1982ApJ. . .257. .527T © 1982.TheAmericanAstronomicalSociety.Allrightsreserved.PrintedinU.S.A. The AstrophysicalJournal,257:527-537,1982June15 report ofthediscoveryacolor-magnituderelationship for spiralgalaxiesbyVisvanathan(1981)cametoour attention. Wewillbediscussingthesamephenomenon, although ourcolor(thedifferenceofbroad-bandob- servations at0.45/imand1.6jam)achievesbetter relationship isevenbetterdefined.Asaresult,weare separation betweenyoungandoldstellarpopulations Visvanathan hasqualitativelyanticipatedsomeofour more optimisticabouttheutilizationofcolordependen- than thecolorusedbyVisvanathan(basedonobserva- cies forthedeterminationofdistancesgalaxies. tions at0.55jamand1.0jam),and,consequently,the conclusions regardingthephysicalunderpinningof correlation betweencolorandmagnitudes.Wewillbe Astronomy, Inc.undercontractwith theNationalScienceFounda- tion. 1 After thisarticlewassubmittedforpublication,the OperatedbytheAssociationof Universities forResearchin © American Astronomical Society • Provided by theNASA Astrophysics Data System (masses) ortheintrinsicluminositiesofspiralgalaxies.Thecorrelationsarederivedfromsamples galaxies whichrangeintypefromSatoIm.Thedispersionstherelationshipsarenotaffectedby mag isfoundfortheVirgoCluster,ifweadoptSandage-Tammanndistancescalenearby color-magnitude correlationcanbeusedasameasuringstick.Adistancemodulusof31.04±0.16 galaxies. type dependenciesexceptatamarginallysignificantlevel.Sincecolorsaredistanceindependent,the parameter: totalmass.Thecolor-magnitudediagramcanbequalitativelyunderstoodiftheinitial lenticular branchthatisspecifiedbyitstotalmass. intermediate state.Itisproposedthatagas-richgalaxywillHeonthespiralbranchatlocation specific starformationrateinspiralsdecreaseswithdecreasingmassand,atthesametime,chemical type, suggestthattheHubblemorphologicalsequenceispredominantlydependentonasingle galaxies evolvebetweenthetwobranches,probabilityseemstobelowofviewingthemin abundances decreaseand/ortheinitialmassfunctionflattenswithdecreasingmass. Subject headings:galaxies:evolution—photometry specified byitstotalmassand,oncegasisdepletedorlost,willrapidlyevolvetoalocationonthe Tight correlationsarefoundbetweenblue-to-infraredcolorsandeithertheHilineprofilewidths The tightrelationshipsbetweencolorandmassorluminosity,essentiallyindependentofgalaxy Spiral andlenticulargalaxiesinhabitquiteseparateregionsonthecolor-magnitudediagram.If A COLOR-MAGNITUDERELATIONFORSPIRALGALAXIES I. PREFACE Received 1981September10;acceptedDecember17 Institute forAstronomy,UniversityofHawaii Steward Observatory,UniversityofArizona 1 Kitt PeakNationalObservatory R. BrentTully M. Aaronson J. R.Mould ABSTRACT AND relationship hasbeenindependentlydiscoveredbyWyse discussing anideawhosemomenthascome,becausethe (1982). lengths (TullyandFisher1977)orinthenearinfrared correlations betweentheglobalHIprofilewidthsof is expectedthattotalmassandluminosityare profile widthisameasureofthemassgalaxy,andit (Aaronson, Huchra,andMould1979).Thesecorrela- systems, whethertheluminositiesareatopticalwave- spiral galaxiesandtheintrinsicluminositiesofthese closely coupled. file widthandbluemagnitudes or1.6jam“H”magni- tions canbeunderstoodphysicallybecausetheHI tudes followpowerlaws,but, forthetwocases, It hasbecomefirmlyestablishedthattherearetight The observedrelationshipsbetween theHIlinepro- II. ACOLOR-MASSRELATIONSHIPFORSPIRAL GALAXIES 1982ApJ. . .257. .527T 2 528 jected Hiprofilewidthat20%ofmaximumintensity parent luminosity)andtriedtosamplethewidestpossiblerangein They consideredgalaxieswithinasmallwindowinapparent The Rubinetalsampleincludesthe“largestidentifiedScgalaxy” dimensions (whichwouldcorrelateroughlywithacommonap- suggested. Alternatively,themannerinwhichRubinetal. steeper slopeforasampleof21Scgalaxies.Smallnumberstatis- in anonrepresentativeway,therelationshipwouldbesteepened. intrinsic propertiesbyselectinggalaxiesoverthewidestpossible sample wascompiledmighthavecontributedtothesteeperslope. tics mayaffecttheirresults,asdeVaucouleursetal.1982have profile-luminosity relationship. of 21areintrinsicallymoreluminousthanany535Sbcthrough (Rubin, Ford,andThonnard1980),twogalaxiesinasample range ofredshifts.Bythuspopulatingtheextremainluminosities et alandAaronson1982ayieldshallowerslopefortheHI by deVaucouleursetal1982.In anyevent,thetypedepen- and Tully1981.ThemuchlargersamplesofbothdeVaucouleurs Sd galaxiesinthe“volume-limited”sampleconsideredbyFisher slopes aredifferent.Thecorrelationbetweenthedepro- Aaronson etal1982¿>). dence foundusinginfraredmagnitudes appearstobesmall(see using bluemagnitudes,although nosignificanteffectisfound where Lareblueluminositiesanddeprojected a strongtypedependenceintheH iprofile-luminosityrelationship data inTable1),wenowfindthat updated bluemagnitudesandHiprofilewidths(see (1977) andbySandageTammann(1976).Using ing galaxies.Theyaccept: Mould, andHuchra(1980)forthesamesetofcalibrat- H iprofilewidths.Thedependencebetweenand and galacticobscurationisshownbyFisherTully and bluemagnitudescorrectedforinchnationeffects the infraredmagnitudeH^qisdisplayedbyAaronson, B 5 2 Rubin,Burstein,andThonnard(1980)foundaconsiderably Rubin, Ford,andThonnard1980Roberts1978alsoreport © American Astronomical Society • Provided by theNASA Astrophysics Data System a b NGC 247... NGC 224... NGC 598... NGC 253... NGC 3031. NGC 2403. NGC 2366. NGC 4236. NGC 5585. NGC 5204. UGC 5666 UGC 8837 b a UGC 8837=HolmbergIV. UGC 5666=IC2574. Name 402 2 r~(»2o)'. ) L~{WÍ,)\ (O w B SAb IBm SXc SXd SAcd SBdm SXm SAab SXcd SXd SBm SAm /7L 10.82 10.15 10.30 10.07 12.49 0.91 4.74 4.38 4.38 6.45 7.69 9.08 TULLY, MOULD,ANDAARONSON 0.5 10.70 10.66 11.24 12.63 11.47 íj y j)b, i 8.34 7.11 8.99 3.58 5.84 9.22 7.20 Local Calibrators TABLE 1 B-H -0.12 2.67 0.14 0.59 2.37 0.14 2.82 1.30 1.46 1.89 1.17 1.09 spiral galaxies.ItisdemonstratedinFigure1thatthis strong correlationbetweenB—Hcolorandthemassof blue andtheinfraredrelationshipsisthattherea claim iscorrect.Thetwodistance-independentparame- compared. Dataforthesampleof94galaxiessatisfies infrared relationshipfollowingtheargumentsgivenby interval betweenbluelightandtheinfrared. ters, B—Hcoloranddeprojectedlineprofilewidth,are Aaronson, Huchra,andMould(1979),oritmaybethat It maybethatwecanunderstandtheslopeof the followingconditions: (1980) canbeemphasized:theslopebetweenluminosity In anyevent,thepointalreadymadebyBottinellietal and theHiprofilewidthvarieswithpassbandin the situationismorecomplexasBurstein(1982)argues. in Figure1providesthefit: been anticipated.Twodetails maybenoted: From equations(1)and(2), a slopeof4.5couldhave through Sbmaylieslightly totheredofmean or Aaronsone/«/.(1982û). Huchra (1980);Mould,Aaronson,and otherwise availableintheliterature. The implicationinthedifferenceslopebetween or aphotoelectricdeterminationcitedintheSecond Reference Catalogue(deVaucouleurs,de galaxies greaterthan30°fromthegalacticplane. and Corwin1976;hereafterRC2). A least-squareslinearregressionanalysisofthedata 1. Galaxieswithmorphological classificationsSa o -1 mo 2. WqmeasuredbyFisherandTully(1981)or 4. Galaxiesinclinedsuchthat45stars producingthebluelightcorrespondstoonlya40% and 0.34maginB—H.SupposemassHmagni- within the6°coreofVirgoClusterconstitutea tional errors.Thenthe1ascatterinpopulationof tudes areperfectlycorrelatedandtherenoobserva- within ±10%,thesegalaxies areallatacommondis- fects willobscuretheintrinsicrelationship.Galaxies suitable samplebecauseit can beassumedthat,to §IV. tance. ThisVirgoClustersample willbeconsideredin The nexttwosectionswillbedevotedtotheapplica- 2. B—Hcolorscanbesubstitutedforilinewidths In ordertodemonstratetheexistenceofacorrelation 1. Itsuggeststhatstellarpopulationsaretightlycou- III. THECOLOR-MAGNITUDERELATIONSHIP:LOCAL CALIBRATORS 529 1982ApJ. . .257. .527T 530 These galaxiesaremembersoftheLocal,M81,Sculptor, galaxies whichhavereceivedsufficientattentionthat nearest systemshaveremainedamatterofdispute their distancesmightbeconsideredreasonablyreliable. Vaucouleurs scale,iscompatiblewiththeexistenceofa (Sandage andTammann1976;deVaucouleurs1978). and M101groups.Infact,theabsolutedistancesofthese either theSandage-Tammannscaleoronde However, therelativedistancesofthesegalaxies,on preference regardingthelocaldistancescale.Fora Tammann scalewillbeassumed,togetherwithaHyades Vaucouleurs scale,refertoBottinellietal.(1980). distance modulusof3.29mag.Thereisnoinferencea and intrinsicluminosity.Consequently,tokeepwith tight correlationbetweenHilineprofilewidth profile widthinformationaredrawnfromAaronson, in Table1.Distances,infraredmagnitudes,andHi calibration oftheHiprofilewidthrelationonde the conventionsofourearlierpapers,Sandage- phological typesaredistinguishedinthisandsubse- Fisher andTully(1981). galactic absorptioneffectsinthemannerdescribedby B systemoftheRC2butcorrectedforinclinationand Mould, andHuchra(1980).Bluemagnitudesareinthe certain oftheintrinsicscattercorrelation.How- quent plotsinthemannerintroducedFigure1.There shown inFigure2forthe12calibratorgalaxies.Mor- ever, theevidenceiscompellingthatatightcorrelation are insufficientgalaxieswithinthissamplealoneto color-magnitude relationshipwillprovideaccuratedis- does exist.Thescatterissufficientlysmallthatthis answer questionsabouttypedependenceortobevery ity bluemagnitudesamongthespiralsinVirgo squares linearfittothedataplottedinFigure2is tances tootherindividualgalaxies.Theformalleast- provided forthesegalaxiesaswasthelocal calibrators. Thecolor-magnitudediagramisplottedin and Huchra(1980).Thesameobservationalmaterialis Cluster observedintheinfraredbyMould,Aaronson, provides adistancetotheVirgo Cluster.Thefitgivesa obvious dependenciesonmorphologicaltypes. Figure 3.Thescatterisgreaterthanin2,butthe slope ofthecorrelationiscompatiblewiththatde- for thelocalcalibratorsisaccepted tobeuniversal,then termined fromthelocalcalibrators,andtherearestillno t a bestfitofthecalibrator curvetotheVirgodata b Then thereareasmallnumberofverynearbyspiral The specificgalaxiesthatwillbeconsideredarelisted The relationshipbetweenB—Hcolorand77iois We identifyinTable2the14galaxieswithhigh-qual- 5 If theslopebetweencolorand magnitudedetermined © American Astronomical Society • Provided by theNASA Astrophysics Data System IV. THECOLOR-MAGNITUDERELATIONSHIPI bs //io= -17.05-2.32(5^’'-7/_).(4) 50 DISTANCE TOTHEVIRGOCLUSTER TULLY, MOULD,ANDAARONSON cal calibrators.Morphologicaltypesaredistinguishedinthesame manner asinFig.1.Thestraightlineistheleast-squaresbestfit. point uncertainty),correspondingtoadistanceof16.1± Virgo Clusterenvironmenthavestructuralpecuharities distance modulusof/a^=31.04±0.16(ignoringzero- which jeopardizethedistanceestimate.Forexample, (1980). IfthesmallerM101groupdistancearguedforin agrees wellwiththatofMould,Aaronson,andHuchra that paperwereadopted,thisresultwoulddecreaseby partial gasdepletionortidaltruncation.Thereisno components ofthetwosamples,ordifferencesinmean that distinguishthemfromthecalibratorsystemsand there maybesystematicdifferencesinthebulge-to-disk ~ 0.1mag. be tousegalaxiesinarichbutlow-densityenvironment, members inthecolor-massrelationshipdisplayed evidence torsuchanomaliesamongtheVirgoCluster ages, ordifferencescausedbygalaxyencounterssuchas like theUrsaMajorCluster,todefineslopeand 1.1 Mpc.ThefitisillustratedinFigure4.Thisresult Figure 1.Obviously,amoresatisfactorysituationwould scatter ofthecolor-magnituderelationship. nitudes hasbeenestablished forspiralandirregular galaxies. Itwasalreadyknown thatcolor-magnitude relationships existedforelliptical andlenticularsystems Fig. 2.—Blue-to-infraredcolor-magnitudediagramforthelo- There mightbeconcernthatgalaxiesinthecrowded A strongcorrelationbetween B—Hcolorsandmag- V. THECOLOR-MAGNITUDERELATIONSHIP EXTENDED TOEARLYSYSTEMS 1982ApJ. . .257. .527T NGC4192 . NGC4178 . NGC 4294. NGC 4216. NGC 4206. NGC 4450. NGC 4388. NGC 4532. NGC 4519. NGC 4501. NGC 4651. NGC 4535. NGC 4698. NGC 4654. NGC 4371. NGC 4264. NGC 4387... NGC 4374... NGC 4442. NGC 4435. NGC 4382. NGC 4377. NGC 4270. NGC 4464... NGC 4458... NGC 4406... NGC 4365... NGC 4261... NGC 4754. NGC 4578. NGC 4550. NGC 4479. NGC 4476. NGC 4468. NGC 4459. NGC 4473... NGC 4472... NGC 4486B. NGC 4486... NGC 4478... NGC 4621... NGC 4552... NGC 4660... NGC 4649... NGC 4636... © American Astronomical Society Name SBdm SAbc SXab IBm SBcd SXb SBd SAb SAab SAb SXc E E E SXcd SAc E E E E E E SAOpec SAO SBO SO SBO SAab Epee E SBO SAO SO SBO SAO SAO SAO SBO SBO Epee E E E E E Virgo Cluster Lenticulars TABLE 2 (10.50) Ellipticals 10.14 10.77 10.34 10.75 10.45 10.85 10.05 10.56 10.17 11.08 Spirals 7.77 7.33 7.15 8.06 8.86 8.46 7.00 7.36 7.95 7.94 7.75 7.07 9.46 9.96 8.40 8.80 8.66 6.18 9.92 7.00 9.90 7.94 9.01 9.15 8.11 8.44 6.57 7.58 7.42 6.49 7.49 7.36 8.91 8.46 1 11.73 11.44 11.17 12.26 10.28 10.62 12.14 12.25 10.05 10.80 11.24 10.97 11.20 11.89 13.07 13.8 12.90 11.35 11.70 10.10 12.65 13.58 10.11 12.95 10.31 10.59 11.30 11.43 12.26 12.40 13.45 13.15 13.8 11.28 12.13 11.03 14.32 B^ 10.46 10.75 10.81 11.84 9.91 9.29 9.56 9.82 Provided bythe NASA Astrophysics Data System B-H (3.82) 2.14 2.95 2.90 2.74 2.31 2.17 2.54 2.16 2.95 2.84 3.45 3.11 2.85 2.89 2.98 2.72 3.53 3.59 3.03 3.19 1.30 3.11 3.05 3.31 3.23 3.35 3.49 3.25 3.25 3.41 1.39 2.99 3.45 3.11 3.66 1.50 1.49 3.22 1.69 2.97 3.39 3.34 3.39 3.39 1 (km s) 465 292 453 447 277 260 531 301 462 305 594 392 398 mo 377 1982ApJ. . .257. .527T 532 metallicity effects,whereastherelativemixofyoung dependences seeninthesamplesofearlygalaxiesare Griersmith 1980).However,ithasbeenclaimedthatthe for earlyspirals(VisvanathanandGriersmith1977; (Baum 1959;deVaucouleurs1961;Visvanathanand in oursamples. Sandage 1977;Frogeletal1978)and,inthevisible, The B—Hcolor-magnituderelationforVirgogalaxies and oldpopulationsisprobablyamoreimportantfactor in thecolor-magnitudediagram,thoughtwobranches of allmorphologicaltypesisshowninFigure5,where galaxies inthe6°Virgocoreareatacommondistance. the assumptioncanbemadethatlargenumberof again betakentoneutralizedistanceeffects.Oncemore, types onacommoncolor-magnitudeplot,caremust (1981 andreferencestherein).Itisseenthattheearly is thedangerofasystematicdifferenceinRC2 nitude plotsofearlysystems,althoughevidencefor dramatic effecthadnotbeenseenbeforeincolor-mag- the samplediscussedbyAaronson,Persson,andFrogel the dataforearlytypegalaxieshavebeenderivedfrom noted (e.g.,Aaronson,Persson,andFrogel1981).There flattening oftherelationatbrightendhasbeen for theearly-typeellipticalsatbrightend.Sucha almost mergeatthehigh-luminositytips. and latemorphologicaltypesoccupyseparatebranches group ofgalaxiesatH_~ 8mag,ascomparedwith growth curveextrapolationsusedtoderiveBforthe elliptical anddisk(spiralorlenticular) systemsinFigure in thesamemannerasFig.1. the brighterobjects.Inany event,thecomparisonof 5 isaproblemsincetheblue andinfraredluminosities axies intheVirgoCluster.Morphologicaltypesaredistinguished os T In ordertocompareearlyandlatemorphological A curiousfeatureofFigure5istheapparentturnover Fig. 3.—Color-apparent-magnitudediagramforspiralgal- © American Astronomical Society • Provided by theNASA Astrophysics Data System TULLY, MOULD,ANDAARONSON The VirgoClustersamplewasshiftedverticallytoachievean optimum fittotherelationshipestablishedbylocalcalibrators alone. (open circles)andVirgoClusterspirals(filledcombined. cals areindicatedbycrosses. morphological typesintheVirgo Cluster. Spiralsareindicatedby filled circles,lenticularsareindicated byopencircles,andellipti- Fig. 4.—Color-magnitudediagramwiththelocalcalibrators Fig. 5.—Color-apparent-magnitude diagramforgalaxiesofall Vol. 257 1982ApJ. . .257. .527T luminosity gradientsaresodifferentbetweenthesevari- Figure 5isthatthelenticularslieclearlyseparatedfrom No. 2,1982 ous classesofgalaxies. are measuredatdifferentisophotallevelsandthe proves tobeanexception:thepeculiarlenticularNGC relationship. OnlyonediskgalaxyintheVirgoCluster relationship totheredofspiralcolor-magnitude selves, thelenticularsdefineaverytightandsteep the spiralsonthiscolor-magnitudediagram.Inthem- 4382 =M85liesatthetipofspiralbranch. Hertzsprung-Russell diagram?Mightgalaxiesspendthe (spiral) branchandsubsequentlyevolvetothered(len- gas richphaseorphasesoftheirlifecycleontheblue proposals include:(i)variationsincontinuousstarfor- ticular) branch?Ifso,theabsenceofinterlopersbetween variables ontheverybroadbasehneblue-infraredcolor. variations inthestellarinitialmass(birth)function,and mation rates,(ii)variationsintheagesofgalaxies,(iii) the twobranchesinVirgoClustersamplesuggests of galaxiesinanattempttoexploretheeffectsthese time scaleoncestarformationisarrested. that thetransitionbetweenbranchesoccursonashort very simpleassumptions,seewherethesemodelsbreak where certainoftheabovemechanismsfailtoexplain ments forthefitarenottrivial.Wewillbeabletoshow models whichdescribethedata.However,require- Like othersbeforeus,wecansucceedingenerating (v) variationsinmetallicity.Wehavecomputedmodels the confinementofstarformationtoperiodicbursts,(iv) the observedrangeincolorsofgalaxies.These down, andthenrefinethemodelswithfurtherassump- characteristics oftheB—Hcolormagnitudediagram. Our procedurewillbetobeginwithmodelsbasedon tions. exp(—//t), thenshorttimeconstants,r,willleadto one adoptsanexponentialrelationship,SFR(¿)~ Hubble sequence(Tinsley1968;LarsonandTinsley star formationrates(SFR)havesuccessfullyreproduced the opticalcolorsandgascontentsofgalaxiesacross els mightcorrespondtohighbulge-to-diskratiosystems. star formationstronglypeakedinthepast.Thesemod- By increasingr,theSFRbecomesmorenearlyconstant axies. and onecanmodeltheoptical colorsoflate-typegal- gests empiricallythatthetime constantforstarforma- 1978). If,followingSearle,Sargent,andBagnuolo(1973), The pointthatdeservestobestressedconcerning Might Figure5betheextragalacticequivalentofa A varietyofproposalshavebeenputforthtoexplain The existenceofthecolor-mass relation(§II)sug- 1. Evolutionarymodelsofgalaxieswithparameterized VI. TOWARDAPHYSICALUNDERSTANDINGOFTHE © American Astronomical Society • Provided by theNASA Astrophysics Data System COLOR-MAGNITUDE RELATION a) TheGas-RichBranch COLOR-MAGNITUDE RELATIONFORSPIRALS 4 5 with theobservations. T —(mass)relationisoptimizedtoobtainabestfit continuous, monotonicallydecreasingorconstantstar galactic initialmassfunctionandsolarabundances, galaxy. Forourfirstmodel,then,wewillassumethe (1978) areintegratedoveratimespanof16Gyr.The mass-to-light ratiosgivenbyStruck-MarcellandTinsley formation overtheageofuniverse.Colorsand tion issomehowinverselyrelatedtothemassof These growthcurvesarefunctionsofmorphological colors tothe(B—H_)system.Thislattersystemis made, itisnecessarytotransformthemodelB—H The transformationisgivenby: not atruecolorbecausethetwomagnitudeswerede- galaxies bluewardofB—H_2.1. galaxies butfailstotallytoexplaintheoccurrenceof from asampleof300galaxies(Aaronsonetal.1982a). color valuesasafunctionofmorphologicaltype,found termined atdifferentisophotallevels.Thetransforma- lustrates thelocusexpectedtobefollowedoncolor- increasing mass).ThedashedcurveinFigure7il- type, butthesedependenciesareeliminatedusingmean tion ismadeusingthebluegrowthcurvesgiveninRC2. magnitude diagramifthismodelhasanyvalidity.The very young. possibility thatstellarsystemsinsomemassrangeare initial massfunctionandmetallicity,butnolonger permitted. Weretainourearlierassumptionsaboutthe if risingstarformationrateswithtime(rnegative)are model providesaverysatisfactorydescriptionofthevaria- Figure 6(thecurvewhichmonotonicallydecreaseswith jeopardized andthereistoomuch freedominthemodelsto in Figure6(solidcurves).Thedottedcurvegivesthe constant starformationrates.Effectively,weadmitthe restrict ther(mass)dependencytorequirefallingor tions incolorseenamongveryredandluminousspiral mean stellaragesforthisr(mass)relationship.The dependency thatispredicted. straight lineinFigure7illustratesthecolor-magnitude will beoffsystematicallyby0.3mag. Toberigorous,weshould (Aaronson etal.1980),butthistimescaleisrequiredbycurrent warrant agreateffortoffinetuning. of starsinglobularclusters. T05 This exercisewasnotpursuedbecause ourconclusionsarenot make minormodificationstothemodels toaccountforthiseffect. mation fromallourmodelcolorstoobservedB—H_ stellar evolutionmodelstoprovideagooddescriptionofthecolors T0 5 tudes aretoface-on,ratherthanabsorption-free,thetransfor- T05 4 5 Before acomparisonwiththeobservationscanbe The t(mass)dependenceisdisplayedgraphicallyin The fitrequiresthefullr(mass)relationshipplotted 2. Theobservedcolor-magnituderelationcanbefitted 16 Gyrconflictswithourestimateoftheageuniverse Therefereepointsoutthatsinceourcorrectionstomagni- B —H-os=1.35(7?/7)_o.—1.95. t5 533 1982ApJ. . .257. .527T 89 7 534 galaxies withB~H_<2wouldhavetobeyoung. have risingstarformationrates. was proposedthatgalaxiesmightformtheirstarsin periodic bursts(Searle,Sargent,andBagnuolo1973; 2 correspondstogalaxieswithB0.Galaxiessuch successively younger.ItistobenotedthatB—7/_o~ the interpretationisalmostcertainlyunacceptable.All magnitude relationwillariseinanaturalwaybecause as M33(B=—19.0,B—H_1.5)wouldhaveto on faintergalaxiesthanbrighterones.Gerola,Seiden, developed toexplaintheopticalcolorsofgalaxies,it Successively lowermassgalaxieswouldhavetobe ity ofinitiationwithtime.Wefollowed200testgalaxies larger onesand,ifso,smallgalaxiescouldbeveryblue. Huchra 1977).Iftheseburstsareoffixedsize,acolor- with time.Thenegativerbranchcorrespondstoincreasingstarformationratesdottedcurvegivesthemeanstellarageas a might actuallybestrongerinsmallergalaxiesthan and Schulman(1980)haveproposedthatthebursts the burstswillproduceamuchstrongerrelativeeffect 200 evolvedgalaxiesinthethirdmodel(bursts;standardIMFandZ).Thesinglefilledcircleshowsonepointcalculatedonbasisof the if thistheoryhasmerit,then theobservedcolor-magni- rence ofgalaxiesasblueany inoursample.However, galaxies lieinthecolor-magnitudediagramasseen distributed uniformlyinthelogarithmofmass-in-stars formation occurredinbursts,withaconstantprobabil- Z). Thesolidcurveillustratestheresultsofsecondmodel(runrestricted;standardIMFandcrossesshowdistribution the function ofmassconsistentwithther(mass)relationship. from 1X10Mto5X10.Burstsalwaysproduced fourth model(t—oo;flattenedIMF;lowZ). Figure 7.Thebursthypothesis canexplaintheoccur- T0 5 tude relationshipwouldbeexpected torepresentonly T T5 tT05 1X 10Mofnewstars.Afterevolving16Gyr,ourtest 0Q 0 Although themodelprovidesagoodfittodata, 3. Whensimilarproblemswerefoundwithmodels To testthisidea,modelswereevolvedinwhichstar Fig. 6.—Empiricalr(mass)relationship.Thepositivebranchcorrespondstodiminishing(approachingconstant)starformationrates Fig. 7.—Theoreticalcolor-magnituderelationship.Thedashedcurveillustratestheresultsoffirstmodel(r>0;standardIMFand © American Astronomical Society • Provided by theNASA Astrophysics Data System Fig. 67 TULLY, MOULD,ANDAARONSON for galaxiesbrighterthanM18.0orredder we aremissingthequiescentanalogsofM33or formation isoccurring.However,itnottenablethat our localcalibrators.Onthebasisofthisargument,we LMC inthenearestfewgroupswhichsupplyuswith B —H_~1.0.Withacarefulinventoryofnearby conclude thattheburstmechanismcouldnotbeoperative the blueandthatlackstructureapparentwhenstar the inclusionofgalaxiesincatalogsthatareveryfaint powerful selectioneffectswhichdiscriminateagainst would havetobemissingmanyfaintredgalaxies. B erably lower. galaxies, itmightbepossibletopushtheselimitsconsid- were discussingtruedwarfgalaxiesbecause,asGerola, M/L asafunctionofageresultingfromchangein chemical abundances.Tocrudelyestimatetheextentof sensitive tothechoicesofinitialmassfunctionand Seiden, andSchulman(1980)haveargued,thereare the upperenvelopeoftruedistribution.Oursample With thesetwomodifications, thelimitingcolorfor the firstoftheseeffects,wecalculatedchangein cation) wereused.Totestformetallicityeffects,wehave the slopeofpowerlawinitialmassfunctionby (1982) andAaronsonMould (1982)havebeenused. clusters intheMagellanicClouds. DatabyPerssonetal converted tothecolor-agerelationships foundforstellar Gunn (1976),andR.Terlevich(1981,privatecommuni- T0 5 v The bursthypothesiswouldbequiteplausibleifwe 4. Thetheoreticalcolor-magnitudediagramisalso —1. DatagivenbyTinsley(1972),and Vol. 257 1982ApJ. . .257. .527T No. 2,1982 (open circles).Thehigh-luminositytrackbetweenthetwobranchesisaqualitativerepresentationofevolutionthatwouldoccurif star (crosses) andVirgoClusterspirals(filledcircles).Theredward,gas-poorbranchisdefinedbythelenticulargalaxiesin A pointforthislimitingcaseisplottedonthetheoreti- system withlowmetallicityandflatIMF. formation werearrestedinourGalaxy.Thelow-luminositytrackshowstheevolutionexpectedaftercessationofstar a poor. Ithasbeenproposedthatsuchconditionsexist ward highermasses,andthesesystemsshouldbemetal- mass functionandmetallicitycanextendthetheoretical cal color-magnitudediagram(Fig.7). case ofsteadystarformationbecomesB—H_\2. ship isprobablytheconsequenceofaninversedependence in theSmallMagellanicCloud(Lequeuxetal1979; galaxies, theinitialmassstarsshouldbeweightedto- color-magnitude relationshiptowardtheblue.Insmall Dennefeld andTammann1980). smaller galaxiestosatisfactorilymodeltheobservations. over thehistoryofagalaxyandgalacticmass.How- of thetimeconstantgoverningratestarformation The alternativesareunattractive. Itisunappealingto H~~ 2,itisnecessarytopostulatetrendstowardlower ever, becausetherelationshipextendsbluewardofB— metallicities and/orshallowerinitialmassfunctionsfor unlikely, aswell,thatstarformation ingalaxieswith mass andageofgalaxiesfainter thanM20.Itis suppose thatthereisastrong correlationbetweenthe T0 5 05 T B Fig. 8.—Thecolor-absolute-magnitudediagramfordisksystems.Theblueward,gas-richbranchisdefinedbythelocalcalibrators We concludethatquitemodestchangesintheinitial To summarize,theobservedcolor-magnituderelation- © American Astronomical Society • Provided by theNASA Astrophysics Data System COLOR-MAGNITUDE RELATIONFORSPIRALS which awaitdiscovery.Itisquitepossible,ofcourse, our samplestherearemanyotherquiescentsystems scatter inthecolor-magnitudediagramshouldbecome and ifanunbiasedsamplecanbedefined,thenthe that theburstmechanismworksatfainterlevels.Ifso, were heldconstantfor12Gyrandthenarrestedentirely in thetwocaseswereidentical:starformationrates of arrestedstarformation.Theformationhistories substantial atsomesufficientlyfaintluminositylevel. and thatforeachgalaxyintheseintervalscontained initial massfunctionandlowermetallicitycolor-age branch onthecolor-magnitude plotisdehneatedbythe relationships whichleadtothe filledcircleinFigure7. galactic initialmassfunctionandsolarabundanceswere for 4Gyr,extendingtothepresent.Infirstcase,a assumed. Inthesecondcase,weusedflattened demonstrated inFigure8. In thisplot,thegas-rich — 18>M20and\