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1982ApJ. . .255. .181M © 1982.TheAmericanAstronomicalSociety.Allrightsreserved.PrintedinU.S.A. The AstrophysicalJournal,255:181-190,1982April1 photographic, certainphotoelectricbands,etc.Duringthe bands andtheirassociatedsuchasphotovisual, have beenaccumulatedprimarilyinthevisualandblue last 20yearsorsointeresthasslowlymigratedintobluer bands (suchasultravioletandX-ray)redder mical questionsaremorelikelytobeansweredwithdata new detectorsandobservingopportunitiesfromspace.It the visualbands,anditisoftennecessarytotransform has alsobecameclearthatmanyofthependingastrono- (such asinfraredandradio)becauseoftheavailability available visualdataintotheseotherbandsinorderto from thesenewerbands.Still,theprincipaldatabaseisin transform itbacktothevisualbandforcomparisonin and thenoncethedatainnewbandsisonhand,to obtain apreliminaryestimateofwhatistobemeasured, order todeterminewhetheranythingnewhasbeen directly. Thetransformationisaccomplishedbysubdi- Johnson bands,whereithasnotyetbeenobtained measured, intotheredandinfraredR,/,J,K learned. function fromthevisualbandwhereithasbeen viding thetotalvisualfunction,whichincludesallstars, into sub-luminosityfunctionsforeachluminosityclass known V—Dcolor,=RJ, J,K,foreachspectraltype, and thensummingtheresultant transformedsub- the bandD.Thesub- functionsforeach luminosity functionsintoatotal luminosityfunctionfor (supergiants throughwhite dwarfs), andapplyingthe For mostofthiscenturyobservationaldataonstars In thispaperwetransformthestellarluminosity © American Astronomical Society • Provided by theNASA Astrophysics Data System Application oftheseluminosityfunctionsandsub-luminositytothestudygalactic J, andKbands,whereithasnotyetbeenobtaineddirectly.Thetransformationisaccomplishedby luminosity class(supergiantsthroughwhitedwarfs),applyingtheknown(V—D)color,DR,I,J, subdividing thetotalvisualfunction,whichincludesallstars,intosub-luminosityfunctionsforeach K, foreachspectraltype,andthensummingtheresultanttransformedsub-luminosityfunctionsintoa total luminosityfunctionforthebandD.Simpleanalyticformswhichaccuratelyfittransformed very redstellarpopulationnotaccountedforinthevisualbandluminosityfunctionisconsidered. luminosity functionsaregiven.Thepossibilityofasystematicerrorresultingfromtheexistence structure, includingstarcountmodelsintheR,/,J,andKbandsisbrieflydiscussed. Subject headings::general—luminosityfunctionspectrophotometry We transformthestellarluminosityfunctionthathasbeenmeasuredinvisualbandintoR,I, STELLAR LUMINOSITYFUNCTIONSINTHER,I,J,ANDKBANDS I. INTRODUCTION OBTAINED BYTRANSFORMATIONFROMTHEVISUALBAND : stellarstatistics Received 1981July10;acceptedOctober16 Institute forAdvancedStudy,Princeton Princeton UniversityObservatory Raymond M.Soneira Gary A.Mamón ABSTRACT AND 181 main sequencearealsoexamined. luminosity classandthefractionofstarsonoff and Kbandresponsefunctionsusedinthispaper(effec- tive wavelengthsof4400Â,550070009000 band responsefunctionswithapproximate blackbodyspectrafor main-sequence dwarfstarsofspectral typeA0toM8derivedfrom and spectraareshownnormalized tothesamepeaksensitivityor photometric temperatureslistedin Paper III.Theresponsefunctions emissivity. Figure 1comparestheJohnson(19656)£,F,R,/,J, Fig. 1.—ComparisonoftheJohnson (1965b)B,V,R,/,J,andK 1982ApJ. . .255. .181M dwarf starsofspectraltypeA0-M8derivedfromthe blackbody spectraformainsequence(luminosityclassV) photometric temperatureslistedbyBahcallandSoneira vity oremissivity. spectra areshownnormalizedtothesamepeaksensiti- both widelyusedandwelldocumented.WhiletheU,B,V the undisputedstandardcolorsysteminwavelength color systemofJohnsonandMorgan(1953)hasbecome (1981a, hereafterPaperIII).Theresponsefunctionsand 1.25 juin,and2.2jum,respectively)withapproximate interval between3000and6000Â,therearealarge the KronRandJbands(Kron,White,Gascoigne the mostcommonlyused,besidesJohnsonsystem,are number ofcompetingsystemsforRandbeyond.Ofthese, 182 system). TheKronRandJbandsarequitesimilarto tively. TheBeckerRbandhasaneffectivewavelengthof the Johnsonbands,butare200and750Abluer,respec- 6400 Â,butafullwidthathalf-maximumofonly430Â band. the JandKbandstolateMdwarfsevenredderstars, possibly fromayettobediscoveredluminosityclassor dwarfs, theRandIbandstoKearlyM clear thattheBandFbandsaremostsensitivetoG is considerableoverlapamongthedifferentbands,it population ofstars(BahcallandSoneira198Ih,hereafter (Buser 1978),afactorof5narrowerthantheJohnsonR 1953) andtheBecker(1946)Rband(fromhisRGU data accumulatedinonebandintoanotherthatisfar Paper IV).Thereisanobviousdangerinextrapolating more seriousthanareductioninaccuracyduetofar removed fromthefirstinwavelength.Theproblemis K will bemissedaltogetherwhenstarsareselectedaccord- lity orevenlikelihoodthatunusuallyredclassesofstars reaching extrapolationinwavelength:thereisapossibi- K data istransformed,suchstars,whichmaycontribute B ing totheirapparentvisualmagnitude.Whenthe visual bandiswelldeterminedouttoonlyM5V(corre- significantly intheredderbandsatrelativelybright discussed furtherin§lid. absolute magnitudes,willbemissing.Thisproblemis sponding toM&+13mag)(PaperIV;Bahcalland dwarfs inthevisualbandwillmanifestitselfatin- B creasingly brighterabsolutemagnitudesfortheR,J, and Kbands.Theseredderbandsarethereforeparti- Soneira 1980a,hereafterPaperI;Bahcalland dim endoftheluminosityfunction.Thetechniquefor cularly wellsuitedforextendingourknowledgeofthe accomplishing thisfromstarcountsisdiscussedexten- in thevisualbandbutasignificant oneintheredderR,J, treated in§II/Sectionlidexamines theavailabledataon sively inPaperIV. population stars;thespheroidstellaris 1980b, hereafterPaperII).TheuncertaintyintheM countsforevidenceonthe existenceofaredpopula- J, andKbands.SectionIII discusses theapplicationof tion ofstarswhichwouldmake anegligiblecontribution v We haveselectedtheJohnsonbandsbecausetheyare While thespectraofFigure1areverybroadandthere The faintendofthediskluminosityfunctionin Discussion inthemaintextof§IIislimitedtodisk © American Astronomical Society • Provided by theNASA Astrophysics Data System MAMON ANDSONEIRA the luminosityfunctionsandsub-luminosity considered inthispapertothestudyofgalacticstructure. know theF—Dcolorforeachstarindistancelimited sity functionfromsomereferenceband,whichwechoose This transformationcanbeconsideredintermsofa sample thatisusedtocalculatetheoriginalfunctioninF. here tobeV,intosomeotherbandD,itisnecessary summing starsinhorizontalstripsgivesthevisuallumin- the Dbandluminosityfunction. osity function,andsummingstarsalongdiagonalstrips (V —D,M)scatterplotforallstarsinthesample: method. Sub-luminosityfunctions,whichspecifythe hence itisnecessarytouseanindirectmeancolor (45° tothehorizontalifaxisscalesaresame)gives tudes plottedarethemeansforeachspectraltypeand number ofstarsbelongingtoeachluminosityclass each absolutemagnitude,M,bysubdividingthetotal to theabsoluteDbandmagnitude,Mby=— luminosity function.Forthenthsub-luminosityfunction, stars ofabsolutevisualmagnitude,M,aretransformed method isthatitneglectstheintrinsicscatterofcolors spectral typeandluminosityclass.Theabsolutemagni- (supergiants throughwhitedwarfs),aredeterminedfor luminosity class.Theproblemwiththemeancolor class. Fortunately,thesequencesinH-Rdiagramare of starsagivenabsolutemagnitudeandluminosity M. Themeancolorsaremorereadilyavailable,and stars inthenthluminosityclasswithabsolutemagnitude C(M), whereisthemeanV-Dcolorfor produce anysignificanterrors. sufficiently narrowthattheuseofmeancolorsshouldnot visual magnitudeforeachoftheluminosityclasses.Each Figure 2showsV—Icolorsasafunctionofabsolute have beentabulated,forexample,byJohnson(1966). v point inthefigurerepresentsmeancolorforagiven have thereforefurthersubdividedtheseluminosityclasses functions Carenotsingle-valuedofM.We into subclassessothattheCaresinglevalued.Atotalof supergiant classes(laandlb),twoeachforthebright v D9Dv giants (II)and(III),oneforthesubgiants v filled circlesdenotethepositive-slopebranches,and shows thesesubdivisonsoftheF—/colordiagram: 11 luminositysubclassesareused:twoforeachofthe sions areidenticalforallbandsdiscussedhere. open circlesthenegative-slopebranches.Thesesubdivi- (IV), mainsequence(V),andwhitedwarfs(VII).Figure2 v constant functions,i.e.,aunit magnitudeintervalinF Dnv does nottransformtoaunitmagnitude intervalinD.The luminosity functionsmustberenormalizedtostarsper unit magnitudeintervalbecausethecolorsCarenot transformed sub-luminosity functions arethenadded the Dband. together togivethedesiredtotal luminosityfunctionin Dnv Dn Dn In principle,inordertotransformthestellarlumino- Such detailedinformationisnotcurrentlyavailable, A complicationarisesbecauseseveralofthecolor After transformationtotheDband,eachofsub- II. THETRANSFORMATIONMETHOD Vol. 255 1982ApJ. . .255. .181M M =—9,andthedim-endcutoff+oo.Thesub- total luminosityfunction,,bythefractionofstarson luminosity functions,„,areestimatedbymultiplyingthe For M>3.7mag,thereareonlywhitedwarfs(classVII) and offthemainsequenceforeachabsolutemagnitude. subclasses, andtheopencirclesdenotenegative-slopesubclassesdefinedsoastomakecolorfunctionsCsinglevalued. and mainsequencestars(classV).FromPaperI, with (l)(My>3.7)=0forallotherclasses.Forthebright (see eq.[3]andTable2,below),withthebright-endcutoff analytic fittothedataofMcCuskey(1966),Luyten No. 1,1982 classes) asafunctionofabsolutemagnitude,weobtain uence starsandseveralclassesofgiants(la-IV).From absolute magnitudesM<3.7mag,therearemainseq- Paper IV,whichspecifiesthetotalnumberofgiants(all (1968), andWielen(1974)givenbyequation(1)ofPaperI where nreferstoclasseslathrough IV,andt(M)isthe diagrams ofallstarsinVolumes 1and2oftheMichigan bd in classn.Thefunctionswere estimatedfromtheH-R fraction ofallgiantswithabsolute magnitudeMthatare F Dn n v mf v The visualbandluminosityfunctionweuseisan Fig. 2.—Mean(V—I)colorsasafunctionofabsolutevisualmagnitudeforeachluminosityclass.Thefilledcirclesdenotethepositive-slope X^M^eeI; n=f=V,VI,VII; © American Astronomical Society • Provided by theNASA Astrophysics Data System n 4>\n(M) =0; 435 v {My)fy{My); (ftniMy) =(j)(My)[l—fy(My)]T(My), f /(M) =0.44exp[1.5x10'+8)*]; n VF My <3.7, (2) 0251 0vh(M)=0(M/, fkvii f(M) =0.15XlO--^!, ynV (j>y(M) =(t)(M[l—fvn(M], n ^V,VI,VII; v a) VisualBandSourceData My >3.7,(1) STELLAR LUMINOSITYFUNCTIONS Fesen 1978).(Notethatxreferstostarsofagiven many oftheregionsrefertopositiveandnegative- manner thattheheightofeachregionnforagiven estimated fromapparentmagnitudelimitedsurveys.) Spectral Catalogwithin100pcoftheSun(Houkand and —inmanyoftheregionsreferto subclassesdefinedsoastomake from theH-RdiagramsofHoukand Fesen(1978).Thedesignations+ with absolutemagnitudeMthatare inluminosityclassnestimated the +and—distinctions). luminosity functionsforeachclass(ignoring color functionsCsinglevalued,asdiscussedabove. slope luminositysubclassesdefinedsoastomakethe that absolutemagnitude.Thedesignations+and-in absolute ,M,correspondstothefractionxat absolute magnitudesothatitcanalsobeaccurately Figure 4adisplaystheresultantvisualbandsub- the colorfunctionsCsinglevalued(see text).Theheightofeachregion that absolutemagnitude. n foragivenabsolutemagnitude,M , correspondstothefractiont„at n v Dn vn Öb v Figure 3showsourestimatesofT(M)insucha Fig. 3.-Fraction,ofallnon-mainsequencestars(giants) nv 183 1982ApJ. . .255. .181M © American Astronomical Society • Provided by theNASA Astrophysics Data System Fig. 4a Fig. 4c Fig. 4e functions givesthetotalluminosityfunction,(f). V, (b)R,(c)I,(d)J,and(e)Kbands.Thesumofallthesub-luminosity Fig. 4.—Sub-luminosityfunctionsforeachluminosityclassinthe(a) Fig. 4d Mj 1982ApJ. . .255. .181M types G5andlater),Vhavebeenobtainedfrom bright giantswereassumedequaltotheclassIsuper- polated asfollows:themeancolorsforluminosityclassII Johnson (1966).Themeancolorsforluminosityclasses spectral typeforluminosityclassesla,lb,III(for giants. MeancolorsforclassIIIspectraltypesearlierthan and spectraltypesnotlistedbyJohnsonwereinter- sequence colors.Meancolorsasafunctionofspectral difference incolorbetweeneachpairoftabulatedJohn- type forluminosityclassIVhavebeenobtainedby G5 wereinterpolatedfromsupergiantandmain- interpolation oftheclassIIIandVvalues.The the interpolatedvaluesshouldbeoforderone-third and isseldomlargerthan0.30mag.Theuncertaintiesin son valuesusedforinterpolationistypically0.10mag, types intoabsolutevisualmagnitudes.Wehaveusedthe these colordifferences. values fromBlaauw(1963)forluminosityclassesla,lb, spectral typeslaterthanF5,forclassIV(all are fromFitzGerald(1969).ValuesforclassIIIwith and II.ValuesforspectraltypesF5earlierinclassIII types), andforclassVspectraltypesK3earlierare from Keenan(1963).ValuesforclassVspectraltypesK5 and laterarefromJohnson(1965a). colors intheKronbandlistedbyGreenstein(1976),using M, aredirectlycalculatedfromtheV—RandI the relationsgivenbyGreenstein(1976)andEggen transformations intotheJohnsonbandsgivenbyFrogel colors arefromMouldandLiebert(1978),usingthe values forabsolutemagnitudesgreaterthan+15are 10 -0.20-0.400.650.790.99 colors asafunctionofabsolutevisualmagnitude.The et al(1978).Table1liststheadoptedwhitedwarfmean 12 0.10-0.20-0.34-0.19-0.23 colors issmallbecausethecontributionofwhitedwarfs polated. Theuncertaintiesinthetransformedluminosity linear extrapolations.FortheJandXbands,colors 15 0.760.64 0.861.371.67 14 0.400.36 0.380.740.81 13 0.250.08 -0.100.110.15 11 -0.05-0.34-0.58-0.49-0.61 functions resultingfromtheuseoftheseextrapolated for absolutemagnitudeslessthan+11arealsoextra- (1971). Similarly,themeanV—JandXwhitedwarf 17 1.701.20 1.822.633.19 V —Icolorsasafunctionofabsolutevisualmagnitude, 16 1.260.92 1.342.002.43 18 1.811.48 2.303.263.95 vK 9 -0.35-0.46-0.72-1.09-1.37 8 -0.50-0.52-0.79-1.39-1.75 The meanV—Dcolors,=R,/,J,Xasafunctionof The H-Rdiagramisneededtotranslatethespectral For whitedwarfstars(classVII),themeanV—Rand © American Astronomical Society • Provided by theNASA Astrophysics Data System My B-VV-RV—IV-JV-K Adopted WhiteDwarfMeanColors b) ColorData TABLE 1 STELLAR LUMINOSITYFUNCTIONS more than15%ofthetotalluminosityfunction sharply peakednearM=+15,neveramountingto the meancolorsCarenotconstantfunctions,aunit magnitude intervalinD,hencethetransformedsub- magnitude intervalinVdoesnottransformtoaunit (see Fig.4). luminosity functionsintheR,I,J,andXbands.Because sub-luminosity functionsaretransformedintosub- luminosity functionsmustberenormalizedtostarsper band becausetheabsolutemagnitudeintervalusedin final rebinningofthesub-luminosityfunctionsinD unit magnitudeinterval.(Thecomputationmethodwe performing thetransformation,0.01mag,ismuchsmaller use automaticallyperformstherenormalizationin the colorgradientdC/dV.) than eitherthefinalmagnitudeintervalof0.2magthatis v used inestimatingthevalueofluminosityfunctionor tions foreachluminosityclassinband. transformation fromtheVband.The dashedcurvesaretheanalytic band luminosityfunctionsthatresultfromadding Dn display. Asexpected,thebasicformofvisuallumino- divided bytheindicatedfactorsforconveniencein together thetransformedsub-luminosityfunctions.Also, approximations givenbyeq.(3)with theparameterslistedinTable2. sity function:asteeplyfallingbrightendandratherflat function andatransformedBbandluminosity included inthefigureareoriginalVluminosity K bands.Thesolidcurvesgivethe calculatedvaluesobtainedby dim endisretainedbyeachofthetransformedluminosity (see below).Thefunctionshavebeenmultipliedor Using themeancolordataof§lib,visualband Figure 4displaystheresultantsub-luminosityfunc- The solidcurvesinFigure5showtheR,I,J,andX Fig. 5.—Totalstellarluminosityfunctions, (p,intheB,V,R,I,J,and c) TheTransformedLuminosityFunctions 185 186 MAMON AND SONEIRA Vol. 255 functions. The R, J, J, and K luminosity functions have ties in the source visual band data and the colors are not 1 3 values (stars mag“ pc“ ) that are greater than the visual well known. For Mv < — 3, the visual luminosity func- luminosity function by factors of order 1.5, 2, 2.5, and 3, tion is uncertain because of the paucity of objects in this respectively, for absolute magnitudes M > 0. Of course, range. The bright-end luminosity function cutoff, Mb, when integrated over a specified range of spectral types, listed in Table 2 corresponds to the brightest absolute the normalizations for all the luminosity functions are magnitude in the visual band for which normalized identical. luminosity function data are available. For the transfor- The several prominent peaks and valleys at the bright mations, the analytic form for the visual luminosity end, M < 0, of the transformed R, /, J, and K luminosity function was extrapolated to — 9 in functions are due to the fact that occasionally order to eliminate “ edge effects ” in the computation. The dCn(Mv)/dMv & 1 over a small range in Mv. Small brightest stars known extend to about —8.5 mag visual. variations to either Cn(Mv) or Tn(Mv) substantially affect In the magnitude range Mv < + 4, the relative propor- the location and size of these features in the computed tions, t„, of the five kinds of giants (classes la-IV) are luminosity functions. The smaller variations at the bright known only roughly at best. Changes of order 20% in the end are caused by the sharp cutoffs introduced in relative proportions of the giant classes produce fluctua- Figure 3. Hence, the features are most likely artifacts of tions in the total R and I luminosity functions of order the computation (see below). 20% and 50%, respectively. For the J and K luminosity In order to smooth over these artificial features and functions, similar variations in the relative proportions of allow the luminosity functions to be used in a convenient the giant classes produce fluctuations of order 100% or manner, we have fitted the computed functions to the more, and occasionally up to an order of magnitude same analytic form used in Paper I, (1000%). These fluctuations result from the interaction of n* lQß(M -M*) the steeply falling total (visual) luminosity function (a (M) = j-j ^ < M < Mc , factor of 10 every 2 magnitudes) with the varying color shifts produced by each giant class. (Shifting even a small fraction of stars from, say, absolute magnitude — 1 to = 0(M ) , M Md . (3) tively small number of stars already at —3.) For the These parameters for the B, V, R, /, J, and K luminosity reddest J and K bands, the color shifts are quite large (up functions are listed in Table 2. The fitted functions have to 4 magnitudes) and differ significantly from one giant been plotted as dashed lines in Figure 5. The quality of the class to another, so that variations in the relative propor- fits is excellent. tions of the giant classes are greatly amplified by the We have also transformed the visual luminosity func- rapidly decreasing luminosity function. tion into the blue (B) band using the R — F color data The faint end of the visual luminosity function is well from Johnson (1966). This allows a comparison with determined out to only Mv æ +13 (M5 V) (see Papers I luminosity functions measured directly in the B band and IV). For the transformed functions, this uncertainty (Paper I) and with other B luminosity functions obtained begins at brighter absolute magnitudes: MR& +11, by transformation from the F band. Our transformed B Mj & + 9, Mj ^ +8, and MK æ + 7. The data, however, luminosity function is plotted as a solid curve in Figure 5 do suggest that the visual luminosity function is approxi- together with the analytic fit to a luminosity function mately constant for +11

TABLE 2 Luminosity Function Parameters Parameter B V R I J K n* 2.55( —3) 4.03( —3) 4.80(-3) L75(-2) 2.50(-2) 2.90(-2) M* 2.20 1.28 1.40 0.85 0.60 2.0 a 0.60 0.74 0.74 0.81 0.80 0.625 ß 0.05 0.04 0.045 0.01 0.01 0.01 1/Ô 2.30 3.40 3.0 5.2 5.65 4.0 Mb < —6 < —6 < -6 < — 6 < —5 < —5 Mc +15 +15 +14 +14 +11 +9 Md >+18 > + 16 > + 13 > + 11 > + 10 > +9

© American Astronomical Society • Provided by the NASA Astrophysics Data System 1982ApJ. . .255. .181M transformed luminosityfunctionsifthereexistsanew missed whenstarsareselectedaccordingtotheirappar- luminosity classorpopulationofstarsthathasnotbeen No. 1,1982 band). However,inthelongerwavelengthbands,suchred ent visualmagnitude(becauseoftheirfaintnessinthe such starsareunusuallyredthentheywillmostlikelybe accounted forinthesourcevisualluminosityfunction.If significant contributionstoalongwavelengthband stars willappearincreasinglybrighterandcouldmake luminosity functionoverabsolutemagnituderangesoth- based onthetraditionalluminosityclassesestablishedin erwise thoughttobecompleteandaccuratelymeasured transformed R,/,J,andKluminosityfunctionswehave the visualband.Hencethereisapossibilitythat densities. Classesofveryredstarsareknown,suchasT calculated inthispaperareunderestimates;theyare, strictly speaking,lowerlimitstotheexpectedvolume Tauri stars(Mendoza1966,1968)andlongperiodvar- iables (Mendoza1967),buttheirnumberdensitiesaretoo mass estimatesofSmak1966).PaperIfoundnoevidence solar neighborhood(Kuhi1964;Oort1958;usingthe low toaffecttheR,/,J,andKluminosityfunctionsin directly andcompareitwiththetransformedfunction. significant, butnotdefinitive—seebelow.) using anargumentbasedonB—Vcolors.(Thetestis for suchanewclassofredstarsintherange20 I 0.4 CD -0.2 -0.4 -0.6 0.8 0.0 T4 1.0 L2 0.2 0.40.60.81.01.2 1.4 1.61.82.0 (B-V) 187 1982ApJ. . .255. .181M of starsintheChiucatalog.Amoredefinitivetestwould chosen accordingtotheirapparentbrightnessinthe is noevidenceforanynewluminosityclassorpopulation require thatthestarsselectedforcolormeasurementbe 188 the mainsequence,havescaleheightsindirectionz reddest bandtobemeasured. perpendicular tothegalacticplaneof250pc,significantly magnitude (PaperIandPaperIII).Whitedwarfstarsare larger thanformainsequencestarsofthesameabsolute main sequencestars. presumed tobedistributedlikethetypicallyolderdim transformed data.TheseparametersfortheÆ,K,R,/,J, dividing bythetotalluminosityfunction.Wehavefitted necessary toknowthefractionofstarsthataregiantsasa function ofabsolutemagnitudeintheplanedisk the resultingfunctiontosameanalyticformusedin luminosity functionsforallthegiantclasses(la-IV)and the Galaxyisnotasaccuratelyknownoverbroada This formaccuratelyfitsvisualbanddataaswellthe Paper III: (z =0).Thisisreadilycalculatedbysummingthesub- population thatmakesupthespheroidalcomponentof range inabsolutemagnitudeasthediskluminosity and KluminosityfunctionsarelistedinTable3. found tohavethesameshapeasdiskluminosity function. InPaperIthespheroidluminosityfunctionwas over whichthespheroidfunctionhasbeenobserved, function intherestrictedrangeofabsolutemagnitudes spheroid componentsinthesolarneighborhoodis800:1 4 M.(4) a C 0.530.44 0.310.086.9(-3)4.7(-3) a 2.4(—31)1.5(—4) 6.5(-4)0.372.02.5 ß 758.0 7.5 4.44.03.0 y 163.5 3.2 1.00.5 M 4.63.7 2.9 2.42.21.6 a Parameter BVRIJ K MAMON ANDSONEIRA Non-Main SequenceParameters TABLE 3 different fromthosefordiskstarsbecausethehigh- sequence, luminosityclassVI)isparalleltothediskmain velocity spheroidstarsaremetal-poor.Inthestandard R, /,J,andKbandsforspheroidstarsare(slightly) sequence butshiftedbluewardbyA(B—P)of0.15mag velocity starsinR—/hasbeendeterminedbyGreenstein high-velocity stars(oftenreferredtoasthesubdwarf 0.20 magforhigh-velocitystars;seePaperI]andshould comparison withdiskstarcolorsforagivenabsoluteV shifts, D=R,/,J,andKofhigh-velocitystarcolorsin color shiftscanbeusedtoestimatethedesiredV—D (B —V,My)H-Rdiagram,themainsequencefor excess orerrorthatresultsfromusingonecolorto magnitude usingthedataofJohnson(1966).(Thecolor estimate anotherisgreatestintheultraviolet[typically (Eggen 1976andPaperI).Thecolorshiftforthehigh- 1959; SimodaandKimura1968). not significantlyaffectourcalculatedcoloroffsetsinthe (1965) andGliese(1968)tobeA(R—/)=0.1mag.These infrared.) Theestimatesforthecoloroffsetsareas are allsufficientlysmallanduncertainthatit A(V —J)=0.3mag,K)0.4mag.Theseoffsets follows: A(F—R)=0.15mag,-/)0.25 unknown, butassumedtobeidenticalthedisklumino- is questionablewhethertheaccuracyofalready sent onlyafirstapproximationintheirdetermination.In poorly knownspheroidluminosityfunctionismuch — 3

FitzGerald, M. P. 1969, Pub. A.S.P., 81, 71. Kuhi, L. V. 1964, Ap. J., 140, 1409. Frogel, J. A., Persson, S. E., Aaronson, M., and Matthews, K. 1978, Ap. Lee, T. A. 1970, Ap. J., 162, 217. J., 220, 75. Luyten, W. J. 1968, M.N.R.A.S., 139, 221. Gliese, W. 1968, in Low Luminosity Stars, ed. S. S. Kumar (New York: McCuskey, S. W. 1966, Vistas Astr., 7, 141. Gordon & Breach), p. 41. Mendoza, E. E. 1966, Ap. J., 143, 1010. Greenstein, J. L. 1965, in Galactic Structure, ed. A. Blaauw and M. . 1967, Bol. Obs. Tonatzintla y Tacubaya, 4, 114. Schmidt (Chicago: University of Chicago Press), p. 361. . 1968, Ap. J., 151, 977. ^ 1976, A.J., 81, 323. Mould, J., and Liebert, J. 1978, Ap. J. (Letters), 226, L29. Houk, N., and Fesen, R. 1978, in I AU Symposium 80, The HR Diagram, Oort, J. H. 1958, in Stellar Populations, ed. D. J. K. O’Connell (Rome: ed. A. G. D. Philip and D. S. Hayes (Dordrecht: Reidel), p. 91. Pontifical Academy of Sciences), p. 415. Johnson, H. L. 1965a, Ap. J., 141, 170. Oort, J. H., and van Herk, G. 1959, Bull. Astr. Inst. Netherlands, 14,299. . 19656, Ap. J., 141, 923. Roman, N. G. 1954, A.J., 59, 307. —. 1966, Ann. Rev. Astr. Ap., 4, 193. Sandage, A. R. 1954, A.J., 59, 162. Johnson, H. L., and Morgan, W. W. 1953, Ap. J., 117, 313. Simoda, M, and Kimura, H. 1968, Ap. J., 151, 133. Keenan, P. C. 1963, in Basic Astronomical Data, ed. K. Aa. Strand Smak, J. I. 1966, in Ann. Rev. Astr. Ap., 4, 19. (Chicago: University of Chicago Press), p. 78. Widen, R. 1974, in Highlights of Astronomy, Vol. 3, ed. G. Contopoulos Kron, G. E., White, H. S., and Gascoigne, S. C. B. 1953, Ap. J., 118,502. (Dordrecht: Reidel), p. 395.

Gary A. Mamón: Princeton University Observatory, Peyton Hall, Princeton, NJ 08544

Raymond M. Soneira: Institute for Advanced Study, Princeton, NJ 08540

© American Astronomical Society • Provided by the NASA Astrophysics Data System