The ACS Fornax Cluster Survey. VIII. The Luminosity Function of Globular Clusters in Virgo and Fornax Early-Type Galaxies and its Use as a Distance Indicator
Daniela Villegas, Andres Jordan, Eric W. Peng, John P. Blakeslee, Patrick Cote, Laura Ferrarese, Markus Kissler-Patig, Simona Mei, Leopoldo Infante, John L. Tonry, Michael J. West
aa r X i v : . [ a s t r o - ph . C O ] A p r Accepted for publication in ApJ.
Preprint typeset using L A TEX style emulateapj v. 05/04/06
THE ACS FORNAX CLUSTER SURVEY. VIII. THE LUMINOSITY FUNCTION OF GLOBULAR CLUSTERSIN VIRGO AND FORNAX EARLY-TYPE GALAXIES AND ITS USE AS A DISTANCE INDICATOR Daniela Villegas , Andr´es Jord´an , Eric W. Peng , John P. Blakeslee , Patrick Cˆot´e , Laura Ferrarese ,Markus Kissler-Patig , Simona Mei , Leopoldo Infante , John L. Tonry , Michael J. West Accepted for publication in ApJ.
ABSTRACTWe use a highly homogeneous set of data from 132 early-type galaxies in the Virgo and Fornax clus-ters in order to study the properties of the globular cluster luminosity function (GCLF). The globularcluster system of each galaxy was studied using a maximum likelihood approach to model the intrin-sic GCLF after accounting for contamination and completeness effects. The results presented hereupdate our Virgo measurements and confirm our previous results showing a tight correlation betweenthe dispersion of the GCLF and the absolute magnitude of the parent galaxy. Regarding the use ofthe GCLF as a standard candle, we have found that the relative distance modulus between the Virgoand Fornax clusters is systematically lower than the one derived by other distance estimators, andin particular it is 0.22 mag lower than the value derived from surface brightness fluctuation measure-ments performed on the same data. From numerical simulations aimed at reproducing the observeddispersion of the value of the turnover magnitude in each galaxy cluster we estimate an intrinsic dis-persion on this parameter of 0.21 mag and 0.15 mag for Virgo and Fornax respectively. All in all, ourstudy shows that the GCLF properties vary systematically with galaxy mass showing no evidence fora dichotomy between giant and dwarf early-type galaxies. These properties may be influenced by thecluster environment as suggested by cosmological simulations.
Subject headings: galaxies: elliptical and lenticular, cD — galaxies: star clusters —globular clusters: general INTRODUCTION
The distribution of globular cluster (GC) magnitudeshas the remarkable property that it is observed to peakat a value of M V ≈ − . mag in a near universal fashion(e.g., Jacoby et al. 1992, Harris 2001, Brodie & Strader2006). This distribution, usually referred to as the GCluminosity function (GCLF), has been historically de-scribed by a Gaussian. By virtue of its near universality,the derived mean or “turnover” magnitude µ has seenwidespread use as a distance indicator (e.g. Secker 1992,Sandage & Tammann 1995), even though some disper-sion and discrepant results have been reported in theliterature (see discussion in Ferrarese et al. 2000a).There is nevertheless no solid theoretical explanation Based on observations with the NASA/ESA Hubble SpaceTelescope, obtained at the Space Telescope Science Institute(STScI), which is operated by the Association of Universities forResearch in Astronomy, Inc., under NASA contract NAS 5-26555. European Southern Observatory, Karl-Schwarzschild-Strasse 2,85748 Garching bei M¨unchen, Germany Departmento de Astronom´ıa y Astrof´ısica, Pontificia Universi-dad Cat´olica de Chile, Av. Vicu˜na Mackenna 4860, 7820436 Macul,Santiago, Chile Harvard-Smithsonian Center for Astrophysics, 60 Garden St,Cambridge, MA 02138 Department of Astronomy, Peking University, Beijing 100871,China Herzberg Institute of Astrophysics, Victoria, BC V9E 2E7,Canada. University of Paris Denis Diderot, 75205 Paris Cedex 13,France GEPI, Observatoire de Paris, Section de Meudon, 5 Place J.Janssen, 92195 Meudon Cedex Institute for Astronomy, University of Hawaii, Honolulu, HI96822 European Southern Observatory, Alonso de C´ordova 3107, Vi-tacura, Casilla 19001, Santiago, Chile for the observed universality of the turnover magnitude.The luminosity function is a reflection of the more fun-damental mass spectrum of the GCs, and as such the“universal” turnover magnitude corresponds to a clustermass of ∼ × M ⊙ . Vast efforts have been undertakenfrom the theoretical point of view in order to explain theunderlying universal mass function. The many publica-tions on this topic can be separated into those tryingto identify some particular initial condition that selectsa certain mass scale for star formation (e.g., Peebles &Dicke 1968, Fall & Rees 1985, West 1993), and thoselooking for a destruction mechanism that selects clus-ters in a particular mass range starting from an initiallywide mass spectrum (e.g., Fall & Rees 1977, Gnedin &Ostriker 1997, Prieto & Gnedin 2008)At the high-mass end (i.e. m gc < µ ) the mass functionof globular clusters resembles very closely the mass func-tion of young clusters and molecular clouds in the MilkyWay and other nearby galaxies (see e.g. Harris & Pudritz1994, Elmegreen & Efremov 1997, Gieles et al. 2006).On the other hand, neither young clusters nor molecu-lar clouds show a turnover on their mass distributions,but they keep rising monotonically following a power-lawto lower masses. Fall & Zhang (2001) used simple ana-lytical models (including evaporation by two-body relax-ation, gravitational shocks and mass loss by stellar evo-lution) to study the evolution of the GC mass function.They showed that, for a wide variety of initial conditions,an initial power-law mass function develops a turnoverthat, after 12 Gyr, is remarkably close to the observedturnover of the GCLF. Vesperini (2000, 2001) reachesa similar conclusion, but finds that a log-normal massfunction provides a better fit to the data. Fainter thanthe turnover, the evolution would be dominated by two- Villegas et al.body relaxation, and the mass function would end uphaving a constant number of GCs per unit mass, reflect-ing the fact that the masses of tidally limited clustersare assumed to decrease linearly with time until theyare destroyed (other authors propose different mass-lossrates, see e.g., Lamers et al. 2006). Brighter than theturnover, the evolution is dominated by stellar evolutionat early times and by gravitational shocks at late times.Recently, McLaughlin & Fall (2008) have shown that theGC mass function in the Milky Way depends on clusterhalf-mass density (i.e. the mean density within a radiuscontaining half the total mass of the GC), in the sensethat the turnover mass increases with half-mass density,while the width of the GC mass function decreases. Butwhile there is currently a fairly good understanding ofthe dynamical processes that shape the GCLF, manydetails are still missing. In particular none of the the-ories proposed has been entirely successful on addressingthe question of how the turnover magnitude can remainconstant regardless of environmental properties and themass of the host galaxy.The use of deep HST data during the last years has re-sulted in high quality GCLF data, reaching 2 magnitudesbeyond the turnover at the distance of the Virgo cluster( ∼ § § § § § § DATA AND GCLF INGREDIENTS
Each one of the 132 galaxies included in this study wasobserved with the Advanced Camera for Surveys (ACS)during a single Hubble Space Telescope (HST) orbit, aspart of the ACS Virgo Cluster Survey (ACSVCS) andthe ACS Fornax Cluster Survey (ACSFCS). The goalsand main observational features of these two surveys areextensively discussed in Cˆot´e et al. (2004) and Jord´anet al. (2007a), respectively. We refer the interested readerto these publications for further details. The surveys targeted a total of 100 galaxies in theVirgo cluster and 43 galaxies in Fornax, and includedobservations in the F475W ( ≈ Sloan g ) and F850LP ( ≈ Sloan z ) passbands, with exposure times of ∼ ∼ g ” and to F850LP as “ z ”, due to theirclose proximity to the corresponding Sloan passbands.Jord´an et al. (2004) describes the pipeline implementedto automate the reduction procedure and analysis ofall images in both surveys. The final output from thispipeline is a preliminary catalog of GC candidates andexpected contamination per galaxy, including photomet-ric and morphological properties, that are later used toevaluate the probability p GC that a given object is a GC(see Jord´an et al. 2009 for details). For the purposesof this study, and as defined on previous ACSVCS andACSFCS papers, we constructed the GC candidate sam-ples by selecting all sources that have p GC ≥ g and z bands, to the same or deeper depththan our images. These control fields were processed us-ing the same pipeline implemented for the science data,and were then used to build customized control fields, asif a given galaxy was in front of it (the details of thisprocess are explained in Peng et al. 2006, were also a fulllist of the control fields used is available). For each ofour target galaxies, the result is a catalog containing 17different estimates of the expected foreground and back-ground contamination. These are later used to obtainan average estimate of the contamination in the field ofview of a given galaxy.The completeness function needs to be built consider-ing four parameters: the magnitude of the source ( m ),its size as measured by the projected half light radius( r h ), its color (( g − z ) ), and the surface brightness ofthe local background over which the object lies ( I b ). Thecompleteness function f ( m, r h , ( g − z ) , I b ) was obtainedby performing simulations that added model GCs of dif-ferent sizes ( r h = (1 , , ,
10) pc), colors (( g − z ) =(0 . , . , . , . mag ), and with King (1966) concentra-tion parameter of c = 1 . f givenan arbitrary set of ( m, r h , ( g − z ) , I b ). The random un-certainty in the mean completeness curve is essentiallyzero, so the completeness limits at 90% and 50% are ro-bust and can be determined with negligible error for agiven population of objects.This paper focuses on the study of the 89 early-typeCLF as distance indicator 3 Fig. 1.—
Left: GCLF histogram for VCC1226 as presented inJord´an et al. (2007b). The lines show the best-fit model (solidblack curve), the intrinsic Gaussian component (dashed curve),the Gaussian component multiplied by the expected completeness(dotted curve), and a kernel density estimate of the expected con-tamination (solid gray curve). Right: The same as shown in theleft hand side, but now using the corrected completeness function. galaxies discussed by Jord´an et al.(2007b) and all 43galaxies of the ACSFCS. Our analysis is restricted tothose galaxies that have more than five GC candidatesand for which we were able to usefully constrain theGCLF parameters. These restrictions exclude 11 galax-ies in the Virgo sample but none in Fornax. GCLF MODEL FITTING
Given the observational information previously de-scribed we aim to recover the parameters of the intrinsicluminosity function of the GCs in a galaxy. We useda maximum likelihood approach similar to the one de-scribed by Secker & Harris (1993). According to thisformalism, and as detailed in Jord´an et al. (2007b), wedescribe the intrinsic GCLF by some function G ( m | Θ),with Θ being the set of model parameters to be fitted,and we assume that the uncertainties on magnitude mea-surements ǫ m have a Gaussian distribution. In absenceof contamination, the probability of observing a GC witha given effective radius R h and apparent magnitude m against a galaxy background I b would be: G T ( m | Θ , R h , I b , ǫ m ) = A [ h ( m | ǫ m ) ⊗ G ( m | Θ) ] f ( m, R h , I b ) , (1) where h ( m | ǫ m ) = (2 πǫ m ) − / exp( − m / ǫ m ), is themagnitude error distribution, which is convolved withthe intrinsic GCLF G ( m | Θ). The normalization factor A is a function of the GCLF parameters Θ and the GCproperties R h , I b , and ǫ m , and it is set by requiring that G T integrates to unity over the whole magnitude rangecovered by the observations.In practice a fraction B of the sources classified asGC candidates in a galaxy are contaminants, so thatthe probability of observing a GC with parameters( m, R h , I b , ǫ m ) is reduced by a factor (1 − B ) and the dis-tribution that accounts for all the observed objects hasto include the contaminants luminosity function b ( m ).Thus, the likelihood of observing a total number of Nobjects with magnitudes m i and properties ( R h , I b , ǫ m )is L (Θ , B ) = N Y i =1 [(1 −B ) G T ( m i | Θ , R h,i , I b,i , ǫ m,i )+ B b ( m i )] , (2) Fig. 2.—
Difference in turnover magnitude produced by usingthe completeness function presented by Jord´an et al. 2007b andthe one we are using here (∆ µ ≡ µ old − µ new ) in the g (top)and z (bottom) bands, vs. the B -band apparent magnitude of theparents galaxy. Jord´an et al. (2007b) have made a detailed descriptionof several parametrization of the GCLF and their variousadvantages and drawbacks. Here we focus on the studyof the Gaussian representation, because of its historicuse in the study of the GCLF as a distance indicator.It is worth noticing that other parametrization such a t function have also been successfully used for this purpose(Secker 1992, Kissler et al. 1994). For the case of a Gaus-sian the set of model parameters will be Θ ≡ { µ, σ m } ,where µ and σ are the turnover and the dispersion in adistribution of the form: dNdm = 1 √ πσ exp (cid:20) − ( m − µ ) σ (cid:21) (3)The coding implementation of the outlined maximumlikelihood procedure is in practice the same used to com-pute the GCLF by Jord´an et al. (2007b) , except thatwe are now using completeness curves customized to theFornax data too. Also, during the analysis of the ACS-FCS data we found a coding mistake in the interpola-tion of the completeness curves previously used to esti-mate the GCLF parameters of the Virgo galaxies. Thebackground information in the completeness curves wassometimes misread in such a way that the completenesslevel assigned to a given background brightness was lowerthan the real value. As the changes in completeness aremore significant for brighter backgrounds, massive galax-ies were more affected than dwarf galaxies. Even thoughit does not have any significant effect over the main con-clusions of Jord´an et al. (2007b), we are reporting theproblem here because it produces a slight change in theturnover magnitudes of the Virgo galaxies. The mas-sive galaxies are the most affected, with their turnovermagnitudes becoming roughly ∼ mag brighter. Thisbehavior can be observed in Figure 1, where we haveplotted side-by-side the z -band GCLF fit for VCC1226as presented in Figure 4 of Jord´an et al. (2007b), and thecurrent fit implemented using the corrected completenessfunction that now also includes a color correction. In Fig-ure 2 we have plotted the observed change in the turnovermagnitude (∆ µ ≡ µ old − µ new ) in both bands, against the B -band apparent magnitude of the parent galaxy, show-ing that the brightest galaxies are the most evidently af- In § µ and σ for the range of GC system sizes in our sample. Villegas et al.
Fig. 3.—
GCLF histograms for the Virgo and Fornax samplegalaxies. For each one of them we present the z- and g -band GCLFsside by side. The VCC/FCC name and B -band magnitude of thegalaxy are indicated in the upper left corner of the left panel, wherewe also indicate the total number of sources N in each histogramand the bin width h used to construct it ( h is calculated as de-scribed in the text). In addition, we show the best-fit model (solidblack curve), the intrinsic Gaussian component (dashed curve),the Gaussian component multiplied by the expected completeness(dotted curve), and a kernel density estimate of the expected con-tamination in the sample (solid gray curve). The solid black curveis the sum of the solid gray and dotted curves. The galaxies areordered by decreasing apparent B -band total luminosity, readingdown from the upper left corner. The parameters of the fits aregiven in Table 1 and 2. The full version of this figure is published inthe electronic edition of the Astrophysical Journal. Sample panelsare shown here for guidance regarding its form and content. fected, unlike the dwarfs whose turnover stays virtuallyunchanged. Some spread can be observed in the case ofthe intermediate-luminosity galaxies, but in all cases thechange in µ is always lower than 0.15 mag .Table 1 lists the corrected values for the GaussianGCLF parameters of the ACSVCS galaxies. Updatedvalues for the evolved-Schechter function fits presentedby Jord´an et al. (2007b) will be presented elsewhere. TheGaussian parameters shown in Table 1 are the ones con-sidered for this publication and they should be used forfuture reference. This table includes, for all the ACSVCSgalaxies: the B -band apparent magnitude from Binggeliet al. (1985), the estimated GCLF parameters in bothbands, the fraction of objects that are considered to becontaminants, and the total number of globular clustercandidates (including contaminants). Table 2 presentsthe equivalent information computed for the ACSFCSgalaxies, including the B -band absolute magnitude fromFerguson (1989a). Figure 3 shows the z and g -band Fig. 4.—
Left: Estimate of Gaussian dispersion in the z band, σ z , vs. the same quantity in the g band, σ g , for the GCLFsof our Fornax sample. Uncertainties are 1 σ . The line marks theone-to-one correspondence between these two quantities. Right:Difference between estimates of Gaussian means in the g and z bands, µ g − µ z , vs. the mean color h g − z i of the GC systemsof our sample galaxies. Uncertainties are 1 σ . The line marks theone-to-one correspondence between these two quantities. GCLF histograms of the sample galaxies, ordered by de-creasing apparent B -band total luminosity. The dashedcurve corresponds to the intrinsic Gaussian componentgiven by Equation 3 and the parameters in Table 2. TheGaussian component multiplied by the expected com-pleteness is represented by the dotted curve, and a kerneldensity estimate of the expected contamination in thesample appears as a solid gray curve. The solid blackcurve is the sum of the solid gray and dotted curves,and corresponds to the net distribution for which thelikelihood in Equation 2 is maximized. The name andapparent B magnitude of the galaxy are indicated in theupper left corner of the left panel, where we also quotethe total number of sources in each histogram and thebin width h . The width of the bins, used only for dis-play purposes here, follows the rule h = 2( IQR ) N − / ,where ( IQR) is the interquartile range of the magnitudedistribution and N is the total number of objects in eachGC sample (Izenman, 1991).As a sanity check of our fitting procedure, in the left-hand side of Figure 4 we compare the Gaussian disper-sion inferred from the GCLF fit in each band, σ g vs. σ z , including only data from the Fornax sample. In theright-hand side of the same figure we have plotted thedifference between estimates of Gaussian means in the g and z bands ( µ g − µ z ), vs. the mean color h g − z i ofthe GC systems of our sample galaxies. From the verytight correlation between the measurements in differentbands we conclude that the GCLF fitting procedure isinternally consistent and also that our error estimationsare realistic. THE σ − M B,gal
RELATION
One of the main results discussed in Jord´anet al. (2006, 2007b) is the existence of a strong corre-lation between the dispersion of the GCLF σ , and the B -band absolute magnitude of the host galaxy M B,gal ,with brighter galaxies showing higher dispersion values.Even though some suggestive evidence on this respectwas previously presented by other authors (e.g. Kundu& Whitmore, 2001) the high precision and homogene-ity of our ACS/HST data unveiled the σ − M B,gal cor-relation as a general trend in GC systems, which waslater extended to still higher galaxy luminosity by Har-ris et al. (2009) using 5 giant elliptical galaxies in theComa cluster. Figure 5 shows this correlation for allCLF as distance indicator 5the 132 galaxies in our sample in both bands, now us-ing the homogeneous z -band absolute magnitudes de-rived from the apparent magnitudes estimated by Fer-rarese et al. (2006) and Cˆot´e et al. (2010, in prepara-tion) and the corresponding distance moduli publishedby Blakeslee et al. (2009). These values were correctedfor reddening assuming A z = 1 . E ( B − V ) (Ferrareseet al. 2006) where the value of E ( B − V ) was taken fromSchlegel et al. (1998). In this figure we have used differ-ent symbols in order to identify the galaxies accordingto their morphological classification, but no particulartrend related to this property seems to be obvious. Thestraight lines drawn in the panels correspond to error-weighted linear characterizations of these trends: σ z = (1 . ± . − (0 . ± . M z,gal + 22) (4)and σ g = (1 . ± . − (0 . ± . M z,gal + 22) . (5)We have excluded from these fits three galaxies forwhich no z-band magnitudes are available: VCC1535,VCC1030, and FCC167. Although shown in Figure 5,FCC21 (=NGC1316) is also not included on the fits be-cause the observed GC system in this galaxy is highlyinfluenced by interaction and proximity with its satel-lite galaxies, and therefore our GCLF fit is not reliable.Unlike Jord´an et al. (2006, 2007b) we have now also ex-cluded from the analysis four galaxies in the Virgo clus-ter (VCC1297, VCC1199, VCC1192 and VCC1327) andtwo galaxies in Fornax (FCC202 and FCC143) becausetheir GC systems appear to be contaminated by theirproximity to massive ellipticals. All these galaxies arenonetheless retained in the Tables for completeness.Equations 4 and 5 confirm the trend previously ob-served in Virgo, and with higher statistical significance,by including the Fornax data. This result shows by itselfthat the GCLF parameters are not universal and dependat least on one parameter, i.e. the luminosity of the par-ent galaxy, adding an additional feature that needs to beaccounted for by theories aiming to explain the shape ofthe GCLF.When the data corresponding to each cluster are fittedindependently the linear characterizations obtained are,in the case of Virgo: σ z = (1 . ± . − (0 . ± . M z,gal + 22) , (6) σ g = (1 . ± . − (0 . ± . M z,gal + 22); (7)and for the Fornax cluster: σ z = (1 . ± . − (0 . ± . M z,gal + 22) , (8) σ g = (1 . ± . − (0 . ± . M z,gal + 22) . (9)This translates into a 0 . − . mag difference in dis-persion at M z ∼
22, and also shows that the linear fitsderived from both sets of data are equivalent within theuncertainties.As discussed in Jord´an et al. (2006) it is rather straight-forward to link this trend in luminosity dispersion witha similar trend in the mass distribution of GCs. It
Fig. 5.—
Top: GCLF dispersion σ z , inferred from Gaussian fitsto the z -band data, vs. galaxy M z,gal . The dashed line correspondsthe linear relation between σ z and M z,gal in eq. 4. Bottom: Samecomparison, but for the Gaussian dispersion of the g -band GCLFs, σ g . The dashed line represents eq. 5. In both panels the blacksymbols correspond to Virgo galaxies, and the red ones to thesample in the Fornax cluster. We have morphologically separatedthe galaxies into elliptical (circles), lenticular (triangles), and dwarf(squares) galaxies. is well known that giant galaxies tend on average tohave more metal-rich GC populations when compared todwarfs, showing also larger dispersions in metallicity (seee.g. Peng et al. 2006). This result, added to the depen-dence of the cluster mass-to-light ratios (Υ) on metallic-ity, opens the possibility that the observed dispersion inthe value of σ might be metallicity-driven. These vari-ations in Υ have a strong dependence on wavelength.In bluer filters (the g -band in our case), variations of afactor of 2 or more in Υ can be observed in the typicalmetallicity range of GCs ( − ≤ [Fe/H] ≤ σ as a con-sequence of changes of Υ in our z -band measurements Villegas et al.should not be higher than ∼ σ observed in the upper panel ofFigure 5 reflects almost entirely a trend in the mass dis-tribution of globular clusters. Moreover, the very similarvalues obtained for σ in the z - and g -bands shows imme-diately that the trend of σ with M B cannot be generatedby metallicity-driven changes in Υ. A RELATIVE VIRGO-FORNAX DISTANCE ESTIMATION
Several methods have been used in order to obtain ac-curate distance estimations for both the Virgo and For-nax clusters, a task that is in general more easily achievedin the case of Fornax due to its more compact nature.The Virgo cluster extends for over 100 deg in the sky,showing a complex and irregular structure, with galaxiesof different morphological type showing different spatialand kinematic distributions. Working on these condi-tions the various distance estimators have reached differ-ent levels of accuracy (see Ferrarese et al. 2000a, 2000b).We will discuss now a compilation of results from theliterature, which are also summarized in Table 3.The HST Key Project to measure the Hubble con-stant aimed at obtaining accurate distances to galaxiesusing the period-luminosity relation for Cepheid vari-ables (their final results are presented in Freedman etal. 2001). It included the identification of Cepheids be-longing to 6 spiral galaxies in Virgo and 2 in Fornax, thatwere used to estimate the distance to their parent galax-ies, and then to the corresponding clusters. This resultedin distance moduli of ( m − M ) V = 30 . ± . mag and( m − M ) F = 31 . ± . mag for Virgo and Fornax re-spectively, which translates into a relative distance mod-ulus of ∆( m − M ) = 0 . ± . mag .D’Onofrio et al. (1997) derived the relative distancebetween Virgo and Fornax by applying the D n − σ (Dressler et al., 1987) and the fundamental plane (Djor-govski & Davis, 1987) relations to a homogeneous sampleof early-type galaxies. The two distance indicators gaveconsistent results with a relative distance modulus of∆( m − M ) = 0 . ± . mag . These results are in closeagreement with the value ∆( m − M ) = 0 . ± . mag later published by Kelson et al. (2000) obtained also byusing the fundamental plane and D n − σ relations builtfrom data calibrated by the aforementioned Cepheid dis-tances to spiral galaxies in both Virgo and Fornax.The planetary nebula luminosity function (PNLF) hasalso been used for measuring distances in the local Uni-verse. Ciardullo et al. (1998) determined a distancemodulus of ( m − M ) V = 30 . ± . mag to M87, ingood agreement with previous measurements (e.g. Ja-coby et al., 1990). McMillan et al. (1993) used thePNLF to determine the distance to three galaxies inFornax, obtaining a mean distance to the cluster of( m − M ) F = 31 . ± . mag . If we consider M87 to beat the center of Virgo, the corresponding relative distancemodulus would be ∆( m − M ) = 0 . ± . mag . Fer-rarese et al. (2000a) calibrated literature measurementsof the PNLF using Cepheids, which led them to estimatea relative distance modulus between Virgo and Fornax of∆( m − M ) = 0 . ± . mag when considering the A-subcluster as indicative of the distance to Virgo.Earlier relative distance modulus results derived by us-ing the GCLF as distance indicator present some hintsof disagreement with the other estimations discussed here. Even though they were working with small andrather heterogeneous samples, previous studies tend toput this value around a very low ∆( m − M ) ∼ . mag (e.g. Kohle et al. 1996, Blakeslee & Tonry 1996, Ferrareseet al. 2000a, Richtler 2003).One of the most reliable distance estimators when itcomes to population II samples is the surface bright-ness fluctuations (SBF) method due to its high internalprecision. The ACS Virgo and Fornax clusters surveys,among whose aims is studying GC properties and mea-suring surface brightness fluctuations, provide us withthe ideal data for comparing the properties of the GCLFas a distance estimator with SBF results. We will discussthese results separately in the next session. SBF distances
The method of SBF was first introduced by Tonry& Schneider (1988), and uses the fluctuations producedin each pixel of an image by the Poissonian distribu-tion of unresolved stars in a galaxy in order to estimatethe distance to the object. The amplitude of those sur-face brightness fluctuations normalized to the underlyingmean galaxy luminosity are inversely proportional to dis-tance and can therefore be used as a distance indicator(see Blakeslee et al. 1999 for a review).The distances to the Virgo galaxies included in theACSVCS have been measured using the SBF method.Mei et al. (2005a) describes the reduction procedure usedfor the surface brightness analysis of the ACSVCS data,and Mei et al. (2005b) presents the calibration for giantand dwarf early-type galaxies. Finally, Mei et al. (2007)introduces the distance catalog for a total 84 galaxies(50 giants and 34 dwarf) for which the SBF method wassuccessfully implemented, delivering at the same timea three dimensional map of the structure of the Virgocluster. These distance values were later updated andthe measurements extended to include the 43 early-typegalaxies of the ACSFCS in Blakeslee et al. (2009). In ouranalysis we will use the consistent set of Virgo and For-nax distances presented by the later publication. Whenno SBF distance is available for one of our sample galax-ies, we assume it is located at the mean Virgo distance(( m − M ) = 31 . mag ) adopted by Mei et al. (2007).This estimate is based on ground-based I-band SBF mea-surements calibrated against Cepheids distances (Tonryet al. 2000, Freedman et al. 2001).From their SBF measurements Blakeslee et al. (2009)derives a relative Virgo-Fornax distance modulusof ∆( m − M ) = (0 . ± . mag , which locatesthe Fornax cluster at a distance of d F = 20 Mpc(( m − M ) F = 31 . mag ). This value is in good agree-ment with the relative distance moduli derived fromthe other distance estimators discussed above andsummarized in Table 3, but it is significantly moreprecise. µ z as Distance Indicator One of the main problems in understanding the prop-erties of the turnover of the GCLF as distance indicatoris the lack of homogeneity in the data. The most com-prehensive compilation of recent data (mainly HST ob-servations) was presented by Richtler (2003), includinga total of 102 turnover magnitudes coming from at least8 different publications. This inhomogeneity introducesCLF as distance indicator 7
Fig. 6.—
GCLF turnover magnitude, µ z , inferred from Gaussianfits to the z -band data, vs. z -band galaxy absolute magnitude M z,gal , for all the galaxies in the ACS Virgo (black symbols) andFornax (red symbols) cluster surveys. The lines represent a si-multaneous error-weighted linear fit performed over both samples,that corresponds to µ z = (23 . ± .
11) + (0 . ± . M z,gal ,plus and offset of ∆( m − M ) = 0 . ± . mag for the galaxiesin Fornax. The sample has been morphologically separated intoelliptical (circles), lenticular (triangles), and dwarf (squares)galaxies. a major source of uncertainty in the analysis, as one hasto rely on each author’s results irrespective of the factthat they might not be using the same procedure to re-duce the data, the observations might not be on the samephotometric band, and they might not even be using thesame analytic form to fit the GCLF.The data we are presenting here are the largest andmost homogeneous set of GCLF fits available to date.Our photometry is also deep enough to cover the GCLFat least 2 magnitudes past the turnover, therefore weare able to obtain reliable estimates of this parameter.In Figure 6 we have plotted the GCLF turnover magni-tude against the z -band absolute magnitude of the par-ent galaxy. The lines show the best linear fit p ( M z,gal )to each cluster’s data, derived by minimizing the valueof χ calculated as: χ = n V X i =1 " µ iz,V − p ( M iz,gal,V ) δ ( µ iz,V ) + n F X j =1 " ( µ jz,F − ∆) − p ( M jz,gal,F − ∆) δ ( µ jz,F ) (10)where the two sums are over the n V and n F galaxiesin Virgo and Fornax respectively, δ ( µ z ) is the estimatederror in µ z , and the offset ∆ = ∆( m − M ) correspondsto the relative distance modulus. In this equation eachone of the M z,gal components was estimated as: M iz,gal = m iz,gal − ( m − M ) V − A iz (11)where ( m − M ) V =31.09 mag is the assumed mean dis-tance modulus to the Virgo cluster. The four galaxies be-longing to the W’ cloud in our Virgo sample (VCC538,VCC571, VCC575, VCC731 and VCC 1025) were ex-cluded from all our distance estimation fits as they areknow to be located much further ( D ∼
23 Mpc) than themean Virgo distance.We have found that the best fit model for Eq. 10 cor-responds to µ z = (23 . ± .
11) + (0 . ± . M z,gal for a value of ∆( m − M )= 0.20 ± mag , where theerror was estimated using bootstrap resampling of thedata. This relative distance modulus represents a factor ∼ ∼ m − M )= 0.42 mag derived by using the SBF method with the same data.It is important to stress that this discrepancy cannot beattributed to the data itself, because we are now using alarge sample of highly homogeneous data. Also the factthat the z -band absolute magnitudes of the galaxies inboth samples were derived from equivalent observationsand performing essentially the same analysis, minimizesthe amount of possible biases.On the other hand, we are aiming to establish the levelof precision at which µ might be useful as a distanceindicator and therefore it seems natural to calibrate itagainst a parameter that is distance independent, whichis not the case for M z,gal . The GCLF dispersion, σ , ap-pears like a good choice due to the already establishedcorrelation between σ and M z,gal . In Figure 7 we haveplotted µ z against σ z for the complete sample in Virgo(black) and Fornax (red), separating the galaxies by mor-phological type. A χ minimization equivalent to Equa-tion 10 was also performed in this case, obtaining as thebest fit model: µ z = (22 . ± . − (0 . ± . σ z . Inthis case the offset between both samples corresponds to∆( m − M )= 0.21 ± mag , where the error was es-timated performing a bootstrap resampling of the data.This independent fit delivers a relative distance modulusthat is consistent with the previously derived value.The observed difference between SBF and GCLFdistances has already been reported by Richtler(2003), attributing this phenomena to the presence ofintermediate-age GCs, which might contaminate thesample. Our sample is made up exclusively of early typegalaxies, which are old stellar systems where the pres-ence of intermediate-age clusters is rarely observed (al-though some cases have been reported in the literature,see e.g. Goudfrooij et al. 2001 for the case of NGC1316 =FCC21, and Puzia et al. 2002 for NGC4365 = VCC731),so it is unlikely that this is the reason of the observed dis-crepancy. Ferrarese et al. (2000a) have consistently re-ported discrepancies between their GCLF estimated dis-tances and those obtained from other estimators (partic-ularly SBF and PNLF). They found the GCLF turnoverin Fornax to be a full 0.5 mag brighter than the value ob-served in Virgo. The internal errors in the GCLF mea-surements and the expected uncertainty due to clusterdepth effects were not found to be enough to explain thescatter in their observations, suggesting the existence ofa second parameter driving the GCLF turnover magni- Villegas et al. Fig. 7.—
GCLF turnover magnitude, µ z , vs. GCLF disper-sion, σ z , both inferred from Gaussian fits to the z -band data,for all the galaxies in the ACS Virgo (black symbols) and For-nax (red symbols) cluster surveys. The sample has been mor-phologically separated into elliptical (circles), lenticular (trian-gles), and dwarf (squares) galaxies. The lines represent a si-multaneous error-weighted linear fit to the data correspondingto µ z = (22 . ± . − (0 . ± . σ z , with an offset of ∆ µ z =0 . ± .
04 for the Fornax data. tude.One obvious way to explain the observed discrepancybetween GCLF and SBF measurements would be a meanage difference for the Virgo and Fornax cluster galax-ies (i.e., the Fornax cluster galaxies might be youngerby some amount, leading to a brighter turnover). Thekey question, then, is determining the age difference thatwould be needed to explain the observed ∼ mag dif-ference. According to the Bruzual & Charlot (2003)models, for a metallicity of Z = 0 .
004 and a Salpeter(1955) initial mass function, the observed offset wouldbe consistent with an age of roughly 9 Gyr for the For-nax cluster when arbitrarily assuming an age of 12 Gyrfor Virgo. This age difference would also translate intoslightly bluer mean colors for the Fornax GCs, whichshould be on average ∼ mag bluer than their Virgocounterparts at a fixed galaxy mass. Performing a linearfit to the GCs mean color h g − z i vs. M z,gal correla-tion of our data we found that both clusters could followthe same trend but including an offset of 0 . ± . mag to redder colors in the case of Virgo. Although al-most consistent with zero, this value is also consistentwith the expected color discrepancy given by the neces-sary age difference. The SBF technique, in which thefluctuations are calibrated against a measure of the stel-lar populations (i.e., color), would have this difference, ifreal, accounted for. The Observed Dispersion on the Value of µ z A relatively large scatter can be observed in theturnover magnitude values displayed in Figure 6. In thissubsection we want to address the question of how muchof this dispersion is intrinsic to the sample and how muchis the result of observational effects. The histograms inFigure 8 give a better illustration of this scatter, wherewe have plotted the distribution of magnitudes aroundthe mean turnover magnitude of each sample, estimatedthough a 3-sigma clipping algorithm. Subtracting themean turnover magnitudes of both samples we obtain:(¯ µ gF − ¯ µ gV ) = 0 . mag and (¯ µ zF − ¯ µ zV ) = 0 . mag ,which delivers a first-order estimate of the relative Virgo- Fig. 8.—
Spread in magnitude around the weighted meanturnover magnitude, for Virgo (top) and Fornax (bottom) in the g (left) and z (right) bands. Fornax distance modulus. We estimate the observed dis-persion on the right ( z -band) panels of Figure 8 in 0.31 mag and 0.28 mag , for Virgo and Fornax respectively,also using a 3-sigma clipping algorithm. We are moreinterested on studying the dispersion on the z -band be-cause is much less sensitive to metallicity variations thanthe g -band.There are then three main factors driving the spread:cluster depth, measurement errors and the intrinsic scat-ter in the turnover magnitude. From their 3D map ofthe Virgo cluster, Mei et al. (2007) have determined thatthe back-to-front depth of the cluster measured from oursample of galaxies is 2.4 ± ± σ of the intrinsicdistance distribution). At the Virgo distance this trans-lates into a dispersion due to line of sight effects of ∼ mag . For the Fornax cluster, Blakeslee et al. (2009) esti-mated a depth of 2.0 +0 . − . Mpc ( ± σ of the distance dis-tribution in the line-of-sight), equivalent to a dispersionof ∼ mag . Therefore for both clusters, the observeddispersion is significantly higher than the one expectedfrom the cluster depth only.Given the observational errors and the known depthsof the two clusters, we would like to determine whetherthere is any intrinsic dispersion in the value of µ . In orderto do that we simulated a distribution of N galaxies (withN being 89 and 43 for Virgo and Fornax respectively)with roughly the same intrinsic turnover magnitude (weincluded a slight trend in luminosity derived from thelower panel of Figure 9), and we assigned them a randomdistance by using a Gaussian depth distribution with ap-propriate width (0.075 mag for Virgo and 0.05 mag forFornax). An additional random error was added to thisdistribution based on the observed uncertainties of oursamples. The final distribution of magnitudes was thenused to measure the dispersion of the simulated samplealso by using a 3-sigma clipping algorithm. This proce-dure was iterated 10000 times for each sample, deliveringa mean expected dispersion in the value of µ of 0.22 mag for Virgo, and 0.23 mag for Fornax. These values areCLF as distance indicator 9lower than the dispersion measured in our samples, so weadded an additional intrinsic dispersion term to the sim-ulations until the observed dispersion was reached. Thisdifference allows for an additional dispersion of 0.21 mag in the case of Virgo and 0.15 mag for the Fornax cluster,which can not be accounted by the cluster depth or theobservational errors alone, and therefore corresponds toan intrinsic dispersion in the value of µ .The z -band histograms shown in Figure 8 are not sym-metric around zero, a higher dispersion can be observedfor positive values of ( µ z − ¯ µ z ). This is consistent withthe fact that the GCLF parameters will always be moreprecisely determined for galaxies with larger GC systemsand they dominate the estimation of an error-weightedmean. As we will discuss in § µ in these systems is responsible for the largerscatter for the positive values of ( µ z − ¯ µ z ). We stressthat, as mentioned above, in the simulations done to es-timate the intrinsic dispersion this slight trend of µ with M z,gal is taken into account. THE UNIVERSALITY OF M TO The use of the GCLF as a distance indicator is basedon the assumption of a universal value of M T O , which hasindeed been shown to be fairly constant (within ± M T O on fac-tors such us the luminosity of the parent galaxy, Hubbletype, mean color of the GC system, and environment,that might lurk in the observed first-order constancy of M T O .Probing for a dependence on Hubble type is importantbecause the usual procedure is to use the Milky Way andM31 (both spiral galaxies) data in order to calibrate theGCLF in distant ellipticals. Our sample consists exclu-sively of early-type galaxies, so we cannot study the effectthat the Hubble type might have on the value of M T O .However, we will discuss this later from the point of viewof the metallicity, as the differences in the GCLF as func-tion of the Hubble type have been attributed to metallic-ity variations between the galaxies (Ashman et al., 1995).We will now address the influence of these factors on ourobserved non-universal GCLF.
Luminosity
The question of whether bright galaxies do have thesame M T O as faint galaxies is particularly interesting tostudy now that the correlation between σ and M gal hasbeen clearly established. Whitmore (1997) has claimedthat dwarf ellipticals have values of M VT O which areroughly 0.3 mag fainter than bright ellipticals, which waspreviously also mentioned by Durrell et al. (1996). Inprinciple this should not represent a problem for the useof the GCLF as a distance indicator, as the method ismostly concentrated on massive galaxies which can betraced to larger distances. Jord´an et al. (2006, 2007b)have also noticed that the turnover mass is slightlysmaller in dwarf systems ( M B ≥ −
18) compared to moremassive galaxies (see also Miller & Lotz (2007), showing
Fig. 9.—
Top: GCLF absolute z -band turnover magnitude( M zTO ) derived from SBF distances (Blakeslee et al. 2009) vs.the absolute z -band magnitude of the parent galaxy ( M z,gal ),for all the galaxies in the ACS Virgo (black) and Fornax (red)cluster surveys. The error-weighted linear fit corresponds to: M zTO = ( − . ± .
18) + (0 . ± . M z,gal . The sample hasbeen morphologically separated into elliptical (circles), lenticular(triangles), and dwarf (squares) galaxies. Bottom: Weighted meanturnover magnitude ( ¯M zTO ) calculated in 1 mag wide bins (contin-uous lines) and over the whole magnitude range (dotted lines), forthe Virgo (black) and Fornax (red) sample. The blue lines alsoshow the corresponding weighted mean values but using the com-bined sample. that this might be partly accounted for by the effects ofdynamical friction.We investigate a possible dependence of µ on M z,gal in Figure 9, which is equivalent to Figure 6 but withthe observed turnover magnitudes now transformed toabsolute turnover magnitudes using SBF distances (Meiet al. 2007, Blakeslee et al. 2009). The observed valuesof µ are relatively homogeneous in the range of M z,gal covered by our observations, between M z,gal ∼ −
24 and M z,gal ∼ −
17, however a tendency for dwarf galaxies toshow slightly less luminous turnover magnitudes seems tobe present. This tendency is characterized by the linearfit: M zT O = ( − . ± .
18) + (0 . ± . M z,gal . The in-terpretation of this trend needs to be considered carefullybecause, due to their low luminosity, dwarf galaxies havesmaller GC systems and the uncertainties on the deter-mination of µ T O are therefore higher. In order to lessenthis problem, in the lower panel of Figure 9 we have plot-ted the weighted mean absolute magnitude in intervalsof 1 magnitude compared to the weighted mean abso-lute magnitude calculated over the whole range of mag-nitudes. The lower luminosity bins tend to have meanmagnitudes that are lower than the general mean both in0 Villegas et al.each cluster and in the combined sample. At the lower lu-minosity bin (in the range between − < M z,gal < − mag lowerthan the general value of -8.51, and 0.3 mag lower thanthe most luminous bin (-24 < M z,gal < -23). From Fig-ure 9 we can confirm then the trend suggested by Whit-more (1997) and reported by Jord´an et al.(2006, 2007b),and we conclude that the luminosity (i.e. mass) of theparent galaxy has an effect on determining the peak ofthe GCLF, with fainter (lower-mass) galaxies having afainter GCLF turnover.Limiting the analysis to only the most massive galax-ies in the sample ( M z,gal < -21) we obtain an averageturnover magnitude of M z = − . mag with a dis-persion of 0.18 mag . These are the galaxies that couldpotentially be used as a distance indicator, and we cansee here that they would deliver an accurate distancemodulus estimation within the cosmic scatter of ± . mag . There are nonetheless environmental dependen-cies that need to be considered before extending thesefindings to other systems because, as we can also ob-serve from Figure 9, the galaxies in the Fornax clustershow absolute turnover magnitudes that are systemat-ically brighter than the Virgo sample. We discus thispoint further in section § Color
One of the most important requirements that a galaxyneeds to fulfill in order to make feasible the use of itsGCLF as a distance estimator is that its GC populationmust be old. The presence of an intermediate-age popu-lation will modify the GCLF by introducing clusters thatwill have brighter magnitudes than the older population.The GC color distribution of our sample of 89 galax-ies in Virgo was presented by Peng et al. (2006), whereit was observed that on average galaxies at all luminosi-ties in the samples ( − < M z,gal < −
17) appear to havebimodal or asymmetric GC color distributions. As dis-cussed in Villegas et al. (2010, in preparation) the useof stellar population models allow us to discard largeage differences between red and blue GCs if we assumethat the mass distribution of GCs does not have a de-pendence on [
F e/H ] inside a given galaxy. With only afew exceptions, the population of blue and red GC ap-pear to be coeval within errors for most of the galaxies,which lead us to concentrate on the problem of differentmetallicities between them. For giant ellipticals, this isalso supported by previous observational studies (Puziaet al. 1999; Beasley et al. 2000, Jord´an et al. 2002), al-though there are examples of massive galaxies that ap-pear to have formed GCs recently triggered by mergers(e.g. NGC 1316, Goudfrooij et al. 2001).With the goal of obtaining an improved calibration forthe value of M T O , Ashman et al. (1995) studied the ef-fects of metallicity on the GCLF showing that changes inthe mean metallicity of the cluster sample produce a shifton M T O , provided the mass distribution does not dependon [Fe/H]. According to Bruzual & Charlot (2003) mod-els, the expected change in z -band turnover magnitude, M zT O , over the range of GC mean metallicity is < mag , which is utterly negligible considering the observa-tional errors.From a different point of view Figure 10 shows thecorrelation between turnover magnitude µ and mean GC Fig. 10.—
Turnover magnitude vs. mean GC color relationshipfor our Fornax cluster data in g (top) and z -bands (bottom). Thelines show the error weighted fit to the data and have a slopes of0 . ± .
27 in the g -band and − . ± .
22 in the z -band. color h g − z i , in both g (top) and z -band (bottom) forall the galaxies in the Fornax sample. From this plotit can be observed that on average µ g remains constantas a function of h g − z i , but µ z tends to be brighterfor redder GC systems. The interpretation of this plotpresents a degeneracy between age and mass. If we as-sume that the Fornax galaxies, and by extension theirGC systems, are all basically coeval, this trend can beexplained by the fact that the z -band turnover betterreflects mass (as it is only loosely dependent on metal-licity), and therefore this is an indication that galaxieswith lower masses (as accounted by the mean metallic-ity of its GC system) might have less-massive turnovervalues, which translates into fainter µ z . In the g -band,and as a consequence also in the nearby V-band, thiseffect is canceled by the fact that the mass-to-light ra-tio gets lower for GCs in lower-mass, lower-metallicitygalaxies. Therefore the historically “constant turnovermagnitude” of the V-band GCLF might just be a conse-quence of the incidental cancellation of these two factorsat this wavelength. Environment
Even if we assume that the GC populations of galaxiesof all morphological types are formed with the same ini-tial mass function irrespective of available gas mass andmetallicity, there is still the environmental factor to playagainst the existence of a universal GCLF. The particularmedia in which the clusters are formed might affect theirCLF as distance indicator 11evolution, shaping an environment-dependent GCLF.Based on data from groups and clusters of galaxiesBlakeslee & Tonry (1996) found evidence that M T O be-comes fainter as the local density of galaxies increases.They used the velocity dispersion of groups of galaxiesin the local universe as a density indicator in order tocompare the values of M T O in different environments.Our data support the evidence presented by Blakeslee &Tonry (1996) in the sense they have also found a relativedistance modulus that is too small compared to the SBFmeasurements. The trend of M T O changing as a functionof environment (as accounted by velocity dispersion) isalso followed by our data. However, it is important tomention that in spite of its lower velocity dispersion theFornax cluster is denser than Virgo (Ferguson 1989b),and therefore the observed tendency seems to be morerelated to the total mass of the cluster than to local den-sity.Also, as discussed in § . − . × M ⊙ ; B¨ohringer et al. 1994; Schindleret al. 1999; McLaughlin 1999; Tonry et al. 2000; Fouqu´eet al. 2001), but it is clear that its total mass is nearlyan order of magnitude higher than the mass of Fornax( ∼ × M ⊙ , Drinkwater et al. 2001). The resultspresented by De Lucia et al. (2006) predict the expectedmean-age difference for clusters of these masses to be ∼ SUMMARY AND CONCLUSIONS
We used ACS/HST data in order to study the GCLF of89 early-type galaxies in the Virgo cluster and 43 galaxiesin the Fornax cluster, which constitute the most homo-geneous set of data used to date for this purpose. TheGCLF of these galaxies was fitted by using a maximumlikelihood approach to model the intrinsic Gaussian dis-tribution after accounting for contamination and com-pleteness effects. From the derived values of the turnovermagnitude and the dispersion of the Gaussian fits we con-clude that:1. The analysis of 43 early-type galaxies belongingto the Fornax cluster shows that the dispersion ofthe GCLF decreases as the luminosity of the hostgalaxy decreases, confirming our previous resultsobtained with Virgo galaxies (Jord´an et al. 2006,2007b).2. By using the GCLF turnover magnitude as a dis-tance indicator on our homogeneous data set we derive a relative distance modulus between theVirgo and the Fornax clusters of ∆( m − M ) GCLF =0 . ± . mag , which is lower than the one de-rived using SBF measurements on the same data,∆( m − M ) SBF = 0 . ± . mag .3. Setting the relative Virgo-Fornax distance as thatgiven by SBF implies a difference in the value of h µ T O i in the two closest clusters of galaxies, sug-gesting that this quantity is influenced by the en-vironment in which a GC system is formed andevolves. These results support a previous studyby Blakeslee & Tonry (1996), who found a corre-lation between GCLF turnover magnitude and ve-locity dispersion of the host cluster, in the sensethat galaxy clusters with higher velocity disper-sions (higher masses) host galaxies with fainterturnovers in their GC systems.4. The discrepancy in the absolute magnitude of theGCLF turnovers in Virgo and Fornax can be ac-counted for if GC systems in the Fornax clusterswere on average ∼ mag for Virgo and Fornax respectively. We show usingsimulations that these values can be only partiallyaccounted by the dispersion produced by clusterdepth and observational uncertainties. The addi-tional dispersion can be modeled by an intrinsicdispersion on the value of µ of 0.21 mag for theVirgo cluster and 0.15 mag for Fornax.6. The measured GCLF turnover is found to besystematically fainter for low luminosity galaxies,showing a ∼ mag decrease on dwarf systems,although we suffer from large uncertainties in thatgalaxy luminosity regime. The luminosity (i.e. ∼ mass) of the parent galaxy seems to play an im-portant role on shaping the final form of the lumi-nosity distribution. This might be at least partlyaccounted for by the effects of dynamical friction ifall other processes that contribute on shaping themass function (two-body relaxation, tidal shocks,etc.) were to lead to a roughly constant M T O (Jord´an et al. 2007b).7. Overall we find that GCLF parameters vary contin-uously and systematically as a function of galaxyluminosity (i.e. mass). The correlations we presenthere show no evidence for a dichotomy between gi-ant and dwarf early-type galaxies at M z ∼ − . M B ∼ −
18) in terms of their GC systems. This is2 Villegas et al.consistent with results presented in several recentstudies (e.g. Graham & Guzm´an, 2003; Gavazziet al. 2005, Cˆot´e et al., 2006), and is at odds withearlier claims by Kormendy (1985).Support for programs GO-9401 and GO-10217 was pro-vided through a grant from the Space Telescope Sci- ence Institute, which is operated by the Associationof Universities for Research in Astronomy, Inc., underNASA contract NAS5-26555. A.J. and L.I. acknowl-edge support from the Chilean Center of Excellencein Astrophysics and Associated Technologies (PFB 06)and from the Chilean Center for Astrophysics FON-DAP 15010003. Additional support for A.J. is providedby MIDEPLAN’s Programa Inicativa Cient´ıfica Mileniothrough grant P07-021-F. This research has made use ofthe NASA/IPAC Extragalactic Database (NED) whichis operated by the Jet Propulsion Laboratory, CaliforniaInstitute of Technology, under contract with the NationalAeronautics and Space Administration.
REFERENCESAshman, K.M., Conti, A., & Zepf, S.E., 1995, AJ, 110, 1164Beasley, M.A., Sharples, R.M., Bridges, T.J., Hanes, D.A., Zepf,S.E., Ashman, K.M., Geisler, D., 2000, MNRAS, 318, 1249Binggeli, B., Sandage, A., & Tammann, G.A., 1985, AJ, 90, 1681Blakeslee, J.P. & Tonry, J.L., 1996, ApJ, 465, 19Blakeslee, J.P., Ajhar, E.A., & Tonry, J.L., 1999, in Post-HipparcosCosmic Candles, ed. A. Heck & F. Caputo (Boston: Kluwer), 181Blakeslee, J.P., Jord´an, A., Mei, S., Cˆt´e, P., Ferrarese, L., Infante,L., Peng, E.W., Tonry, J.L., West, M.J., 2009, ApJ, 694, 556B¨ohringer, H., Briel, U. G., Schwarz, R. A., Voges, W., Hartner,G., & Trumper, J. 1994, Nature, 368, 828Bruzual, G. & Charlot, S., 2003, MNRAS, 344, 1000Brodie, J.P. & Strader, J., 2006, ARA&A, 44, 193Ciardullo, R., Jacoby, G.H., Feldmeier, J.J., Bartlett, R.E, 1998,ApJ, 492, 62Cˆot´e, P., Blakeslee, J.P., Ferrarese, L., Jord´an, A., Mei, S., Merritt,D., Milosavljevic, M., Peng, E.W., Tonry, J.L., & West, M.J.,2004, ApJS, 153, 223Cˆot´e, P., Piatek, S., Ferrarese, L., Jord´an, A., Merritt, D.,Peng, E.W., Ha¸segan, M., Blakeslee, J.P., Mei, S., West, M.J.,Milosavljevi, M., Tonry, J.L., 2006, ApJS, 165, 57Cˆot´e, P., Ferrarese, L., Jord´an, A., Blakeslee, J.P., Chen, C.W.,Infante, L., Merritt, D., Mei, S., Peng, E.W., Tonry, J.L. 2007,ApJ, 671, 1456De Lucia, G., Springel, V., White, S.D.M., Croton, D., Kauffmann,G., 2006, MNRAS, 366, 499Djorgovski, S., Davis, M., 1987, ApJ, 313, 59D’Onofrio, M., Capaccioli, M., Zaggia, S.R., Caon, N., 1997,MNRAS, 289, 847Dressler, A., Lynden-Bell, D., Burstein, D., Davies, R.L., Faber,S.M., Terlevich, R., Wegner, G., 1987, ApJ, 313, 42Drinkwater, M.J., Gregg, M.D., & Colless, M., 2001, ApJ, 548,L139Durrell, P.R., Harris, W.E., Geisler, D., & Pudritz, R.E., 1996, AJ,112, 972Elmegreen, B.G., & Efremov, Y.N., 1997, ApJ, 480, 235Fall, S. M. & Rees, M. J., 1977, MNRAS, 181, 37Fall, S. M. & Rees, M. J., 1985, ApJ, 298, 18Fall, S.M., Zhang, Q., 2001, ApJ, 561, 751Ferguson, H. C. 1989a, AJ, 98, 367Ferguson, H. C. 1989b, Ap&SS, 157, 227Ferrarese, L., Mould, J.R., Kennicutt, R.C., Huchra, J., Ford H.C.,Freedman, W.L., Stetson, P.B., Madore, B.F., Sakai, S., Gibson,B.K., Graham, J.A., Hughes, S.M., Illingworth, G.D., Kelson,D.D., Macri, L., Sebo, K., Silbermann, N.A. 2000a, ApJ, 529,745Ferrarese, L., Ford, H.C., Huchra, J., Kennicutt, R.C., Mould, J.R.,Sakai, S., Freedman, W.L., Stetson, P.B., Madore, B.F., Gibson,B.K., Graham, J.A., Hughes, S.M., Illingworth, G.D., Kelson,D.D., Macri, L., Sebo, K., Silbermann, N.A., 2000b, ApJS, 128,431Ferrarese, L., Cˆot´e, P., Jord´an, A., Peng, E.W., Blakeslee, J.P.,Piatek, S., Mei, S., Merritt, D., Milosavljevi´c, M., Tonry, J.L.,West, M.J., 2006, ApJS, 164, 334Fioc, M. & Rocca-Volmerange, B., 1997, A&A, 326, 950Fouqu´e, P., Solanes, J. M., Sanchis, T., & Balkowski, C. 2001,A&A, 375, 770 Freedman, W.L., Madore, B.F., Gibson, B.K., Ferrarese, L.,Kelson, D.D., Sakai, S., Mould, J.R., Kennicutt, R.C., Ford,H.C., Graham, J.A., Huchra, J.P., Hughes, S.M.G., Illingworth,G.D., Macri, L.M., Stetson, P.B., 2001, ApJ, 553, 47Gavazzi, G., Donati, A., Cucciati, O., Sabatini, S., Boselli, A.,Davies, J., Zibetti, S., 2005, A&A, 430, 411Gieles, M., Larsen, S.S., Scheepmaker, R.A., Bastian, N., Haas,M.R., Lamers, H.J.G.L.M., 2006, A&A, 446, 9Graham, A.W., & Guzm´an, R., 2003, AJ, 125, 2936Gnedin, O.Y. & Ostriker, J.P., 1997, ApJ, 474, 223Goudfrooij, P., Alonso, M.V., Maraston, C. & Minniti, D., 2001,MNRAS, 328, 237Harris, W.E., & Pudritz, R.E., 1994, ApJ, 429, 177Harris, W.E., 2001, in Star Clusters, ed. L. Labhardt & B. Binggeli(Berlin: Springer), 223Harris, W.E., Kavelaars, J.J., Hanes, D.A., Pritchet, C.J., Baum,W.A., 2009, AJ, 137, 3314Izenman, A.J., 1991, J. Am. Stat. Assoc., 86, 205Jacoby, G.H., Ciardullo, R., Ford, H.C., 1990, ApJ, 356, 332Jacoby, G.H., Branch, D., Ciardullo, R., Davies, R.L., Harris, W.E.,Pierce, M.J., Pritchet, C.J., Tonry, J.L., Welch, D.L., 1992,PASP, 104, 599Jord´an, A., Cˆot´e, P., West, M.J. & Marzke, R.O., 2002, ApJ, 576L,113Jord´an, A., Blakeslee, J.P., Peng, E.W., Mei, S., Cˆot´e, P., Ferrarese,L., Tonry, J.L., Merritt, D., Milosavljevic, M., & West, M.J. 2004,ApJS, 154, 509Jord´an, A., McLaughlin, D.E., Cˆot´e, P., Ferrarese, L., Peng, E.W.,Blakeslee, J.P., Mei. S., Villegas, D., Merritt, D., Tonry, J.L., &West, M.J. 2006, ApJ, 651, L25.Jord´an, A., Blakeslee, J.P., Cˆot´e, P., Ferrarese, L., Infante, L., Mei,S., Merritt, D., Peng, E.W., Tonry, J.L. & West, M.J., 2007a,ApJS, 169, 213Jord´an, A., McLaughlin, D.E., Cˆot´e, P., Ferrarese, L., Peng, E.W.,Mei. S., Villegas, D., Merritt, D., Tonry, J.L., & West, M.J.2007b, ApJS, 171, 101Jord´an, A., Peng, E.W., Blakeslee, J. P., Cˆot´e, P., Eyheramendy,S., Ferrarese, L., Mei, S., Tonry, J.L., West, M.J., 2009, ApJS,180, 54Kelson, D.D., Illingworth, G.D., Tonry, J.L., Freedman, W.L.,Kennicutt, R.C., Mould, J.R., Graham, J.A., Huchra, J.P.,Macri, L.M., Madore, B.F., Ferrarese, L., Gibson, B.K., Sakai,S., Stetson, P.B., Ajhar, E.A., Blakeslee, J.P., Dressler, A., Ford,H.C., Hughes, S.M.G., Sebo, K.M., Silbermann, N.A., 2000, ApJ,529, 768King, I.R., 1966, AJ, 71, 64Kissler, M., Richtler, T., Held, E.V., Grebel, E.K., Wagner, S.J.,Capaccioli, M., 1994, 1994, A&A, 287, 463Kohle, S., Kissler-Patig, M., Hilker, M., Richtler, T., Infante, L.,Quintana, H., 1996, A&A, 309, 39Kormendy, J. 1985, ApJ, 295, 73Kundu, A., Whitmore, B.C., 2001, 2001, AJ, 121, 2950Lamers, H.J.G.L.M. & Gieles, M. 2006, A&A, 455, L17McLaughlin, D. E., 1999, AJ, 117, 2398McLaughlin, D.E. & Fall, S.M., 2008, ApJ, 679, 1272McMillan, R., Ciardullo, R., Jacoby, G.H., 1993, ApJ, 416, 62Mei, S., Blakeslee, J.P., Tonry, J.L., Jord´an, A., Peng, E.W., Cˆot´e,P., Ferrarese, L., Merritt, D., Milosavljevic, M., & West, M.J.,2005a, ApJS, 156, 113.
CLF as distance indicator 13
Mei, S., Blakeslee, J.P., Tonry, J.L., Jord´an, A., Peng, E.W., Cˆot´e,P., Ferrarese, L., West, M.J., Merritt, D., & Milosavljevic, M.,2005b, ApJ, 625, 121Mei, S., Blakeslee, J.P., Cˆot´e, P., Tonry, J.L., West, M.J., Ferrarese,L., Jord´an, A., Peng, E.W., Anthony, A., & Merritt, D., 2007,ApJ, 655, 144Miller, B.W. & Lotz, J.M., 2007, ApJ, 670, 1074Peebles, P.J.E. & Dicke, R.H., 1968, ApJ, 154, 891Peng, E.W., Jord´an, A., Cˆot´e, P., Blakeslee, J.P., Ferrarese, L.,Mei, S., West, M.J., Merritt, D., Milosavljevic, M., & Tonry,J.L., 2006, ApJ, 639, 95Prieto, J.L. & Gnedin, O.Y., 2008, ApJ, 689, 919Puzia, T.H., Kissler-Patig, M., Brodie, J.P., & Huchra J.P., 1999,AJ, 118, 2734Puzia, T.H., Zepf, S.E., Kissler-Patig, M., Hilker, M., Minniti, D.,Goudfrooij, P., A&A, 391, 453Richtler T., 2003, LNP Vol. 635: Stellar Candles for theExtragalactic Distance Scale, 635, 281Salpeter, E.E., 1955, ApJ, 266, 713 Schlegel, D.J., Finkbeiner, D.P., & Davis, M., 1998, ApJ, 500, 525Secker, J., 1992, AJ, 104, 1472Secker, J. & Harris, W. E., 1993, AJ, 105, 1358Schindler, S., Binggeli, B., & B¨ohringer, H. 1999, A&A, 343, 420Springel, V., White, S.D.M., Jenkins, A., Frenk, C.S., Yoshida, N.,Gao, L., Navarro, J., Thacker, R., Croton, D., Helly, J., Peacock,J.A., Cole, S., Thomas, P., Couchman, H., Evrard, A., Colberg,J., Pearce, F., 2005, Nature, 435, 629Tonry, J. L., & Schneider, D. P. 1988, AJ, 96, 807Tonry, J. L., Blakeslee, J. P., Ajhar, E. A., & Dressler, A. 2000,ApJ, 530, 625Schlegel, D.J., Finkbeiner, D.P. & Davis, M., 1998, ApJ, 500, 525Vesperini, E., 2000, MNRAS, 318, 841Vesperini, E., 2001, MNRAS, 322, 247West, M.J., 1993, MNRAS, 265, 755Whitmore, B. C. 1997, in The Extragalactic Distance Scale, ed. M.Livio, M. Donahue, & N. Panagia (Baltimore: STScI), 254
TABLE 1Gaussian GCLF parameters for all ACSVCS galaxies. ID B gal µ g σ g µ z σ z ˆ β N (1) (2) (3) (4) (5) (6) (7) (8)VCC 1226 9.31 23.947 ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± CLF as distance indicator 15
TABLE 1Gaussian GCLF parameters for all ACSVCS galaxies.
VCC 1545 14.96 24.099 ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± B -band magnitude. (3) and (4) Maximum likelihood estimates of the Gaussian mean µ and dispersion σ of the g -band GCLF. (5) and (6) Same as cols. (3) and (4), but for the z band. (7) Fraction of the sample thatis expected to be contamination. (8) Total number N of all objects (including contaminants and uncorrected for incompleteness) with p GC ≥ .
5. (*) These galaxies were excluded from the analysis because of their close proximity to massive elliptical galaxies.
TABLE 2Gaussian GCLF parameters for all ACSFCS galaxies. ID B gal µ g σ g µ z σ z ˆ β N (1) (2) (3) (4) (5) (6) (7) (8)FCC 21 9.4 26.350 ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± B -band magnitude. (3) and (4) Maximum likelihood estimates of the Gaussian mean µ and dispersion σ of the g -band GCLF. (5) and (6) Same as cols. (3) and (4), but for the z -band. (7) Fraction of the sample thatis expected to be contamination. (8) Total number N of all objects (including contaminants and uncorrected for incompleteness) with p GC ≥ .
5. (*) These galaxies were excluded from the analysis because of their close proximity to massive elliptical galaxies.
TABLE 3Literature compilation of relative distance modulus between Virgoand Fornax clusters
Method ∆( m − M ) ReferenceCepheids 0 . ± .
20 1Fund. Plane 0 . ± .
15 20 . ± .
17 3PNLF 0 . ± .
21 4, 50 . ± .
10 6GCLF 0 . ± .
09 70 . ± .
11 80 . ± .
27 60 . ± .
28 9SBF 0 . ± ..