The Central Regions and the Globular clusters of Early-Type

Galaxies

Results from the ACS Virgo and [Fornax] Cluster Surveys

Andrés JordánESO - Garching

ajordan@eso.org

The SurveysSurvey of 100+43 early-type galaxies in Virgo+Fornax & their GCs with ACS on board HST: ACSVCS and ACSFCS

Scientific Objectives Include:

Properties of GCs in early type galaxies [ rh (Jordán et al 2005), colors (Peng et al 2006), masses (Jordán et al 2006; 2007), GCs & LMXBs (Jordán et al 2004, Sivakoff et al 2006), CMDs (Mieske et al 2006),...]

Surface Brightness Fluctuations and the Extragalactic Distance Scale [ Mei, Blakeslee, Tonry, et al. 2005ab, 2007]

The Structure of the Surface Brightness Profiles of Early Type Galaxies and their Nuclei [ Ferrarese et al 2006ab; Côté et al 2006]

The properties of new families of hot stellar systems [ Dwarf Globular Transition Objects (a.k.a. UCDs) -- Hasegan et al. 2005; Diffuse Star Clusters (a.k.a. Faint Fuzzies) -- Peng et al 2006]

The VCS/FCS Team

John P. Blakeslee

Patrick Côté (PI of VCS)

Laura Ferrarese

Leopoldo Infante

Andrés Jordán (PI of FCS)

Simona Mei

David Merritt

Eric W. Peng

John L. Tonry

Michael J. West

+ M. Takamiya, M. Hasegan, C. L. Sarazin, G. Sivakoff, D. E. McLaughlin, S. Piatek, S. Mieske, M. Milosavljevic, G. Djorgovski, M. Kissler-Patig, D. Villegas

The Galaxy Sample• 100 + 43 galaxies spanning a factor of ~ 500 in L

• -21.8 < MB < -15.1

• E, S0, dE, dE,N, dS012 JORDAN ET AL.

Fig. 3.— Distribution of Fornax Cluster Catalog (FCC) galaxies on the plane of the sky. The outlined region is the area surveyedin constructing the FCC (Ferguson 1989a). The symbol size is proportional to the galaxies’ blue luminosity. This figure shows the 340galaxies within the FCC survey limits that are classified as likely members (i.e., membership codes 1 and 2) of the Fornax cluster, with norestriction on morphological type. Red symbols denote the full sample of 43 early-type galaxies from the ACS Fornax Cluster Survey. Twogalaxies that are part of the ACS Fornax Cluster Survey but lie outside of the FCC survey region are labeled (NGC1340 and IC2006). Thescale of this figure is the same as Figure 2 in Cote et al. (2004).

In the time since the VCC was compiled, Virgo has been thesubject of numerous spectroscopic surveys. As a result, radialvelocities are now available for many additional galaxies (e.g.,Binggeli et al. 1993; Drinkwater et al. 1996). According toNED, 897 of the 1851 galaxies originally classified byBinggeli et al. (1987) as certain or possible members of Virgonow have published radial velocities. The upper histogram inFigure 1 shows the distribution of radial velocities for these897 galaxies, based on the latest NED data. For comparison,the filled histogram shows the distribution of radial velocitiesfor ACS Virgo Cluster Survey galaxies. It is clear that thevelocity distribution for the ACSVCS program galaxiesclosely resembles that of the entire Virgo sample.

The irregular structure of the cluster is apparent in Figure 2,which shows the distribution of 1726VCCmembers or possiblemembers on the sky (black circles). This is somewhat fewerthan the 1851 members or possible members listed in theVCC since we show only those galaxies that have !B1950 ! 5",meaning that they are not associated with the Southern Ex-tension of Virgo (Sandage et al. 1985). For comparison, the redsymbols show the 100 galaxies from the ACS Virgo ClusterSurvey, which fall in the declination range 7":2 # !B1950 # 18":2.

Sandage et al. (1985) examined the luminosity function ofVirgo Cluster galaxies in detail, including its dependence onmorphology. Numerous subsequent studies have used more

sensitive photographic plates (e.g., Impey et al. 1988; Phillippset al. 1998) or wide-field CCD mosaic cameras (Trentham &Hodgkin 2002; Sabatini et al. 2003) to explore the faint-endbehavior of the Virgo luminosity function and to search forbright galaxies with compact sizes or extreme surface bright-nesses that might have gone undetected by Sandage et al.(1985). While the precise form of the faint-end of the Virgoluminosity function remains a matter of debate, the varioussurveys generally agree on a high level of completeness of theVCC for BT P 18, the completeness limit estimated by Binggeliet al. (1987).

The upper panel of Figure 3 shows the luminosity functionof 956 early-type galaxies judged by Binggeli et al. (1987) tobe members of Virgo. The lower panel of this figure showsthe same luminosity function in logarithmic form. The filledhistogram (upper panel ) and filled circles (lower panel ) showthe corresponding luminosity functions for the ACS VirgoCluster Survey program galaxies, which have 9:31 # BT #15:97 (corresponding to a factor of $450 in luminosity). Notethat these galaxies are all considerably brighter than the VCCcompleteness limit of BT % 18 (indicated by the arrows inFig. 3). The inset in the upper panel of this figure shows thecompleteness of the ACS Virgo Cluster Survey as a functionof magnitude—the dotted curve shows the completeness in0.5 mag bins, while the dashed curve shows the variation in

Fig. 2.—Distribution of VCC galaxies on the plane of the sky, adapted from Binggeli et al. (1987). The symbol size is proportional to blue luminosity. This figurecontains a total of 1726 galaxies, with no restriction on morphological type, that are classified as members or possible members of the Virgo Cluster and havedeclinations greater than !B1950 ’ 5" (meaning that they are not associated with the Southern Extension of Virgo). The M and W Clouds as defined by Sandage et al.(1985) are shown by the dotted regions. Red symbols denote the full sample of 100 early-type galaxies from the ACS Virgo Cluster Survey.

ACS VIRGO CLUSTER SURVEY. I. 227No. 1, 2004

Observational Setting

Each galaxy is observed in the Sloan g & z bands (F475W & F850LP) in 1 orbit.

GC census is > 90% complete; GCs & nuclei partially resolved.

Filter combination ideal for SBF --> distances!

Côté et al 2004, ApJS, 153, 223; Jordán et al 2007, ApJS in press

1. Côté et al. (2004): I. Introduction to the Survey, ApJS, 153, 223

2. Jordán et al. (2004): II. Data Reduction Procedures, ApJS, 154, 209

3. Jordán et al. (2004): III. Chandra and HST Observations of Low-Mass X-ray Binaries and Globular Clusters in M87, ApJ, 613, 279

4. Mei et al. (2005) IV. Data Reduction Procedures for Surface Brightness Fluctuation Measurements with the Advanced Camera for Surveys, ApJS, 156, 113

5. Mei et al. (2005) V. SBF Calibration for Giant and Dwarf Early-Type Galaxies, ApJ, 625, 121

6. Ferrarese et al. (2006): VI. Isophotal Analysis and the Structure of Early-Type Galaxies, ApJS, 164, 334

7. Hasegan et al. (2005) VII. Resolving the Connection Between Globular Clusters and Ultra-Compact Dwarf Galaxies, ApJ, 627, 203.

8. Côté et al. (2006): VIII. The Nuclei of Early-Type Galaxies, ApJS, 165, 57

9. Peng et al. (2006) IX. The Color Distributions of Globular Cluster Systems in Early-Type Galaxies, ApJ, 639, 95

10. Jordán et al. (2005) X. Half-light Radii of Globular Clusters in Early-Type Galaxies: Environmental Dependencies and a Standard Ruler for Distance Estimation, ApJ, 634, 1002

11.Peng et al. (2006) XI. The Nature of Diffuse Star Clusters in Early-Type Galaxies, ApJ, 639, 828

12.Ferrarese, L., et al. (2006). A fundamental Relation Between Compact Stellar Nuclei, Supermassive Black Holes and Their host Galaxies, ApJ, 644, L21

13. Jordán, A., et al. (2006) Trends in the Globular Cluster Luminosity Function of Early-Type Galaxies, ApJ, 651, L25

The ACS Virgo Cluster Surveys: Publications

14. Jordán, A. et al. (2007) The ACS Virgo Cluster Survey. XII. The Luminosity Function of Globular Clusters in Early-Type galaxies, ApJS, in press

15.Mei, S., et al. (2007) The ACS Virgo Cluster. XIII. SBF Distance Catalog and the Three-dimensional Structure of the Virgo Cluster, ApJ, 655, 144

16.Mieske, S., et al. (2006) The ACS Virgo Cluster Survey. XIV. Analysis of Color-Magnitude Relations in Globular Cluster Systems, ApJ, 653, 193

17.Sivakoff, G. et al. (2007) The Low-Mass X-ray Binary and Globular Cluster Connection in Virgo Cluster Early-type Galaxies: Optical Properties, ApJ, in press.

The ACS Virgo Cluster Survey: Publications (cont)

The ACS Fornax Cluster Survey: Publications

1. Jordán, A. et al. (2007) The ACS Fornax Cluster Survey. I. Introduction to the Survey and Data Reduction Procedures, ApJS, in press [astro-ph/0702320]

2. ....stay tuned....

ACSVCS - The Structure of

Early-Type Galaxies:

Cores, Stellar Nuclei and

Everything in BetweenFerrarese et al. (2006): The ACSVCS VI. Isophotal Analysis and the Structure of Early-

Type Galaxies, ApJS, 164, 334Côté et al. (2006): The ACSVCS VIII. The Nuclei of Early-Type Galaxies, ApJS, 165, 57

Mihos et al 2005

2 deg ~ 600 kpc

Early-Type Galaxies: a Definition

• Binney & Tremaine (1994): Elliptical galaxies. These are smooth, featureless Population II systems containing little or no gas and dust

8 arcmin ~ 40

NGC 4526

VCC 1661

VCC 21

NGC 4371

M 87NGC 4350

NGC 4526

VCC 1661

VCC 21

NGC 4371

M 87NGC 4350

•The nuclear regions of galaxies are now thought to play a key role in galaxy formation and evolution (e.g. AGN feedback)

• Numerous correlations have been uncovered between the mass of the nuclear super massive black holes and global galaxy

properties (sigma, MB, ...)

• We have analyzed the surface brightness profiles for all 100 galaxies of the ACSVCS (Ferrarese et al 2006).

• The spatial resolution of ACS/HST allows the study of SB profiles from sub-arcsecond scales (10-100 pc) up to kpc scales, allowing us to probe the relation between nuclear and global structure

ACSVCS: Surface Brightness Profiles

The ACS Virgo Cluster Survey. VI. Isophotal Analysis and Surface Brightness Profiles 101

Fig. 111.— Representative g!band surface brightness profiles for six galaxies in the ACS Virgo Cluster Survey, from the brightest (VCC1226) to the faintest (VCC 1661) galaxy in the sample, plotted as a function of the geometric mean radius. All galaxies are “regular”ellipticals, in the sense of not displaying significant morphological peculiarities (with the exception of the possible presence of a nuclearcomponent). The galaxies are arranged, from top to bottom, in order of increasing total B-band magnitude (decreasing luminosity). Theyhave been shifted in the vertical direction for clarity; the value of the g!band surface brightness profile at 0!!.049 is listed on the left-hand-side next to each galaxy profile, and tickmarks on the ordinate axis are separated by 1 mag arcsec"2. For each galaxy, we overplot thebest-fit Sersic (dashed) and core-Sersic (solid) model, with addition of a King model for nucleated galaxies (VCC 1720, VCC 1422 andVCC 1661).

Ferrarese, Coté, Jordán, et al 2006, ApJS, 164, 334

Surface Brightness Profiles

I(r) = I !!1 +

"rb

r

#!$"/!

exp!!bn

"r! + r!

b

r!e

#1/(!n)$• Sérsic or Core - Sérsic with the addition of a King (1966) profile, characterized

by a concentration parameter c=log(rt/rc) and two scale parameters (the overall flux I and the half light radius rh)

SersicCore-Sersic

King Profile

I(r) = Ie exp

!!bn

"#r

re

$1/n

!1%&

• VCC Frequency of nucleation for ACSVCS galaxies: fN(VCC) ≃ 25%

• ACSVCS Frequency of nucleation for ACSVCS galaxies: fN(VCC) ≃ 66%-82%

•Refs: Carollo, Stiavelli & Mack 1998; Matthews et al 1999; Böker et al. 2002, 2004; Balcells et al. 2003, Lotz et al. 2004; Graham & Guzman 2003; Grant et al. 2005

Frequency of Nucleation

•Nuclei are on average ! 25" brighter than a typical globular cluster.

•The vast majority are resolved, excluding 2 body relaxation around a central SBH as the main formation mechanism.

•The scaling of half-light radii with luminosity is consistent with a formation scenario in which nuclei form through repeated mergers of globular clusters.

• Nuclei: 2 ! rh ~ 62 pc; < rh > = 4.2 pc

rh ∝ L(Nucleus)0.5

• Globular Clusters: < rh > = 2.7 pc

Radii of Nuclei in Early-Type Galaxies

ACSVCS - Central Massive Objects:

Connecting Stellar Nuclei and

Supermassive Black Holes

Ferrarese, L., et al. (2006). A Fundamental Relation Between Compact Stellar Nuclei, Supermassive Black Holes and Their host Galaxies, ApJ, 644, L21

Côté et al. (2006): The ACSVCS. VIII. The Nuclei of Early-Type Galaxies, ApJS, 165, 57

From Mass Deficit to Mass Excess10 JORDAN ET AL.

Fig. 1.— Representative surface brightness profiles for nine early-type galaxies from the ACSVCS spanning a factor of ! 460 in blueluminosity; the B"band magnitude of each galaxy is listed in the corresponding panel. In each panel, we show the azimuthally-averagedbrightness profile in the g475 and z850 bands plotted as a function of mean geometric radius (lower and upper profiles, respectively). Thesolid curves show Sesic models fitted to the profiles beyond ! 0.!!2-2!!. Note the gradual progression from a central light “deficit” to “excess”,with a transition at MB ! "20 (see Ferrarese et al. 2006a and Cote et al. 2006 for details).

Jord

án et al 2

007, A

pJS, in

press

Ferrarese et al 2006, A

pJS, 1

64, 3

34

Coté et al 2

006, A

pJS, 1

65, 5

7

Ferrarese & Merritt (2000), Gebhardt et al. (2000), Ferrarese & Ford (2005)

The M -! Relation for SBHs

The M -! Relation for Central Massive Objects

NGC 205

M33

Ferrarese et al 2006b

From ! to Mass: M = "Re!2/G

M CMO/ M Galaxy = 0.17% (0.06% - 0.50%)

Also: Coté et al. 2006; Wehner & Harris 2006; Rossa et al.2006.

• There appears to be a fundamental connection between nuclei, found predominantly in the fainter galaxies, and the SBHs found in bright galaxies. They both comprise the same fraction (0.2%) of the total galactic mass.

• Are nuclei the low-mass counterparts of the SBHs found in the brighter galaxies?

• Can nuclei and SBHs coexhist?

Ferrarese et al 2006, ApJ, 644, L21

The Luminosity (Mass) Distribution of GCs

Jordán, A., et al. (2006): Trends in the GC Luminosity Function of Early-Type Galaxies, ApJ, 651, L25

Jordán, A., et al. (2007): The ACSVCS. XII. The Luminosity Function of GCs in Early-Type Galaxies, ApJS, in press [astro-ph/0702496]

The GC[L/M]F

• We have analyzed the GCMF of 89 ACSVCS galaxies by fitting Gaussians and evolved Schechter Functions (Jordán et al 2006 ApJ, 651, L25; Jordán et al 2007, ApJS, in press [astro-ph/0702496])

JORDAN ET AL. 15

Fig. 8.— GCLFS!

Jordán et al 2007, ApJS, in press [astro-ph/0702xxx]

The GC[L/M]F

• We have uncovered a significant & remarkably regular correlation of ! with MB,gal

2962 KUNDU & WHITMORE Vol. 121

FIG. 6.ÈTop : vs. from the Gaussian !t to the V - and I-band GCLFs. Middle : Variation of and with the mean V [I color of the cluster system.pV

pI

pV

pIBottom : Variation of and with the absolute magnitude (mass) of the host galaxy. The width of the GCLF in the V and I bands appear to be wellp

VpIcorrelated, while there is a weak trend of the more metal-rich clusters in more luminous galaxies having wider GCLFs.

the GCLF turnover migrates to fainter numbers for moredistant galaxies. We can further check for the internal con-sistency of the GCLF and its utility as a distance indicatorby comparing the turnovers in V and I. In Figure 8 we plotthe turnover luminosity in the V band versus that in the Iband. It is immediately apparent that and are verym

V0 m

I0

tightly correlated. The uncertainties are larger for thefainter systems, as is only to be expected from the complete-ness limits.

Ashman, Conti, & Zepf (1995) showed that if the massfunction of GCs is universal, the position of the peak of theGCLF is slightly dependent on the metallicity ; for the Vand I bands it shifts to fainter magnitudes for more metal-rich systems, the e†ect being larger in V . In Figure 9 we plotthe variation in versus the mean metallicities fromm

V0 [ m

I0

Table 3 for candidates with mag. Wed(mV0 [ m

I0) \ 0.15

have also included M87 (Kundu et al. 1999) in the plots. It isevident that for both the variable width !ts and the““ constant width ÏÏ !ts the di†erence between the turnoversincreases with metallicity in a manner consistent with theAshman et al. (1995) prediction. The amplitude of this varia-tion is also consistent with the Ashman et al. values.

But how well do these turnover luminosities trace thedistance to the galaxy? While the recent compilations ofKavelaars et al. (2000) and Whitmore (1996) show that theGCLF is an excellent distance indicator Ferrarese et al.(2000), in their comparison of various distance indicators,

suggest that the utility of the GCLF as a distance indicatoris questionable. In order to test the consistency we comparethe GCLFs with the weighted distance moduli of individualgalaxies calculated by Ferrarese et al and the SBF distancesmeasured by Neilsen, Tsvetanov, & Ford (1999). We notethat in most cases Neilsen uses the same HST as we do. Thedistances measured by these two groups, and the Table 1distances are listed in Table 6 (cols. [2]È[4]).

To calculate the absolute magnitude of the turnoverluminosity we compared the GCLFs with the best deter-mined turnovers (i.e., uncertainty less than 0.1 mag) with theweighted distance moduli of three other distance indicatorsfrom Ferrarese et al. (2000) and Neilsen (1999). The turn-over magnitudes for both the !xed width and variablewidth cases along with the standard deviation and numberof galaxies used in calculating the di†erence are listed in theupper half of Table 5. It is evident that the GCLF turnoveris in excellent agreement with the distance measurementsusing other methods, and that the !xed width Gaussians aremore accurate than the variable width ones. In comparingthe Neilsen values with the Ferrarese et al. numbers (againrestricting the Neilsen sample to those with an uncertaintyof less 0.1 mag for the sake of consistency) we !nd that theuncertainty in the di†erence, 0.14 mag, is comparable withthe GCLF values (0.11 and 0.14). Thus the GCLF is asaccurate a distance indicator as the SBF. In fact, as theweighted Ferrarese et al. distances include SBF measure-

Kundu &

Whitm

ore

2001

Jordán et al 2006, ApJ, 651, L25Jordán et al 2007, ApS, in press

L26 JORDAN ET AL. Vol. 651

Fig. 1.—Gaussian dispersion, , vs. galaxy, , for the z-band GCLFs ofj Mz B, gal

89 ACSVCS galaxies. The GCLF width varies systematically, being narrowerin fainter galaxies. The two anomalously high points at andM p !21.2B, gal

!19.9 correspond to the galaxies VCC 798 and VCC 2095, both of which havelarge excesses of faint, diffuse clusters (Peng et al. 2006b). The large star isplotted at the spheroid luminosity (de Vaucouleurs & Pence 1978) and GCLFdispersion (Harris 2001) of the Milky Way. The large triangle marks the bulgeluminosity (Kent 1989) and GCLF dispersion (Harris 2001) of M31.

full list of GC candidates for each galaxy. We additionallyeliminate two galaxies for which we were unable to obtainuseful measurements of the GCLF parameters. This leaves afinal sample of 89 galaxies that are studied here and in J06.Also as part of the ACSVCS, we have measured the distances

to 84 of our target galaxies using themethod of surface brightnessfluctuations (SBF; Mei et al. 2006). We use these SBF distancesto transform the observed GC and galaxy magnitudes into ab-solute ones whenever possible. For those galaxies lacking anSBF distance, we adopt the mean distance modulus to the VirgoCluster: mag or Mpc (see MeiA(m!M) S p 31.09 ADS p 16.50

et al. 2005, 2006).We use an approach similar to that of Secker & Harris (1993)

to characterize the GCLFs; parametric models are fitted to theobserved luminosity functions via a maximum likelihoodmethod that takes into account photometric errors, incomplete-ness, and the luminosity function of contaminants. Full tech-nical details are given in J06, where we consider two parametricmodels for the GCLF. The first, on which this Letter will focus,is the standard Gaussian distribution,

2 !1/2 2 2dN/dz p N (2pj ) exp [!(z! m ) /2j ]. (1)tot z z z

The second is a simple analytical modification of a Schechter(1976) function designed to account for the effects of clusterevaporation (two-body relaxation) on a GC mass function thatis assumed to have initially resembled that of the young clustersforming today in local mergers and starbursts. Full details onthese two models are given in J06, where we fit each of themto the separate g- and z-band GCLFs of our 89 program gal-axies. In this Letter we present only the results of Gaussianfits to the z-band GCLFs.

3. RESULTS

Figure 1 shows our main result: GCLFs are narrower in lowerluminosity galaxies. The straight line in this plot of Gaussiandispersion against absolute galaxy magnitude shows the least-squares fit

j p (1.12! 0.01)! (0.093! 0.006)(M " 20). (2)z B, gal

It has been reported before that the GCLFs in lower lumi-nosity galaxies tend to show somewhat lower dispersions (e.g.,Kundu &Whitmore 2001). However, the size and homogeneityof the ACSVCS data set make this the most convincing dem-onstration to date of a continuous trend in GCLF shape overa range of!400 in galaxy luminosity. Monte Carlo simulationsand alternate constructions of GCLF samples show that theobserved decrease in dispersion is not an artifact of small-number statistics in the faint galaxies (J06).Past investigations have pointed to a dependence of the

GCLF dispersion on the Hubble type of the GC host galaxies(e.g., Harris 1991). Figure 1 includes data points at the locationof the bulge magnitude and GCLF dispersion of the MilkyWay(large star) and M31 (large triangle). Since both systems fallcomfortably on the relation defined by our data for early-typegalaxies, we conclude that the underlying fundamental corre-lation is one between j and , rather than between j andMB, gal

Hubble type.A natural question at this point is whether the observed trend

in GCLF dispersion with galaxy magnitude implies a similartrend in the GCmass function. This is not a foregone conclusionfor the following reason: GC systems are known to have sys-

tematically redder and broader (or more strongly bimodal) colordistributions in brighter galaxies than in faint ones (see, e.g.,Peng et al. 2006a). Equivalently, GCs in giant galaxies aremore metal-rich, on average, and have larger dispersions in[Fe/H] than those in low-mass dwarfs. Since cluster mass-to-light ratios, U, are functions of [Fe/H] in general, it is con-ceivable that the average GC U could change systematically ingoing from bright galaxies to fainter ones, and that the spreadof U-values within a single GC system could also vary sys-tematically as a function of galaxy magnitude. The possibilitythen exists that narrower GCLFs for faint galaxies might resultfrom these systematics in U combined with a more nearly in-variant spread in GC masses. We can show easily, however,that this is not the case.The systematics in U versus [Fe/H] just mentioned are also

a function of wavelength. In bluer filters, such as B, V, or g,mass-to-light ratios of old stellar systems do change signifi-cantly (increasing by factors of 2 or more) in going from clustermetallicities to , typical of GCs. But[Fe/H] " !2 [Fe/H] p 0at the much redder wavelengths of our z-band data (l !pivot

; Sirianni et al. 2005), this strong metallicity dependence˚9055 Aalmost completely disappears. We have used the PEGASE pop-ulation synthesis model of Fioc & Rocca-Volmerange (1997)to compute as a function of metallicity for clusters with aUz

Kennicutt (1983) stellar initial mass function (IMF) and variousfixed ages t. For Gyr, we find thatt p 13 U ! 1.6 Mz ,

at an extreme , decreasing to a minimum!1L [Fe/H] p !2.3,

of at , and then increasing!1U ! 1.5 M L [Fe/H] ! !0.7z , ,

slightly to at . In other words,!1U p 1.7 M L [Fe/H] p 0z , ,

we always have for any of the globular clustersU ! 1.6! 0.1z

in any of our sample galaxies, no matter how red or blue theclusters are, or how broad or narrow the GC color/metallicity

• This is driven by a model-independent steepening of the GCLF for M >~MTO

• Dynamical friction cannot account for the steepening at high masses

---> systematic variations in the initial cluster mass function? (probably!)

L28 JORDAN ET AL. Vol. 651

Fig. 3.—Slope of the power law that best fits our z-band GCLF data, , forbz

masses , plotted against host galaxy absolute5 63# 10 ! (M/M ) ! 2# 10,

magnitude, . The large star and triangle show b-values for the Milky WayMB, gal

and M31, respectively, measured in the same mass regime using the data fromHarris (1996) and Reed et al. (1994) assuming a V-band mass-to-light ratio

. The bright side of the GCLF is steeper in fainter galaxies.M/L p 2V

the GCLF become progressively steeper in fainter galaxies.However, various observational uncertainties make it difficultto determine precisely the form of the faintest tail of the GCLF.Thus, in J06 we show that good fits to our GCLFs can also beobtained using an alternate model with a universal exponentialshape at magnitudes fainter than the turnover and that the down-ward scatter in for faint galaxies persists in such a modelMTO

and so is not an artifact of any assumed Gaussian symmetry.Here we concern ourselves only with the brighter half of theGCLF, which is observationally better defined.We have performed maximum likelihood fits of exponential

models (corresponding to power-law mass0.4(b !1)zzdN/dz ! 10distributions, ) to the GCLFs at absolute mag-!bzdN/dM ! Mnitudes (cluster masses ! –5!8.7 " z " !10.8 3# 10 2#

) in 66 of our galaxies. Such distributions accurately610 M,

describe the bright sides of giant galaxy GCLFs (Harris &Pudritz 1994; Larsen et al. 2001), and with , they alsob ! 2z

give good matches to the mass functions of young star clustersin nearby mergers and starbursts (Zhang & Fall 1999).Figure 3 shows the results of this exercise. There is a clear

steepening in the power-law exponent, from in brightb ! 1.8z

galaxies to in the faintest systems. However the faintb ! 3z

side of the GCLF behaves in detail, the bright side alone sug-gests that smaller galaxies were unable to form very massiveclusters in the same relative proportions as giant galaxies.A potential complication here is dynamical friction. A cluster

of mass on an orbit of radius r in a galaxy with circularMspeed will spiral into the center of the galaxy on a timescaleVc

(Binney & Tremaine 1987). In the Milky Way!1 2t ! M r Vdf c

and larger galaxies, Gyr for all but the very mostt 1 13df

massive clusters at small radii, and thus dynamical friction doesnot significantly affect their GCLFs (e.g., Fall & Zhang 2001).In dwarfs with low , however, can be interestingly shortV tc df

for smaller GCs at larger r, suggesting, perhaps, that the processmight significantly deplete the bright side of the GCLF in smallgalaxies and contribute to the type of trend seen in Figure 3.However, Vesperini (2000, 2001) has modeled the GCLF evo-lution over a Hubble time in galaxies with a wide range ofmass, and his results strongly suggest that dynamical frictiondoes not suffice to explain our observations. In particular, thewidths of the Gaussian GCLFs in his models do not decrease,even in dwarf galaxies, to anywhere near the extent seen inthe data. Thus, any significant galaxy-to-galaxy variations inthe shape of the GCLF above the turnover mass probably reflectinitial conditions (see J06 for further discussion).In summary, the gradual narrowing of the GCLF as a func-

tion of galaxy luminosity, or the steepening of the mass dis-tribution above the classic turnover point, presents a new con-straint for theories of GC formation and evolution. In our view,it is the cluster formation process in particular that is likely tobe most relevant to the observed behavior at the high-mass endof the GCLF. Exactly what factors might lead to more massivegalaxies forming massive clusters in greater relative numbers,is an open question of some interest.

Support for program GO-9401 was provided through a grantfrom the Space Telescope Science Institute, which is operatedby the Association of Universities for Research in Astronomy,Inc., under NASA contract NAS5-26555.

Facility: HST(ACS/WFC)

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