosphericmodel,we The finalresultsofthemodelatmospheres-equivalent ( +0.05±0.03)t -0.03 ±0.14 + 0.22±0.05f + 0.19±0.15 (0.27 ±0.06)tt A [Ca/Fe] + 0.04 + 0.05 + 0.07 -0.20 -0.21 -0.17 + 0.15 + 0.07 ( +0.22±0.03)t + 0.17±0.14 (0.34 ±0.05)tt B 0.12 ±0.04Î 0.29 ±0.15 [Ca/Fe] + 0.22 + 0.15 + 0.09 -0.09 + 0.30 + 0.13 + 0.36 + 0.18 181 1978ApJ. . .221. .175F A8 AB 9 9 + {square, V—I;triangle.B—V).Thesolidlinebisectingthe consistent withanalysisoftemperaturesensitiveCaitransi- evolution models{solidcurves),andT^f-colorrelationships tions {openparallelogram),composition-dependentstellar seven linepairsisforcedtobethesameinbothstars.Thevalues result whentheaveragecalciumabundancedeterminedfrom calcium abundancetoincreasewithincreasingTtt,inthe The evolutionarytracksextendfromtheZAMS{dots)tot= solar atthetop.(Horizontaltickmarksindicatestepsof0.2.) gram isthe(T,Teff)trajectoryobtainedbyrequir- for thesamevalueof[Ca/H].)TheA5513linepairwas decreasing metallicitytomatchincreasingeffectivetempera- increase fromunityatthebottomofparallelogramtotwice parallelograms representsthelocusofT,tvalueswhich the sevenremaininglinepairsbesameinaCenA ing thattheaverage[Ca/H]abundanceratiobasedon tures. that themeasuredCaiequivalentwidthsforceinferred of theinferredcalciumabundance(relativetoSun) 182 seven linepairs.Thecurvebisectingtheopenparallelo- results differedsignificantlyfromthoseoftheother omitted fromthisandlatercomparisonsbecauseits opposite sensetothestellarstructuremodels,whichrequire 8 x10years.Crossesindicatestepsof2Notice the measuredequivalentwidthsandmagnitudeof ratios. estimates are,unfortunately,relativelylarge—atleast designate theparticularvaluesofabundance tion tracksforaCenAand B(§IIIabove).Thetick increasing Tisclearlyapropertyofthemodel and B.Labelsonthe“averageabundance”trajectory years. Notetheimportantresult thatthebehaviorof 0.04 representcomposition-dependent systemevolu- and B.However,thetrendofincreasing[Ca/H]with nonthermal broadeninginthephotospheresofaCenA atmospheres owingtothepronouncedtemperature marks onthesecurvesdesignate ageinstepsof2x10 sensitivity oftheLTECa-Caionizationequilibrium. Q eff eilet eii ±0.15 dex.Theyariseprimarilyfromuncertaintiesin Fig. 3.—RangeofeffectivetemperaturesforaCenAandB The uncertaintyinthesedifferentialabundance The curvesinFigure3labeled Z=0.02and © American Astronomical Society • Provided by theNASA Astrophysics Data System FLANNERY ANDAYRES AB increasing metallicity.Itisclearfromthisfigurethat, tracks aremuchmorenearlyconsistent.Infact,the the (r,r)rangeoccupiedbysystemfora the systemevolutiontracksisoppositetothatof intersection ofthestellarevolutionand probably toohottobeconsistentwiththemeasured calcium (see,e.g.,Ayresetal.1976). enhancement oftheothermetalsfollowsthat atmospheres comparisonssuggestsZ^0.03,in equivalent widths,whereasthetwicesolarmetallicity despite theratherlargeuncertaintiesindetermining model atmospheres—equivalentwidthcomparison: have constructedanevolutionarymodelforaCentauri differential curve-of-growthanalysis,ifthegeneral quantitative agreementwithFrenchandPowell’s solar-type age{t~5billionyears)decreaseswith which is-consistentwiththeobservedpropertiesof binary. Thatthesystemispartiallyevolvedfollows respect toBthanwouldbeexpectedforanunevolved directly fromtheobservedsteepnessofmass- luminosity relation:componentAis30%brighterwith [Ca/H], thesolarcomposition(Z=0.02)tracksare if weusemodelswithsolarmetallicity,thentomatch the microturbulentbroadening,mightalterthose Three piecesofevidencefavorthehighermetallicity. with respecttoasolarcalibrationmodel(Z=0.02). We didthisfortwometallicitiesZ=0.02and0.04 mined byfittingtheabsoluteluminositiesofstars. the observedabsoluteluminosityrequiresthat the mixinglengthforbothcomponentsofaCento the otherhand,temperaturesofevolutionary temperatures impliedbytheV—Icolorsaremore helium abundancebesubstantiallylowerthanforthe be thesameasforsolarcalibrationmodel.Third, We havearbitrarily(butperhapsreasonably)forced models aresensitivetothemixing-lengthparameter. reliable thantemperaturesderivedfromB—V.On line blanketing.Inparticular,wefeelthatthehigher tures derivedfromcolorindicesaresuspectowingto temperatures foraCenAandB,butbothsidesofthis results. Second,theevolutionarymodelswithen- abundances ofAandBtobeuptwicesolar,but, system. Theheliumabundanceandagecanbedeter- helium abundancepredictedfromnucleosynthesisin comparison areuncertain.Ontheonehand,tempera- hanced metallicityagreebetterwithestimatedeffective as discussedin§IV,systematicerrors,particularly First, FrenchandPowell(1971)directlymeasurethe eff independent argumentsallfavorstellarstructure the bigbang(seeTrimble1975).Takentogether,these The lowvalueisevenlessthantheminimumprimordial highest possibledispersionand comparedtointegrated solar model,Y=0.206comparedto0.256. models enhancedinmetalswithrespecttotheSun. sunlight observationsdegraded tothesameresolution. abundance analysesbasedon spectratakenwiththe Clearly, itisdesirableto resolvethisissuewith For theevolutionarysequence withtwicesolarmetals, ABQ Using standardassumptionsandtechniques,we v. DISCUSSION Vol. 221 No. 1, 1978 EVOLUTION OF a CEN SYSTEM 183 the age of a Cen is 6 x 109 years and the helium TABLE 5 abundance, Y = 0.246, is essentially solar. The Space Motion of the Sun and a Centauri a) a Centauri A and B as Solar Analogs Parameter Sun a Centauri Because so much information is available for a Cen, ir (radial) (kms-1) -9.2 + 24.0 and because the binary is so bright, the system is well 6 (angular) (km s-1) + 12.0 + 12.5 1 + 6.9 + 12.7 suited for the application of solar-type observational Z (perpendicular)1 (km s " ). . and analytical techniques. An example is the study of |t;| (km s" ) 16.6 29.9 Ri (kpc) 9.9 9.6 chromospheric and coronal properties. These are Rz (kpc) 11.3 11.7 0.08 0.14 revealed typically by relatively weak emission cores in * (kpc)2 1/2 1 strong visible and near-ultraviolet Fraunhofer lines, <ü > (kms- ) 17.4 26.8 or by faint (relative to the optical continuum) EUV emission features. Recent studies have suggested that the lower chromosphere of a Cen A is qualitatively inner, Ru and outer, R2, radii appropriate to epicyclic similar to the solar case, at least based on the similarity motion, and the scale height Z of the motion perpendic- of Ca il, Mg ii, and La core emission strengths ular to the orbital plane. These are also listed in (Boesgaard and Hagen 1974 ; Ayres et al. 1976 ; Dupree Table 5. We have used the values given by Mihalas 1977). However, no detection of coronal or transition- for the solar distance from the galactic center, 10 kpc, region emission lines in the EUV spectrum of a Cen and the Oort constants, (A, B) = (15, -10) kms-1 kpc"1. has yet been reported. If a Cen A indeed possesses a The guiding centers about which the epicyclic motion corona unlike the solar example, but similar chromo- occurs are at 10.609 and 10.635 kpc for the Sun and spheric properties, these characteristics are potentially a Cen, respectively, and separate in angle at the slow useful in distinguishing between competing theories rate of only 0.07 radians per 109 years. Unless the of chromosphere-corona heating and energy balance. orbits have been fortuitously aligned by an unlikely This comparison is particularly useful because a Cen A close encounter involving one of the systems, the and the Sun are so similar in terms of mass, age, separation of the stars arises both from motion along surface gravity, and . the epicyclic ellipses with radial and tangential range We also point out the opportunity for very detailed of 2.1 by 3.3 kpc and 1.4 by 2.2 kpc for the binary and comparisons of abundance distributions in the Sun the Sun, respectively, and from a secular drift of and a Cen, owing to the suitability of the binary 0.7 kpc per 109 years between the guiding centers. system for high-dispersion optical and infrared During this motion, the time average rms velocities, spectroscopy. Such studies might shed some light on <¿;2>1/2, of the Sun and a Cen with respect to the the properties of the perhaps quite different samples of instantaneous local standard of rest are 17 and the interstellar medium from which our Sun and the 27 km s“1, respectively. Finally, note that the vertical a Cen system separately condensed. Studies of the scale height for a Cen, 140 pc, and the Sun, 80 pc, are rotation-vibration bands of carbon monoxide (CO) comparable with the scale height of gas and dust, would be especially useful in this regard. Relative 125 pc (Mihalas 1968). intensities of weak, unsaturated lines in the 2.4/xm first overtone bands should accurately reflect the atmos- c) Constraints on Accretion Hypotheses pheric temperatures of the two stars, while the absolute Newman and Talbot (1976) and Auman and line strengths should indicate unambiguously whether a,b McCrea (1976) have proposed that accretion from the Zcno is enhanced relative to the solar value. Further- interstellar medium could have substantially enriched more, observations of isotopic lines such as from 13 16 12 18 the metallicity of the solar surface with respect to the C 0 and C 0 in the 5 fundamental bands interior. To our knowledge the actual structure and might provide insight into the nuclear history of the evolution of the Sun under these circumstances has stellar material. These measurements would comple- not been calculated ; however, based on homogeneous ment recent studies of light element abundances in models of lower metallicity, the effect is likely to lower a Cen [e.g., Boesgaard and Hagen 1974 (Li); Dravins the flux of solar neutrinos, perhaps by enough to and Hultqvist 1977 (Be)]. remove the apparent conflict between theory and experiment (Bahcall and Davis 1976). Since the b) The Relative Galactic Motion of captured material will be mixed at least throughout a Centauri and the Sun the surface convection zone, it is important to know The components of a Cen are similar to the Sun not the extent of that zone in an accreting star, but, again, only in terms of mass and age, but also in terms of to our knowledge such models have not been cal- galactic orbits. In Table 5 we list the galactic motion culated. The accretion rate varies as M2V~3 (Hoyle of a Cen and the Sun derived from the observed space and Lyttleton 1939), and therefore is most effective 1 velocity of the binary, Fr = — 24 km s“ (Allen 1973); for low relative velocities F. In the cited references on 1 1 /xa =-0.4904 syr" , /x, =+0':712yr- (SAO Star solar accretion it is estimated that accretion will be Catalog 1966), and the solar velocity with respect to most effective for a relative velocity between the Sun the dynamical local standard of rest (Mihalas 1968). and an interstellar cloud in the range 2-10 km s"1. In Following Mihalas (chap. 13), we have determined the addition, accretion can occur only if the infall velocity

© American Astronomical Society • Provided by the NASA Astrophysics Data System 1978ApJ. . .221. .175F _1 2 -1 ing solarwind.Applicationofthissimpletheoryto is sufficienttooverwhelmthepressureofoutflow- a Cenprovidessomecomplications.Fortheentire appropriate tovelocitiesbetween2and10kmslies binary ofmass2.03Mtheaccretionradius,2GM/V, in therange900and36AU,comparedtoavariation in thebinaryseparationof35to12AU.Themaximum velocities ofthecomponentsaboutcentermass are 6.8and8.2kms.Therefore,atlowvelocity, 184 velocity, capturecouldoccurontotheindividual accretion isessentiallyintothebinary;butathigh throughout themasscontainedinsurfaceconvec- 0 tion zone.ForthenonaccretingmodelsofaCenA, components. respectively (seeTable3fortheevolutionaryvariation). the convectionzonesof0.01,0.06,and0.01M, inhomogeneous, accretingmodel,thedifferencein B, andtheSun,discussedin§III,wefindmassesfor Although thesevaluesmaynotbeappropriateforan effective temperaturesofaCenAandBguarantees in theirconvectionzones.Therefore,theagreement metallicity ofaCenAandBasobservedbyFrench substantial differencesinthefractionalmasscontained has eitherbeennegligible,orsubstantialenoughto and Powell(1971)indicatesthataccretionontoaCen Q pect totheSun,coupledwithsimilarityingalactic In bothcases,themetalenrichmentofaCenwithres- saturate bothconvectionzones(i.e.,AM^0.06M). circuited theGalaxyabout20times,andtherefore unless thebulkofaccretionoccursinaverysmall accretion toexplainthesurfacemetallicityofSun, the surfaceconvectionzoneofSunwithout have passedthroughspiralarmsmanytimes,severe number ofsignificantevents.Sincebothsystemshave orbits andage,wouldmakeitdifficulttoinvoke constraints mustapplyforaccretiontohavealtered ratio AY=ÆAZwithRintherange3to5(e.g.,see similarly affectingaCen. the evolutionarymodels.ForAY=+0.05even metals inourGalaxyarethoughttoproduceacorre- in planetarynebulaemightnotreflecttheinitial sponding enhancementinheliumaccordingtothe exceed theobservedbrightness,andadditional enrichment impliedbytheapparentmetalenhance- helium abundancearedifficulttoobtainandinterpret. Audouze andTinsley1976;Peimbert1977Perrinetal brightening wouldhavetooccurproducethesteep ZAMS luminosityofthemodelBcomponentwould ment ofaCen,AY=+0.05to+0.10,isruledoutby abundances oftheparentstar.Infact,helium subject tosystematicerrorssincemeasurementsofthe 0 For example,theratiosofheliumtometalsobserved Allen, C.W.1973,Astrophysical Quantities(3ded.;London: Alexander, J.B.,andBranch,D. 1973,M.N.R.A.S.,164,19P. 1977). Observationaljustificationforthisrelationis Material accretedontoastarmustbemixedatleast d) TheGalacticEnrichmentofHeliumandMetals The processesresponsiblefortheenrichmentof Athlone). © American Astronomical Society • Provided by theNASA Astrophysics Data System FLANNERY ANDAYRES REFERENCES ratio ofluminositytomass,asdiscussedin§III. the propertiesof138starsinsolarneighborhood. Perrin etalfavorjR~5toaccountfortheirstudyof what differentfromthosedeterminedhere—inpartic- ular ~0.1maghigherluminositiesforbothaCenA However, theparameterstheylistforaCenaresome- regard theobservationaljustificationforthisrelation well becorrectthatAY~3AZ,butatpresentwe be correspondinglylessreliable.Statistically,itmay and B—andparametersformoredistantstarsshould the otherhand,differenceinZbetweenSun as suspectandciteaCencounter-example.On and aCenisconsistentwiththeideathatthereexists Tinsley 1976). stellar mediumatanyonetime(seeAudouzeand substantial dispersioninthemetallicityofinter- the Hyadescluster(Eggen1969),relativetoother luminosity lawappropriateforthevisualbinariesin relation AYä3AZmighthold(Faulkner1967).A stars, providedoneofthefirstindicationsthata recent redeterminationoftheconvergentpointdis- tance byHanson(1975)asrevisedMcAlister(1977) is inagreementwithotherdistanceindicatorsforthe ing thedistancetoclustercenterisapparently masses andluminositiesoftheHyadesbinariesstill are notwellknown.Eventhoughthedebateconcern- Hyades, d=44pc(vanAltena1974).However,the resolved, andtheorbitaldeterminationsofEggenhave that theshallowslopeisonlyareflectionofun- been confirmedbyWickes’s(1975)interferometric value ofabout4.7(see§III).However,itisverylikely is observedtobeabout1.0comparedapredicted the mass-luminosityrelation(formerlyHyades cluster center.Althoughthe10%increasein possible errorsofabout30%inmassand20% measurements, theuncertainlocationofbinary to publication,andA.N.Coxforhisadviceonthe provide asunambiguousacomparisonwithstellar cluster center.Therefore,theHyadesbinariesdonot not changetheslopeofmass-luminositylaw,which more thanamagnitude),adjustingthedistancedoes binary ADS3475isdisplacedbynearly8°fromthe luminosity. Forexample,theapparentlymostmassive stars withrespecttotheclustercenterintroduces link forallowingustousetheirresultsonaCenprior evolution modelsasdoestheaCensystem. certainty inlocatingthebinarieswithrespectto distance haseliminatedthediscrepantzero-pointin useful discussions. stars wereoverluminouswithrespecttotheirmassby We alsothankR.L.KuruczandG.B.Rybickifor applicability ofolderopacitytablestothisproblem. Allen, R.G.1976,Ph.D.thesis, UniversityofArizona,in Audouze, J.,andTinsley,B.1976, Ann.Rev.Astr.Ap.,14,43. Historically, thediscrepancybetweenmass- We aregratefultoK.W.KamperandA.J.Wesse- preparation. e) HyadesMass-LuminosityRelation Vol. 221 No. 1, 1978 EVOLUTION OF a CEN SYSTEM 185 Auman, J. R., and McCrea, W. H. 1976, Nature, 262, 560. Hoyle, F., and Lyttleton, R. A. 1939, Proc. Cambridge Phil. Avrett, E. H. 1977, in The Solar Output and Its Variations, in Soc. Math. Phys. Sei., 35, 405. press. Iben, I., Jr. 1967, Ann. Rev. Astr. Ap., 5, 571. Ayres, T. R. 1977, Ap. /., 213, 296. Iben, I., Jr., and Mahafîy, J. 1976, Ap. J. {Letters), 209, L39. Ayres, T. R., Linsky, J. L., Rodgers, A. W., and Kurucz, R. L. Johnson, H. L. 1956, Sky Tel, 16, 470. 1976, Ap. J., 210, 199. . 1966, Ann. Rev. Astr. Ap., 4, 193. Bahcall, J. N., and Davis, R. 1976, Science, 196, 264. Johnson, H. L., Mitchell, R. L, Iriarte, B., and Wisniewski, Beckers, J. M., Bridges, C. A., and Gilliam, L. B. 1976, Air W. Z. 1966, Comm. Lunar Planetary Lab., 4, 99. Force Geophysical Lab., ERP No. 565. Kamper, K. W., and Wesselink, A. J. 1977, private com- Blanco, V. M., Demers, S., Douglass, G. G., and FitzGerald, munication. M. P. 1970, Pub. U.S. Naval Obs., Vol. 21. Kron, G. E., Gascoigne, S. C., and White, H. S. 1957, A.J., 62, Boesgaard, A. M., and Hagen, W. 1974, Ap. J., 189, 85. 205. Cameron, A. G. W. 1973, Space Sei. Rev., 15, 121. Labs, D. 1975, in Problems in Stellar Atmospheres and En- Carbon, D. F., and Gingerich, O. 1969, Proceedings of the 3rd velopes (New York: Springer-Verlag), p. 1. Harvard-Smithsonian Conference on Stellar Atmospheres, Labs, D., and Neckel, H. 1970, Solar Phys., 15, 79. ed. O. Gingerich (Cambridge: MIT Press), p. 377. McAlister, Harold A. 1977, Ap. J., 215, 159. Christensen-Dalsgaard, J., and Gough, P. O. 1976, Nature, Mihalas, D. 1968, Galactic Astronomy (San Francisco: 259, 89. Freeman). Cousins, A. W. J., and Lagerweij, H. C. 1967, M.N.A.S. So. Newman, M. J., and Talbot, R. J., Jr. 1976, Nature, 262, 559. Africa, 26, 83. Peimbert, M. 1975, Ann. Rev. Astr. Ap., 13, 113. Cox, A. N. 1976, private communication. Perrin, M. N., Hejlesen, P. M., Cayrel de Strobel, G., and Cox, A. N., and Stewart, J. N. 1969, Sei. Infor., USSR Acad. Cayrel, R. 1977, Astr. Ap., 54, 779. Sei., Vol. 15. Powell, A. L. T., and French, V. A. 1970, Ap. Letters, 6, 131. Dravins, D., and Hultqvist, L. 1977, Astr. Ap., 55, 463. Saio, H., and Shibata, Y. 1974, Sei. Reports Tohoku Univ., Dupree, A. K. 1977, private communication. 1st Ser., 57, No. 3, 87. Eggen, O. J. 1969, Ap. J., 150, 241. Schild, R., Peterson, D. M., and Oke, J. B. 1971, Ap. J., 166, Eggleton, P. P. 1971, M.N.R.A.S., 151, 351. 95. Eggleton, P. P., Faulkner, J., and Flannery, B. P. 1973, Astr. Smithsonian Astrophysical Observatory. 1966, Star Catalog Ap., 23, 325. (Washington: Government Printing Office). Faulkner, John. 1967, Ap. J., 147, 617. Thomas, J. A., Hyland, A. R., and Robinson, G. 1973, Fowler, W. A., Caughlan, G. R., and Zimmerman, B. A. 1975, M.N.R.A.S., 165, 201. Ann. Rev. Astr. Ap., 13, 69. Trimble, V. 1975, Rev. Mod. Phys., 47, 877. French, V. A., and Powell, A. L. T. 1971, Royal Obs. Bull., No. van Altena, W. F. 1974, Pub. A.S.P., 86, 217. 173, p. 63. van de Kamp, P. 1958, in Handbuch der Physik, ed. S. Flügge Gasteyer, C. 1966, A.J., 71, 1017. (Berlin: Springer-Verlag), Vol. 50, p. 188. Haisch, B. M., Linsky, J. L., Lampton, M., Paresce, F., and Wiekes, W. C. 1975, A.J., 80, 1059. Margen, B. 1977, Ap. J. {Letters), 213, LI 19. Willstrop, R. V. 1965, Mem. R.A.S., 69, 83. Hanson, R. B. 1975, A.J., 80, 379. Hayes, D. S., and Latham, D. W. 1975, Ap. J., 197, 593.

Thomas R. Ayres: JILA, University of Colorado, Boulder, CO 80309 Brian P. Flannery: Center for Astrophysics, 60 Garden Street, Cambridge, MA 02138

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