Dean E. McLaughlin

The ACS Virgo Cluster Survey. X. Half-Light Radii of Globular Clusters in Early-Type Galaxies: Environmental Dependencies and a Standard Ruler for Distance Estimation

We have measured half-light radii, rh, for thousands of globular clusters (GCs) belonging to the 100 early-type galaxies observed in the ACS Virgo Cluster Survey and the elliptical galaxy NGC 4697. An analysis of the dependencies of the measured half-light radii on both the properties of the GCs themselves and their host galaxies reveals that, in analogy with GCs in the Galaxy but in a milder fashion, the average half-light radius increases with increasing galactocentric distance or, alternatively, with decreasing galaxy surface brightness. For the first time, we find that the average half-light radius decreases with the host galaxy color. We also show that there is no evidence for a variation of rh with the luminosity of the GCs. Finally, we find in agreement with previous observations that the average rh depends on the color of GCs, with red GCs being ~17% smaller than their blue counterparts. We show that this difference is probably a consequence of an intrinsic mechanism, rather than projection effects, and that it is in good agreement with the mechanism proposed by Jordan. We discuss these findings in light of two simple pictures for the origin of the rh of GCs and show that both lead to a behavior in rough agreement with the observations. After accounting for the dependencies on galaxy color, galactocentric radius, and underlying surface brightness, we show that the average GC half-light radii rh can be successfully used as a standard ruler for distance estimation. We outline the methodology, provide a calibration for its use, and discuss the prospects for this distance estimator with future observing facilities. We find rh = 2.7 ± 0.35 pc for GCs with (g - z) = 1.2 mag in a galaxy with color (g - z)gal = 1.5 mag and at an underlying surface z-band brightness of μz = 21 mag arcsec-2. Using this technique, we place an upper limit of 3.4 Mpc on the 1 σ line-of-sight depth of the Virgo Cluster. Finally, we examine the form of the rh distribution for our sample galaxies and provide an analytic expression that successfully describes this distribution.

MASSES OF STAR CLUSTERS IN THE NUCLEI OF BULGELESS SPIRAL GALAXIES

In the last decade star clusters have been found in the centers of spiral galaxies across all Hubble types. We here present a spectroscopic study of the exceptionally bright (10 6 –10 8 L� )butcompact( re � 5 pc) nuclear star clusters in very late type spirals with the Ultraviolet and Visual Echelle Spectrograph at the VLT. We find that the velocity dispersions of the nine clusters in our sample range from 13 to 34 km s � 1 . Using photometric data from the Hubble Space Telescope WFPC2 and spherically symmetric dynamical models, we determine masses between 8 ; 10 5 and 6 ; 10 7 M� . The mass-to-light ratios range from 0.2 to 1.5 in the I band. This indicates a young mean age for most clusters, in agreement with previous studies. Given their high masses and small sizes, we find that nuclear clusters

Dynamics of the Globular Cluster System Associated with M87 (NGC 4486). II. Analysis

We present a dynamical analysis of the globular cluster system associated with M87 (=NGC 4486), the cD galaxy near the dynamical center of the Virgo Cluster. The analysis utilizes a new spectroscopic and photometric database, which is described in a companion paper. Using a sample of 278 globular clusters with measured radial velocities and metallicities and new surface density profiles based on wide-field Washington photometry, we study the dynamics of the M87 globular cluster system both globally (for the entire cluster sample) and separately (for the metal-rich and metal-poor globular cluster samples). This constitutes the largest sample of radial velocities for pure Population II tracers yet assembled for any external galaxy. Our principal findings are summarized as follows:

The Efficiency of Globular Cluster Formation

The specific frequencies of globular cluster systems, SN ∝ tot/LV,gal ∝ Mgcs/Mstars, are discussed in terms of their connection to the efficiency of globular cluster formation in galaxy halos, which is claimed to reflect a generic aspect of the star formation process as it operates even at the current epoch. It is demonstrated that the total masses of GCSs are little affected by the dynamical destruction of low-mass clusters at small galactocentric radii. This permits direct, empirical estimates of the cluster formation efficiency by mass, cl ≡ M/M, even after 1010 yr of GCS evolution. However, the standard practice of using only the stellar luminosities of galaxies as indicators of their initial total gas masses (and thus relating SN to cl in one step) leads to serious conceptual problems, which are reviewed here. The first specific frequency problem, which is the well-known tendency for many brightest cluster galaxies to have higher than average SN, is a global one; the second specific frequency problem is a local one, in which the more extended spatial distribution of GCSs relative to halo stars in some (not all) bright ellipticals leads to SN-values that increase with radius inside the galaxies. Extending similar suggestions in the recent literature, it is argued that these trends in SN do not reflect any such behavior in the underlying cl; rather, both of these problems stem from neglecting the hot, X-ray emitting gas in and around many large ellipticals, and both may be alleviated by including this component in estimates of M. This claim is checked and confirmed in each of M87, M49, and NGC 1399, all of which have been thought to suffer from one or the other of these SN problems. Existing data are combined to construct GCS surface density profiles that extend over nearly the whole extents of these three galaxies, and a nonparametric, geometrical deprojection algorithm is developed to afford a direct comparison between the volume density profiles of their GCSs, stars, and gas. It is found, in each case, that ρcl ∝ (ρgas + ρstars) at radii beyond roughly a stellar effective radius, inside of which dynamical evolution may have depleted the initial GCSs. The constant of proportionality is the same in all three galaxies: cl = 0.0026 ± 0.0005. Taken together, these results suggest that GCSs generally should be more spatially extended than stellar halos only in gas-rich galaxies that also have a high global specific frequency. The implication that cl might have had a universal value is supported by global GCS data for a sample of 97 giant ellipticals, brightest cluster galaxies, and faint dwarfs. The total globular cluster populations in all of these early-type systems are in excellent agreement with the predictions of a constant cl at the level observed directly in M87, M49, and NGC 1399; all systematic variations in GCS specific frequency between galaxies are shown to result entirely from different relations, in different magnitude ranges, between M and the present-day LV,gal. An identical cl is also calculated for the Population II spheroid of the Milky Way and is indicated (although less conclusively) for the ongoing formation of open clusters. The inferred universal cluster formation efficiency, of 0.25% by mass, should serve as a strong constraint on general theories of star and cluster formation. The associated inference of a nonuniversal formation efficiency for unclustered stars is considered, particularly in terms of the suggestion that this might result, both in dwarf galaxies and at large galactocentric radii in the brightest ellipticals, from feedback and galactic winds. Implications for a merger-formation model of early-type GCSs, and for the proposed existence of intergalactic globulars in clusters of galaxies, are briefly discussed.

The ACS Virgo Cluster Survey. XII. The Luminosity Function of Globular Clusters in Early-Type Galaxies*

We analyze the luminosity function of the globular clusters (GCs) belonging to the early-type galaxies observed in the ACS Virgo Cluster Survey. We have obtained maximum likelihood estimates for a Gaussian representation of the globular cluster luminosity function (GCLF) for 89 galaxies. We have also fit the luminosity functions with an evolved Schechter function, which is meant to reflect the preferential depletion of low-mass GCs, primarily by evaporation due to two-body relaxation, from an initial Schechter mass function similar to that of young massive clusters in local starbursts and mergers. We find a highly significant trend of the GCLF dispersion σ with galaxy luminosity, in the sense that the GC systems in smaller galaxies have narrower luminosity functions. The GCLF dispersions of our Galaxy and M31 are quantitatively in keeping with this trend, and thus the correlation between σ and galaxy luminosity would seem more fundamental than older notions that the GCLF dispersion depends on Hubble type. We show that this narrowing of the GCLF in a Gaussian description is driven by a steepening of the cluster mass function above the classic turnover mass, as one moves to lower luminosity host galaxies. In a Schechter function description, this is reflected by a steady decrease in the value of the exponential cutoff mass scale. We argue that this behavior at the high-mass end of the GC mass function is most likely a consequence of systematic variations of the initial cluster mass function rather than long-term dynamical evolution. The GCLF turnover mass MTO is roughly constant, at MTO (2.2 ± 0.4) × 105 M☉ in bright galaxies, but it decreases slightly (by ~35% on average, with significant scatter) in dwarf galaxies with MB,gal -18. It could be important to allow for this effect when using the GCLF as a distance indicator. We show that part, although perhaps not all, of the variation could arise from the shorter dynamical friction timescales in less massive galaxies. We probe the variation of the GCLF to projected galactocentric radii of 20-35 kpc in the Virgo giants M49 and M87, finding that the turnover point is essentially constant over these spatial scales. Our fits of evolved Schechter functions imply average dynamical mass losses (Δ) over a Hubble time that vary more than MTO, and systematically but nonmonotonically as a function of galaxy luminosity. If the initial GC mass distributions rose steeply toward low masses as we assume, then these losses fall in the range 2 × 105 M☉ Δ < 106 M☉ per GC for all of our galaxies. The trends in Δ are broadly consistent with observed, small variations of the mean GC half-light radius in ACSVCS galaxies, and with rough estimates of the expected scaling of average evaporation rates (galaxy densities) versus total luminosity. We agree with previous suggestions that if the full GCLF is to be understood in more detail, especially alongside other properties of GC systems, the next generation of GCLF models will have to include self-consistent treatments of dynamical evolution inside time-dependent galaxy potentials.

Dynamics of the Globular Cluster System Associated with M49 (NGC 4472): Cluster Orbital Properties and the Distribution of Dark Matter*

Using the Low Resolution Imaging Spectrometer on the Keck I and II telescopes, we have measured radial velocities for 196 globular clusters (GCs) around M49 (NGC 4472), the brightest member of the Virgo Cluster. Combined with published data, they bring the total number of GCs with measured radial velocities in this galaxy to 263. In terms of sample size, spatial coverage, velocity precision, and the availability of metallicity estimates from Washington photometry, this radial velocity database resembles that presented recently for M87 (NGC 4486), Virgos cD galaxy and its second-ranked member. We extract the projected kinematics of the full sample of GCs and of separate subsamples of 158 metal-poor and 105 metal-rich GCs. In agreement with previous results for the global GC kinematics based on smaller data sets, we find that the GC system as a whole exhibits a slow overall rotation that is due almost entirely to a net rotation of the metal-poor GC subsystem alone. In a spatial average, the metal-rich GCs show essentially no rotation. As a function of galactocentric position, the metal-poor GCs rotate roughly about the photometric minor axis of M49 and at an approximately constant level of ΩR ~ 100-150 km s-1 out to R 2Reff. The metal-rich GC system shows some evidence (at roughly 1 σ significance) for weak rotation (ΩR ~ 50 km s-1) beyond R 0.5Reff, also about the galaxys minor axis, but in the opposite direction from the metal-poor GCs. Outside of R ~ Reff, the line-of-sight velocity dispersion of the metal-poor GCs exceeds that of their metal-rich counterparts by ~50%. We also note the presence of a well-defined grouping of 10 metal-rich GCs that are located at opposite poles along the galaxys major axis and that appear to be rotating at nearly 300 km s-1 about the minor axis. This grouping may be the relic of a past merger or accretion event. The dynamics of the GC system is modeled by using published catalogs and number counts to define three-dimensional GC density distributions as input to a Jeans equation analysis. We show that the GC radial velocities alone point unequivocally, and independently of X-ray observations, to the need for a massive dark halo associated with M49 and the Virgo B subcluster around it. We then use a mass model for M49/Virgo B, constructed without reference to any GC data and described in detail in a forthcoming paper, to infer the orbital properties of the M49 globulars. The GC system as a whole is shown to be consistent with an almost perfectly isotropic velocity ellipsoid. It is more difficult to draw any firm conclusions on the orbital (an)isotropy of the two metallicity subsamples, as a result of the large uncertainties in their individual spatial density profiles and the poorly observationally defined kinematics of the metal-rich GCs in particular. After M87, M49 is the second elliptical galaxy for which we have been able to demonstrate velocity isotropy in the GC system overall, when no division based on GC color or metallicity is attempted. Thus, the data for these two galaxies lend support to the general assumption of isotropy when using GC kinematics to study the dark matter distribution in early-type galaxies. We also compare the kinematic properties of the GC system of M49 to those of M87, M31, and the Milky Way, the other galaxies for which samples of 100 or more GC velocities have been accumulated. We argue that, contrary to the traditional view of GCs as nonrotating, or slowly rotating, systems, rotation may in fact be a common by-product of the formation of GC systems. However, the quantitative details of the rotation are still not clear, particularly with regard to the question of possible differences between metal-poor and metal-rich globulars.

Dynamical insight into dark matter haloes

We investigate, using the spherical Jeans equation, self-gravitating dynamical equilibria satisfying a relation ρ/σ 3 ∝ r −α , which holds for simulated dark matter haloes over their whole resolved radial range. Considering first the case of velocity isotropy, we find that this problem has only one solution for which the density profile is not truncated or otherwise unrealistic. This solution occurs only for a critical value of αcrit = 35/18 = 1.94, which is consistent with the empirical value of 1.9 ± 0.05. We extend our analysis in two ways: first, we introduce a par ,

A Hubble Space Telescope Census of Nuclear Star Clusters in Late-Type Spiral Galaxies. II. Cluster Sizes and Structural Parameter Correlations

We investigate the structural properties of nuclear star clusters in late-type spiral galaxies. More specifically, we fit analytical models to Hubble Space Telescope images of 39 nuclear clusters in order to determine their effective radii after correction for the instrumental point-spread function. We use the results of this analysis to compare the luminosities and sizes of nuclear star clusters to those of other ellipsoidal stellar systems, in particular the Milky Way globular clusters. Our nuclear clusters have a median effective radius of e = 3.5 pc, with 50% of the sample falling in the range 2.4 pc ≤ re ≤ 5.0 pc. This narrow size distribution is statistically indistinguishable from that of Galactic globular clusters, even though the nuclear clusters are, on average, 4 mag brighter than the old globular clusters. We discuss some possible interpretations of this result. From a comparison of nuclear cluster luminosities with various properties of their host galaxies, we confirm that more luminous galaxies harbor more luminous nuclear clusters. It remains unclear whether this correlation mainly reflects the influence of galaxy size, mass, and/or star formation rate. Since the brighter galaxies in our sample typically have stellar disks with a higher central surface brightness, nuclear cluster luminosity also correlates with this property of their hosts. On the other hand, we find no evidence for a correlation between the presence of a nuclear star cluster and the presence of a large-scale stellar bar.

Structural parameters for globular clusters in M31 and generalizations for the Fundamental Plane

The structures of globular clusters (GCs) reflect their dynamical states and past histories. High-resolution imaging allows the exploration of morphologies of clusters in other galaxies. Surface brightness profiles from new Hubble Space Telescope observations of 34 GCs in M31 are presented, together with fits of several different structural models to each cluster. M31 clusters appear to be adequately fit by standard King models and do not obviously require alternate descriptions with relatively stronger halos, such as are needed to fit many GCs in other nearby galaxies. The derived structural parameters are combined with corrected versions of those measured in an earlier survey in order to construct a comprehensive catalog of structural and dynamical parameters for M31 GCs with a sample size similar to that for the Milky Way. Clusters in M31, the Milky Way, Magellanic Clouds, the Fornax dwarf spheroidal, and NGC 5128 define a very tight fundamental plane with identical slopes. The combined evidence for these widely different galaxies strongly reinforces the view that old GCs have near-universal structural properties, regardless of host environment.

Structural Parameters for Globular Clusters in NGC 5128

We present new imaging measurements of 27 individual globular clusters in the halo of the nearby elliptical galaxy NGC 5128, obtained with the Hubble Space Telescope Imaging Spectrograph and Wide Field Planetary Camera 2. We use the cluster light profiles to determine their structural parameters (core and half-light radii, central concentration, and ellipticity). Combining these with similar data for selected inner halo clusters from Holland et al., we now have a total sample of 43 NGC 5128 globular clusters with measured structural properties. We find that classic King model profiles match the clusters extremely well and that their various structural parameters (core and half-light radius, central surface brightness, and central concentration) fall in very much the same range as do the clusters in the Milky Way and M31. We find half a dozen bright clusters that show tentative evidence for extratidal light that extends beyond the nominal tidal radius, similar in nature to several such objects previously found in the Milky Way and M31; these may represent clusters being tidally stripped or possibly ones in which anisotropic velocity distributions are important. We also confirm previous indications that NGC 5128 contains relatively more clusters with large ( > 0.2) ellipticity than does the Milky Way. Instead, the -distribution of the NGC 5128 clusters strongly resembles that of the old clusters in the Large Magellanic Cloud and also in M31. Finally, calculations of the cluster binding energies Eb as defined by McLaughlin show that the NGC 5128 clusters occupy the same extremely narrow region of the parametric fundamental plane as do their Milky Way counterparts. Our data are thus strongly consistent with the claim that the globular clusters in both NGC 5128 and the Milky Way are fundamentally the same type of object: old star clusters with similar mass-to-light ratios and King model structures.