We have determined the masses and mass-to-light ratios of 50 Galactic globular clusters by comparing their velocity dispersion and surface brightness profiles against a large grid of 900 N-body simulations of star clusters of varying initial concentration, size and central black hole mass fraction. Our models follow the evolution of the clusters under the combined effects of stellar evolution and two-body relaxation allowing us to take the effects of mass segregation and energy equipartition between stars self-consistently into account. For a subset of 16 wellobserved clusters, we also derive their kinematic distances. We find an average mass-to-light ratio of Galactic globular clusters of =1.98 ± 0.03, which agrees very well with the expected M/L ratio if the initial mass function (IMF) of the clusters was a standard Kroupa or Chabrier mass function. We do not find evidence for a decrease in the average mass-to-light ratio with metallicity. The surface brightness and velocity dispersion profiles of most globular clusters are incompatible with the presence of intermediate-mass black holes (IMBHs) with more than a few thousand M in them. The only clear exception is ω Cen, where the velocity dispersion profile provides strong evidence for the presence of a ~40 000 M IMBH in the centre of the cluster.

N-body modelling of globular clusters: masses, mass-to-light ratios and intermediate-mass black holes

The total mass M_GCS in the globular cluster (GC) system of a galaxy is empirically a near-constant fraction of the total mass M_h = M_bary + M_dark of the galaxy, across a range of 10^5 in galaxy mass. This trend is radically unlike the strongly nonlinear behavior of total stellar mass M_star versus M_h. We discuss extensions of this trend to two more extreme situations: (a) entire clusters of galaxies, and (b) the Ultra-Diffuse Galaxies (UDGs) recently discovered in Coma and elsewhere. Our calibration of the ratio \eta_M = M_GCS / M_h from normal galaxies, accounting for new revisions in the adopted mass-to-light ratio for GCs, now gives \eta_M = 2.9 \times 10^{-5} as the mean absolute mass fraction. We find that the same ratio appears valid for galaxy clusters and UDGs. Estimates of \eta_M in the four clusters we examine tend to be slightly higher than for individual galaxies, butmore data and better constraints on the mean GC mass in such systems are needed to determine if this difference is significant. We use the constancy of \eta_M to estimate total masses for several individual cases; for example, the total mass of the Milky Way is calculated to be M_h = 1.1 \times 10^{12} M_sun. Physical explanations for the uniformity of \eta_M are still descriptive, but point to a picture in which massive, dense star clusters in their formation stages were relatively immune to the feedback that more strongly influenced lower-density regions where most stars form.

http://iopscience.iop.org/article/10.3847/1538-4357/836/1/67/pdf

Galactic Dark Matter Halos and Globular Cluster Populations. III. Extension to Extreme Environments

We present a detailed study of the nuclear star clusters (NSCs) and massive black holes (BHs) of four of the nearest low-mass early-type galaxies: M32, NGC205, NGC5012, and NGC5206. We measure dynamical masses of both the BHs and NSCs in these galaxies using Gemini/NIFS or VLT/SINFONI stellar kinematics, Hubble Space Telescope (HST) imaging, and Jeans Anisotropic Models. We detect massive BHs in M32, NGC5102, and NGC5206, while in NGC205, we find only an upper limit. These BH mass estimates are consistent with previous measurements in M32 and NGC205, while those in NGC5102 and NGC5206 are estimated for the first time, and both found to be $<$$10^6~M_{\odot}$. This adds to just a handful of galaxies with dynamically measured sub-million $M_{\odot}$ central BHs. Combining these BH detections with our recent work on NGC404's BH, we find that 80\% (4/5) of nearby, low-mass ($10^9-10^{10}~M_{\odot}$; $\sigma_{\star}\sim20-70$ km/s) early-type galaxies host BHs. Such a high occupation fraction suggests the BH seeds formed in the early epoch of cosmic assembly likely resulted in abundant seeds, favoring a low-mass seed mechanism of the remnants, most likely from the first generation of massive stars. We find dynamical masses of the NSCs ranging from $2-80\times10^6~M_{\odot}$ and compare these masses to scaling relations for NSCs based primarily on photometric mass estimates. Color gradients suggest younger stellar populations lie at the centers of the NSCs in three of the four galaxies (NGC205, NGC5102, and NGC5206), while the morphology of two are complex and are best-fit with multiple morphological components (NGC5102 and NGC5206). The NSC kinematics show they are rotating, especially in M32 and NGC5102 ($V/\sigma_{\star}\sim0.7$).

/pdf/nearby-early-type-galactic-nuclei-at-high-resolution-3hbyt1j5bw.pdf

Nearby Early-type Galactic Nuclei at High Resolution: Dynamical Black Hole and Nuclear Star Cluster Mass Measurements

We present a family of self-consistent, spherical, lowered isothermal models, consisting of one or more mass components, with parameterised prescriptions for the energy truncation and for the amount of radially biased pressure anisotropy. The models are particularly suited to describe the phase-space density of stars in tidally limited, mass-segregated star clusters in all stages of their life-cycle. The models extend a family of isotropic, single-mass models by Gomez-Leyton and Velazquez, of which the well-known Woolley, King and Wilson (in the non-rotating and isotropic limit) models are members. We derive analytic expressions for the density and velocity dispersion components in terms of potential and radius, and introduce a fast model solver in PYTHON (LIMEPY), that can be used for data fitting or for generating discrete samples.

A family of lowered isothermal models

We present dynamical distance estimates for 15 Galactic globular clusters and use these to check the consistency of dynamical and photometric distance estimates. For most of the clusters, this is the first dynamical distance estimate ever determined. We extract proper-motion dispersion profiles using cleaned samples of bright stars from the Hubble Space Telescope proper-motion catalogs recently presented in Bellini et al. (2014) and compile a set of line-of-sight velocity-dispersion profiles from a variety of literature sources. Distances are then estimated by fitting spherical, non-rotating, isotropic, constant mass-to-light (M/L) dynamical models to the proper-motion and line-of-sight dispersion profiles together. We compare our dynamical distance estimates with literature photometric estimates from the Harris (1996, 2010 edition) globular cluster catalog and find that the mean fractional difference between the two types is consistent with zero at just $-1.9 \pm 1.7 \%$. This indicates that there are no significant biases in either estimation method and provides an important validation of the stellar-evolution theory that underlies photometric distance estimates. The analysis also estimates dynamical M/L ratios for our clusters; on average, the dynamically-inferred M/L ratios agree with existing stellar-population-based M/L ratios that assume a Chabrier initial mass function (IMF) to within $-8.8 \pm 6.4 \%$, implying that such an IMF is consistent with our data. Our results are also consistent with a Kroupa IMF, but strongly rule out a Salpeter IMF. We detect no correlation between our M/L offsets from literature values and our distance offsets from literature values, strongly indicating that our methods are reliable and our results are robust.

Hubble Space Telescope Proper Motion (HSTPROMO) Catalogs of Galactic Globular Clusters. III. Dynamical Distances and Mass-to-Light Ratios

From a study of the integrated light properties of 200 globular clusters (GCs) in M31, Strader et al. found that the mass-to-light ratios are lower than what is expected from simple stellar population (SSP) models with a `canonical' stellar initial mass function (IMF), with the discrepancy being larger at high metallicities. We use dynamical multi-mass models, that include a prescription for equipartition, to quantify the bias in the inferred dynamical mass as the result of the assumption that light follows mass. For a universal IMF and a metallicity dependent present day mass function we find that the inferred mass from integrated light properties systematically under estimates the true mass, and that the bias is more important at high metallicities, as was found for the M31 GCs. We show that mass segregation and a flattening of the mass function have opposing effects of similar magnitude on the mass inferred from integrated properties. This makes the mass-to-light ratio as derived from integrated properties an inadequate probe of the low-mass end of the stellar mass function. There is, therefore, no need for variations in the IMF, nor the need to invoke depletion of low-mass stars, to explain the observations. Finally, we find that the retention fraction of stellar-mass black holes (BHs) is an equally important parameter in understanding the mass segregation bias. We speculatively put forward to idea that kinematical data of GCs can in fact be used to constrain the total mass in stellar-mass BHs in GCs.

Rosemary L. Shanahan

Papers

Biases in the inferred mass-to-light ratio of globular clusters: no need for variations in the stellar mass function