1982ApJ. . .262. .700Z 9 ical andobservationalstudiesoftheseanomalous laws ofeithertheclassicalorPopulationIICepheids variable thatdoesnotobeytheperiod-luminosity{P-L) large masses(~1.591lo)>however,forthiswouldmean masses wereproducedbymassexchangeinclosebinary (see Zinn1980andHirshfeldforreviews).Theoret- spheroidal galaxieshaverevealedaclassofCepheid © 1982.TheAmericanAstronomicalSociety.Allrightsreserved.PrintedinU.S.A. The AstrophysicalJournal,262:700-708,1982November15 Cepheids haveshownthattheyaremoremassivethan that starformationoccurredinthedwarfspheroidals anomalous Cepheidswereprobablynotbomwiththeir the PopulationIICepheidsbyfactorsof2-3.The NGC 5466,whichhasavery lowdensityincomparison required lengthoftimeinsystemswherecloseencoun- evolve intoanomalousCepheidswillnotsurviveforthe shown thataclosebinarysysteminitiallyconsistingof systems. Renzini,Mengel,andSweigart(1977)have et alarguethatbinariesoftheproperconfigurationto Cepheid andawhitedwarf.Toexplainthepresenceof two ~0.99Hstarscanevolveintoananomalous and theirabsenceinsystemsofhighdensity,Renzini anomalous Cepheidsinsystemsoflowstellardensity ~ 1X10yrago.Itappearsmorelikelythattheirlarge the .ItisVI9inmetal-poor globularcluster ters betweenstarsoccurfrequently. 0 The investigationsofthevariablestarsindwarf Only oneanomalousCepheid hasbeendiscoveredin © American Astronomical Society • Provided by theNASA Astrophysics Data System l/2 x/1 THE MASSOFANOMALOUSCEPHEIDINGLOBULARCLUSTERNGC5466 been measuredfromspectrophotometricscans.ThepositionofVI9inthe6-loggdiagramrulesout (HB)starsinNGC5466andthetypecRRLyraevariableTVBoo.Thefollowing mass, 1.56io3o9Ho,whichisconsistentwiththetheorythatlargemassesofanomalous relation yields:911!(VI9)/911!(TVBoo)=2.33±0.40.Thus,itappearsthatV19isapproximately The surfacegravitymeasurementsindicatethatVI9ispulsatinginthefirstharmonicratherthan mass ratiosareobtained:^(V^y^iHB)=1.64±0.76and9H(V19)/91t(TVBoo)2.03±0.62. fundamental mode.AssumingthefirstharmonicmodeforVI9andTVBoo,Q=P(p) days) andluminosity(M=—\.21)thataresimilartothoseoftheanomalousCepheidsindwarf earlier byZinnandDahnthatVI9hasthesameradialvelocityasNGC5466aperiod(0.82 Cepheids resultfromthetransferofmassinclosebinarysystems. spheroidal .OurobservationsofVI9havebeencomparedwithsimilaronesthree strong casethatV19isanunusualCepheidvariableandamemberofNGC5466.Ithadbeenshown the possibilitiesthatitisanRRLyraeoraBLHercuhsvariable,whichstrengthensalready twice asmassiveHBstars.TheQ—P{p)relationyieldsthemostpreciseestimateforV19’s Subject headings:clusters:globular—:CepheidspulsationRRLyrae e v The effectivetemperatureandsurfacegravityoftheanomalousCepheidVI9inNGC5466have I. INTRODUCTION Robert ZinnandChristopherR.King Received 1982April9;acceptedMay25 Yale UniversityObservatory ABSTRACT 700 _1 mass ofVI9,wehaveobtained spectrophotometryofit naries inclusters. evidence ofbinariesinglobularclusters(seeTrimble exist inNGC5466.Sincethereisverylittleother evolution ofclosebinaries,thenitfollowsthatbinaries of starclustersandtheformation andsurvivalofbi- tion isofsomeimportancetotheoriesthedynamics with mostotherglobularclusters(seePetersonandKing masses andhencethecolorsluminositiestoexpect under way.ThemassofVI9providesanestimatethe magnitudes, andcolorsofthebluestragglersmaybe may besurveyedforbluestragglers,andthenumbers, progenitors oftheanomalousCepheidsarethoughtto presence inNGC5466establishesthatanomalous 1980; Margon,Downes,andGunn1981),thisobserva- compared withtheoreticalpredictions.Suchasurveyis glers. NGC5466issufficientlyclosetotheSunthatit for thebluestragglers. spend asignificantfractionoftheirlivesasbluestrag- Cepheids existinglobularclustersandtheGalaxy.The Cepheids inthedwarfspheriodalgalaxies. and thatitsperiod(0.82days)luminosity(M= the sameradialvelocityasNGC5466(+116kms) 1975). ZinnandDahn(1976)haveshownthatV19has — 1.27)placeitontheP-Lrelationofanomalous v If theanomalousCepheidsareaconsequenceof In ordertoderiveamoreaccurate estimateofthe The importanceofVI9goesbeyondthefactthatits 1982ApJ. . .262. .700Z x/2 was uncertainbyafactorof1.6becauseitnot light curveandahighmeaneffectivetemperature{(T), known whetherVI9ispulsatinginthefundamentalor binary hypothesis.OurmeasurementsofV19’smean pulsating inthefundamentalmode,itsmassmustbe harmonic mode.Nonetheless,anunambiguousde- Dahn (1976)obtainedfromtheQ=P{p)relation one canarguethatitisprobablypulsatinginthefirst the firstharmonicmode.SinceVI9hasasinusoidal color ofVI9toestimateits(T).Ourspectrophotome- surface gravity((g))allowustoruleoutthefundamen- termination ofthemodeisveryimportant.IfVI9 also improvestheprecisionofmassestimate. try yieldsamuchmoreprecisevaluefor(7)),andthis tal mode.ZinnandDahn(1976)usedthemeanB—V and afewcomparisonstars.ThemassthatZinn ~2.5 91lo>whichistoolargetobeexplainedbythe relation andfromitsvaluesof(L),(T),(g). variable TVBoo.TheratiosofV^’smasstothemasses VI9 hasbeencomparedwiththreehorizontalbranch values ofmassthemselvesbecausesystematicerrors errors thatexistintheobservationsormodelatmo- Both ofthesemethodsaresensitivetoanysystematic e of theseotherstarsaregivenmoreweightthanthe (HB) starsinNGC5466andwiththefieldRRLyrae sphere calculationsusedtoanalyzethem.Consequently, VI9 (starL)maybefoundinGuffey’s1961paperon should largelycanceloutintheratios. where gmaybeestimatedfromthesizeofBalmer portant tocompareVI9withapulsatingstarthathas pulsating starmaybeapproximatedbyastaticmodel and afindingchartshowingtheirpositionsthatof e discontinuity. colors (Cuffey1961)suggestthattheyheintheTrange crowded byotherstarsandbecausetheirbroad-band the color-magnitudediagramofNGC5466.TheseHB pulsation andapproximatemassareknown.Thebest stars wereselectedforobservationbecausetheyarenot similar Ughtandcolorvariationswhosemodeof to make(see,e.g.,OkeandBonsack1960),itisim- atmosphere. Whilethisappearstobeasafeassumption object forsuchacomparisonwouldhavebeenan necessary observationsofsuchafaintstar((F)~16.6) RR LyraevariableinNGC5466,buttoobtainthe e e 1/2 The massofVI9isdeterminedfromtheß=P(p) The HBstarsthatwereobservedareUstedinTable2, We assumeinouranalysisthattheatmosphereofa © American Astronomical Society • Provided by theNASA Astrophysics Data System TV Boo...0.31311.05 0.6:0.100.130.22 0.04 V19 0.82114.75 0.610.120.160.25 0.05 P(days)(V) AK (B-V)(U-B)(U~B)^ maxin II. OBSERVATIONS MASS OFANOMALOUSCEPHEID Light CurveParameters TABLE 1 d was inconvenienttoobservetheobjectsofsomelarger period ofVI9issufficientlyclosetolthatalarge investigation overseveralobservingrunsbecausethe in theDracogalaxy(ZinnandSearle1976).Itwas programs, includingtheoneonanomalousCepheids range inphaseisnoteasilyobservedduringafew convenient tospreadtheobservationsforpresent intervals intherange5840-8080A.Theremainderof telescope andthemultichannelscannerattimeswhenit bands centeredatintervalsof360Aintherange5820- intervals intherange3240-5640Aand360seven resolution of160Ain14bandscenteredat (the TVBooobservationsandthreeofVI9)weremade consecutive nights.Theobservationsobtainedin1975 resolutions of160Ain16bandscenteredat at aresolutionof80Ain31wavelengthbandscentered ing multichanneldatawereusedtoremovetheatmo- observations. Thestarswereobservedattimesofgood on precisionsofthevaluesTandginferredfrom at 80Áintervalsintherange3220-5700Àanda Three orfourstandardstarswereobservedeachnight, out oftheaperture.Thestandardtechniquesforreduc- of thescanner(10")toensurethatseeingand 7980 A.ThesedifferencesinresolutionhadUttleeffect the observationsweremadein1976and1977using Zinn 1978),£(£-F)=0.00isadoptedfortheNGC very Ukelythattheyarereddenedbythesameamount. high galacticlatitudes(67°and73°,respectively),itis Wisniewski, andJohnson1966)metalabundance ble 1,datafromZinnandDahn1976Fitch, would haverequiredaprohibitivelylargeamountof atmospheric dispersiondidnotcastsomeoftheUght seeing, nearthemeridian,andwithlargestaperture had nosignificanteffectonouranalysis. we learnedthatTVBooundergoessmallvariationsin (see §III)aresimilartothoseofVI9.TVBoowasalso observed becauseitsUghtandcolorvariations(seeTa- and thedataforeachobservingrun(~4nights)were spheric extinctionandthespectrumofnightsky. results areaffectedifdifferentialreddeningsofE(B—V) on thesky.SincebothTVBooandNGC5466heat Firmaniuk, andKreiner1979).Thesepecuharitieshave selected becauseitUesonly14°awayfromNGC5466 amphtude andsecularchangesinperiod(Zessewitsch, 5466 starsandTVBoo.Welaterconsiderhowthe Since NGC5466appearstobeunreddened(Searleand telescope time.Instead,thetypecvariableTVBoowas e — ±0.02exist.Aftertheobservationshadbeenmade, The observationswereobtainedwiththe5mHale 701 1982ApJ. . .262. .700Z performance oftheinstrumentoratmosphericex- reduced togetheronceitwasdeterminedthattherewere Vega byHayesandLatham(1975).Consequently,we no significantvariationsfromnighttointhe have appliedtoourobservationsthecorrectionsgivenin in moredetailbelow. Zessewitsch, Firmaniuk,andKreiner(1979),respec- move theerrorsduetooldercalibration. Oke andSchild(1970)calibrationofVega,whichisnow ephemerides givenbyZinnandDahn(1976) Hayes andLatham’s(1975)Table7,whichshouldre- generally thoughttobeinferiorthecalibrationof 702 () ofVI9andTVBoowerecalculatedfromthe tinction. Thefluxesofthestandardstarsweretiedto tively. Thescannerobservationshavebeenreducedto two colors,rn—mandw,whicharedescribed in magnitudes,thePaschenandBalmercontinuaare plot of1/Àagainstfluxdensityperfrequencyinterval very nearlylinear(seeFig.1).Wehavefounditconve- continuum andthesizeofBalmerdiscontinuity.Ina 364580 This smoothingtechniqueminimizes theeffectsof nient tofitstraightUnesthesecontinua,bythe bands. Thefluxesgivenbythe modelatmospherecalcu- lations aresmoothedinexactly thesameway,which method ofleastsquares,andthenusecolorsbasedon random errorsofthefluxesin theindividualwavelength the linestocharacterizespectralenergydistribution. Table 2isajournaloftheobservations.Thephases T andgareestimatedfromtheslopeofPaschen e © American Astronomical Society • Provided by theNASA Astrophysics Data System V19 TV Boo. HB stars: H H C S4R5-3 HJD-2,440,000.0. Star 2911.810 2562.698 2561.791 2951.672 2917.838 2917.762 2561.855 2951.752 2561.884 2561.798 3334.678 2917.8 2917.8 2562.879 2562.852 2562.707 2561.861 2561.823 a 2917.8 2915.8 2563.904 HJD 0.811 0.710 0.632 0.347 0.151 0.058 0.736 0.350 0.691 0.444 0.626 0.088 0.809 0.722 0.259 0.554 0.430 Journal ofObservations 1.55 1.46 1.35±0.05 1.54 1.64 1.62 1.55 1.45 1.46 1.501 ±0.024 1.53 ±0.06 1.332 1.336 1.398 1.455 1.48 1.55 1.525 1.317 1.552 1.49 ZINN ANDKING 1 36 1 TABLE 2 45 A inthesensethatVI9emitsrelativelylessfluxthis because theirPaschencontinuahaveverysimilarslopes. between thescansoverwavelengthrange3220-3780 Notice, however,thattherearesubstantialdifferences X4500 andX8000pointsonthislinearecalledm continua. Theseparticularscanswerechosenfordisplay Boo andtheUnesfittedtotheirPaschenBalmer dard stars. numbers countsinthechannels,andfromuncer- À. ThedifferencebetweentheÀ3600pointonthisline facilitates theircomparisonwiththeobservations.A lower gthanTVBoo. discontinuity. Thestandarderrorsofm—and fitted tothewavelengthbandsinrange~3200-3600 measure ofthePaschenslope.Astraightlinewasalso m, respectively,andtheirdifferenceisusedasa range thandoesTVBoo.ThisisevidencethatVI9hasa tainty involvedwiththefluxcalibrationsviastan- about thefittedHues,whichwasconsistentwith and m,—isusedasameasureoftheBalmer straight Unewasfittedtothewavelengthbandsbetween (1979) modelatmospheres,which arefluxconstantand ~ 4500-8000Á,omittingthebandcontainingHß.The —m wereestimatedfromthescatterofpoints 45 458036 80 4536 45 Figure 1showsrepresentativescansofVI9andTV The observationshavebeen compared withKurucz’s -0.40 ±0.04 -0.227 -0.192 -0.066 -0.121 d -0.02 -0.19 -0.25 -0.06 -0.24 -0.23 -0.42 0.14±0.03 0.02 0.03 0.12 0.14 0.040 0.071 0.072 0.023 ‘45 :0.010 ‘80 6620 ±130 6930 7320 7010 6800 6850 6600 6550 7560 6950 6830 6820 6920 7270 ±50 7620 7450 7150 7700 7660 8200 8190± 160 in. ANALYSIS 2.33d 2.17 2.44 2.17 2.27 2.01 2.12 2.57±0.10 2.61 2.60 2.60 3.15 = 2.80 2.80 2.56 2.53 3.01 2.95 3.07 1.93 1.91 logg : 0.30 0.23 Vol. 262 1982ApJ. . .262. .700Z No. 2,1982 blanketing. FromthefluxestabulatedbyKurucz,we include theeffectsofhydrogen—andmetal—line have calculatedtheaveragefluxdensityperhertzin lines werefittedtotheBalmerandPaschencontinuaof each wavelengthbandofthescanner.Theseaverage fluxes wereexpressedinmagnitudes,and,followingthe same procedureusedtoreducetheobservations,straight proximately thesamemetallicity.Thefollowingob- is possibletocomparethestarswithmodelsofap- the models.Thecolorsm—andwere from theobservations.SinceKuruczcalculatedmodels then calculatedandcomparedwiththeonesderived with theäSof13.1thatButler(1975)measuredfrom high dispersionspectrogram.Thisvalueisconsistent for threedifferentmetallicities([A/FI]=0,—1,2),it limit becausePrestonremarksthatTVBoohasthe [A/H] ——2. servations indicatethatthestarshavemetalhcitiesnear is visibleinonlyoneofhisninespectrograms. weakest Klineofthevariablesinhissampleandthatit one low-dispersionspectrogram.Preston(1959)had Butler andDeming(1979),whoobtained[Fe/H]= earlier obtainedaASof8,butthismaybeonlylower per frequencyintervalinmagnitudes(m)isplottedagainst1/À.Themscalearbitrary.Errorbarsarewiththedifferencesbetween has alargerBalmerdiscontinuity. have recentlyrecalibratedSearleandZinn’sobserva- the scanswheretheyexceedsizeofdatapoints.NoticethatwhilePaschencontinuatwoaresimilar,scanV19 scalecalibratedbyButler’s(1975)observa- giants. Theyobtained[Fe/Ff]——1.93±0.07ona light, ZinnandDahn(1976) obtained AS=7±1,which Searle andZinn(1978)fromscannerobservationsofred tions ofRRLyraevariables.BellandGustafsson(1982) Lyrae variablescorresponds to [Fe/H]^—1.35±0.23. tions usingspectrumsynthesistechniquesandhaveob- 3645so tained [A/H]=—2.0±0.4forNGC5466. according toButler’s(1975)AS-[Fe/H] relationforRR — 2.42fromtheequivalentwidthsoftwoFenUnesina The metallicityofTVBoohasbeenmeasuredby The metallicityofNGC5466hasbeenmeasuredby Fig. 1.—RepresentativescansofVI9andTVBooareplottedalongwiththelinesusedtodefinem—m.Fluxdensity From onespectrogramofVI9 takenatminimum 364580 © American Astronomical Society • Provided by theNASA Astrophysics Data System MASS OFANOMALOUSCEPHEID ab variablesthatButleranalyzed,andthesedifferences interpreted intermsof[Fe/H]. However, VI9isverydifferentinTandgfromthetype plotted withthemodelgridsfor[A/H]=—1and—2. must betakenintoaccountbeforeV19’sASmay This figureshowsthatregardlessofwhichvalue minimum light,isnear6600K.VI9therefore~500 [A/H] isadoptedforVI9,itslowestT,whichoccursat K hotterthantypeabvariablesatminimumlight(see Oke 1966;Manduca1981),whichdefineButler’s(1975) e e with Kurucz’s(1979)models(solid circles)for6500<7^8000 VI9 andTVBoodonotoverlapin thisdiagram. interpolate betweenthemodels.Notice thattheobservationsof and 2.0areshowninFigure 4.Dahn’sphotoelectric and TVBoo,itisnecessarytodeterminetheirmean Figure 3ifE(B—V)>0.03. TV Boohave,asexpected,theatmosphericparameters when ourobservationsarecomparedwiththegridsof results. ThevaluesofTandloggthatareobtained stars inNGC5466,whichdonothetheHBregionof evidence forasmallreddeningisprovidedbytheHB (1976) ruleoutthesepossibiUtiesandsomecombination (1978) andtheASmeasurementbyZinnDahn metalUcity mustbegreaterthan[A/H]=—1(seeFig. reddening mustbegreaterthanis(i?—K)=0.05orits differences maybesafelyignored. that wouldalsoplaceVI9intheHBregion.Additional 2). ThereddeningmeasurementsbySearleandZinn of HBstars.ForVI9toheintheregion,its Mihalas (1966)andKurucz(1979)aresoclosethatthe atmospheres, theycanbecompareddirectlywithour sons ofobservationswithMihalas’s(1966)gridmodel e ±0.3. Eventhoughtheseresultsarebasedoncompari- e e e The positionofVI9inFigure3rulesoutthepossibil- To proceedwiththecalculationofmassesVI9 Figure 3showsthattheHBstarsinNGC5466and Vol. 262 1982ApJ. . .262. .700Z with arecomparabletothesizesoferrorsin interval. Theredoesnotappeartobeabetterphotoelec- interval 0.15-0.60,andwehadtointerpolateoverthis used forTVBooeventhoughitdoesnotcoverthe measurements. StudiesofRRLyraevariables(e.g.,Oke, The loggcurvesareverycrudebecausethevariations maximum nearlightandisessentiallycon- Figure 4weredrawnbyhandthroughthedatapoints. tometry byFitch,Wisniewski,andJohnson(1966)was Giver, andSearle1962)haveshownthatgreachesa tric lightcurveintheliterature.Theothercurves TV Boo.TheVcurveswereadoptedfromthephotometrypub- No. 2,1982 stant foralongperiodnearminimumlight.Thecurves lished byZinnandDahn(1976)Fitchetai(1966).TheT Table 2). log gcurvesweredrawnbyhandthroughthedatapoints(from e TV Boo...7230±502.71±0.06 0.60±0.051.704±0.020-2.12±0.060.38±0.06 ...0.67±0.06 V19 7010±1002.22±0.10-1.27±0.022.444±0.008 -2.56±0.110.77±0.202.53±0.371.56±:0.23 H 7680±1102.98±0.21 0.78±0.041.636±0.016-1.95±0.220.49±0.26 C 8200±1603.07±0.30 0.85±0.041.616±0.016-1.98±0.310.43±0.34 S4R5-3 ...8190±1603.15±0.30 0.97±0.041.568±0.016-1.90±0.310.47±0.34 Fig. 4.—PlotsofVmag,T,andloggagainstforVI9 e © American Astronomical Society • Provided by theNASA Astrophysics Data System Star (T)log(Mlog log9H/ 9H91t911! ev 0 MASS OFANOMALOUSCEPHEID Physical Parameters TABLE 3 2 in Figure4.SincetheobservationsofVI9andTVBoo within therangeofobservationalerrors. been estimatedbyintegratingcurvesthatarelessthan ble witheachother.Consequently,thevaluesof(7^) which iscompletelyinsignificant.Sincethelightcurve ble, althoughunlikely,thatthevaluesof(g)we not veryimportant.Forexample,thestraightaverages portant tonotethattheexactshapesofthesecurvesare were calculatedfromtheloggcurvesinFigure4and We haveassumedthatthisisthecaseforbothvariables The integraloveronecycleoftheaccelerationtermin bles (seeTable3).Theuncertaintiesinthesevalueshave given byequation(1)havebeenadoptedforbothvaria- do notcompletelycovertheirlightcycles,itisconceiva- of thedatapointsyieldvalues(logg)=2.15±0.06 optimum fitstothedatapointsbutthatnonethelesshe of TVBoovariesshghtlyinamplitude,itisnotclear equations yieldvaluesof(T)thatdifferbyonly20K, are closetothevaluesobtainedbyintegratingcurves and 2.63±0.04forVI9TVBoo,respectively,which that theVandTcurvesinFigure4arestrictlycompati- correct oneinprinciple.ForVI9andTVBoo,these in Figure4weredrawnwiththesefactsmind.They 3. Becausetheloggcurvesarequitecrude,itisim- then integratedtoyieldthevaluesof(g)listedinTable the variablesareverysmall(AR/R~0.05).Valuesofg and that(g)—G?f\i/(R),sincetheRvariationsof this expressionshouldbezeroifthemotionisperiodic. Several authorshavearguedthatequation(2)isthe and calculated bytheequations than dostraightaveragesofthedata. should providebetterestimatesofthemeanvalueg e e The gatanyphasemaybewrittenas From thecurvesinFigure4,valuesoi(T)havebeen e /2 (T) =(f\(L)/L)'Tdy\(2) e G2 g =GJl/R+dR/dt.(3) (T)=fTd (1) e 705 1982ApJ. . .262. .700Z 706 both variables,itseemslikelythatthesystematicerrors have obtainedaresystematicallyinerrorbysignificant because itdependsontheratioofvalues(g). would beinthesamedirectionandhaveroughly masses ofthevariableswouldnotbeaffectedmuch have ameanMof+0.60,whichwithCuffeys’(1961) by assumingthattheRRLyraevariablesinNGC5466 the samemagnitudes.Inthiscase,ratioof amounts. Sincethecoverageisaboutsamefor photometry yieldsadistancemodulusof16.02forthe 3 forVI9andtheHBstarsinNGC5466wereobtained calculated byadoptinga=0.01forthevalueof(V) cluster. ThestandarddeviationofthevaluesMwere given byDahn’sphotoelectricphotometryofVI9(Zinn from 11observationsCuffeyobtained(V)=14.74and Guffey’s photometryofthestarsinNGC5466appear the RRLyraevariables,anda=0.03forVmagni- and Dahn1976),a=0.02forthemeanVmagnitudeof variables inMl5showthatthetypecwithina the comparisonstarS4R3-18,Dahnobtained(V)— to beonthesamemagnitudescale.ForV19and tude oftheHBstars.Dahn’sphotometryVI9and RR LyraevariablesinNGC5466.Theobservationsby According torecentworkbySandage(1982),the cluster donotvarymuchin(M),andwehaveadopted luminosity oftheHBvariesconsiderablywith[Fe/H] between TVBooandNGC5466isnotpreciselyknown ignored thispossibihtybecausethedifferencein[Fe/H] variables inNGC5466byasmallamount.Wehave NGC 5466,itmaybemoreluminousthantheRRLyrae because heliumabundance(Y)and[Fe/H]areanticor- Sandage, Katern,andSandage(1981)of31typec v luminosities ofthestarsandtheirmass-to-lightratiosin mass thatweobtainforTVBoobyasmallamount,but related. SinceTVBoomaybemoremetal-poorthan estimate oftheuncertaintyinluminosityTVBoo. the dispersionofMl5variables,a=0.05,asan 7B wereusedtotransform(M)into.The change substantially. 14.75^0.01 andF=14.966±0.003,respectively,while solar unitswerethencalculatedfromtheformulae: the ratioofmassesVI9andTVBoowouldnot sally accepted.Itwouldhavetheeffectofraising and becausetheY-[Fe/H]anticorrelationisnotuniver- v K= 14.93. The constantsintheseequations wereevaluatedusing and v K vbol The absolutevisualmagnitudes(M)listedinTable It isassumedthatTVBoohasthesame(M)as v The bolometriccorrectionsinKurucz’s(1979)Table v © American Astronomical Society • Provided by theNASA Astrophysics Data System log =-4 <7;>+10.607.(5) log(L>=-0.4,log