The dynamical state of the Globular Cluster M10 (NGC 6254)

Studying the radial variation of the stellar mass function in globular clusters (GCs) has proved a valuable tool to explore the collisional dynamics leading to mass segregation and core collapse. In order to study the radial dependence of the luminosity and mass function of M 10, we used ACS/HST deep high resolution archival images, reaching out to approximately the cluster's half-mass radius (rhm), combined with deep WFPC2 images that extend our radial coverage to more than 2 rhm. From our photometry, we derived a radial mass segregation profile and a global mass function that we compared with those of simulated clusters containing different energy sources (namely hard binaries and/or an IMBH) able to halt core collapse and to quench mass segregation. A set of direct N-body simulations of GCs, with and without an IMBH of mass 1% of the total cluster mass, comprising different initial mass functions (IMFs) and primordial binary fractions, was used to predict the observed mass segregation profile and mass function. The mass segregation profile of M 10 is not compatible with cluster models without either an IMBH or primordial binaries, as a source of energy appears to be moderately quenching mass segregation in the cluster. Unfortunately, the present observational uncertainty on the binary fraction in M10 does not allow us to confirm the presence of an IMBH in the cluster, since an IMBH, a dynamically non-negligible binary fraction (~ 5%), or both can equally well explain the radial dependence of the cluster mass function.Comment: 15 pages, 8 figures, accepted for publication on Ap

The Globular Cluster Luminosity Function and Specific Frequency in Dwarf Elliptical Galaxies

The globular cluster luminosity function, specific globular cluster frequency, S_N, specific globular cluster mass, T_MP, and globular cluster mass fraction in dwarf elliptical galaxies are explored using the full 69 galaxy sample of the HST WFPC2 Dwarf Elliptical Galaxy Snapshot Survey. The GCLFs of the dEs are well-represented with a t_5 function with a peak at M_{V,Z}^0(dE,HST) = -7.3 +/- 0.1. This is ~0.3 magnitudes fainter than the GCLF peaks in giant spiral and elliptical galaxies, but the results are consistent within the uncertainties. The bright-end slope of the luminosity distribution has a power-law form with slope alpha = -1.9 +/- 0.1. The trend of increasing S_N or T_MP with decreasing host galaxy luminosity is confirmed. The mean value for T_MP in dE,N galaxies is about a factor of two higher than the mean value for non-nucleated galaxies and the distributions of T_MP in dE,N and dE,noN galaxies are statistically different. These data are combined with results from the literature for a wide range of galaxy types and environments. At low host galaxy masses the distribution of T_MP for dE,noN and dI galaxies are similar. This supports the idea that one pathway for forming dE,noN galaxies is by the stripping of dIs. The formation of nuclei and the larger values of T_MP in dE,N galaxies may be due to higher star formation rates and star cluster formation efficiencies due to interactions in galaxy cluster environments.Comment: 53 pages, 13 figures, 12 tables, accepted by the Astrophysical Journa

Using distant globular clusters as a test for gravitational theories

We propose to determine the stellar velocity dispersions of globular clusters in the outer halo of the Milky Way in order to decide whether the dynamics of the universe on large scales is governed by dark matter or modified Newtonian dynamics (MOND). We show that for a number of galactic globular clusters, both the internal and the external accelerations are significantly below the critical acceleration parameter $a_0$ of MOND. This leads to velocity dispersions in case of MOND which exceed their Newtonian counterparts by up to a factor of 3, providing a stringent test for MOND. Alternatively, in case high velocity dispersions are found, these would provide the first evidence that globular clusters are dark matter dominated.Comment: 5 pages, 1 figure, accepted for publication in MNRA

Biases in the determination of dynamical parameters of star clusters: today and in the Gaia era

The structural and dynamical properties of star clusters are generally derived by means of the comparison between steady-state analytic models and the available observables. With the aim of studying the biases of this approach, we fitted different analytic models to simulated observations obtained from a suite of direct N-body simulations of star clusters in different stages of their evolution and under different levels of tidal stress to derive mass, mass function and degree of anisotropy. We find that masses can be under/over-estimated up to 50% depending on the degree of relaxation reached by the cluster, the available range of observed masses and distances of radial velocity measures from the cluster center and the strength of the tidal field. The mass function slope appears to be better constrainable and less sensitive to model inadequacies unless strongly dynamically evolved clusters and a non-optimal location of the measured luminosity function are considered. The degree and the characteristics of the anisotropy developed in the N-body simulations are not adequately reproduced by popular analytic models and can be detected only if accurate proper motions are available. We show how to reduce the uncertainties in the mass, mass-function and anisotropy estimation and provide predictions for the improvements expected when Gaia proper motions will be available in the near future.Comment: 14 pages, 8 figures, accepted for publication by MNRA

The dynamical distance to M15: estimates of the cluster's age and mass and of the absolute magnitude of its RR Lyrae stars

Newly determined high-precision relative proper motions determined from the Hubble Space Telescope Wide Field Planetary Camera 2 are used along with radial velocity measurements to determine the dynamical distance to the globular cluster M15. A comparison of the proper motion and radial velocity dispersions from a sample of 237 stars, located at an average radial distance of about 10" from the cluster center, yields a cluster distance of 9.98+/-0.47 kpc. This distance agrees to within the stated errors to other distance estimates but places this object about 5% closer than the currently adopted value of 10.4 kpc. Using this new distance, we estimate that RR Lyrae stars having [Fe/H]=-2.15 have a value of M-v(RR)=0.51+/-0.11. We also estimate that M 15 has an age of about 13.2 Gyr, which places it among the oldest of the Galactic globular clusters. From a comparison of the observed velocity dispersion with results from recent N-body calculations, we derive a total cluster mass for M 15 of M-C=4.5x10(5) M-circle dot

Dynamical evolution of the mass function and radial profile of the Galactic globular cluster system

Evolution of the mass function (MF) and radial distribution (RD) of the Galactic globular cluster (GC) system is calculated using an advanced and a realistic Fokker-Planck (FP) model that considers dynamical friction, disc/bulge shocks and eccentric cluster orbits. We perform hundreds of FP calculations with different initial cluster conditions, and then search a wide-parameter space for the best-fitting initial GC MF and RD that evolves into the observed present-day Galactic GC MF and RD. By allowing both MF and RD of the initial GC system to vary, which is attempted for the first time in the present Letter, we find that our best-fitting models have a higher peak mass for a lognormal initial MF and a higher cut-off mass for a power-law initial MF than previous estimates, but our initial total masses in GCs, M_{T,i} = 1.5-1.8x10^8 Msun, are comparable to previous results. Significant findings include that our best-fitting lognormal MF shifts downward by 0.35 dex during the period of 13 Gyr, and that our power-law initial MF models well-fit the observed MF and RD only when the initial MF is truncated at >~10^5 Msun. We also find that our results are insensitive to the initial distribution of orbit eccentricity and inclination, but are rather sensitive to the initial concentration of the clusters and to how the initial tidal radius is defined. If the clusters are assumed to be formed at the apocentre while filling the tidal radius there, M_{T,i} can be as high as 6.9x10^8 Msun, which amounts to ~75 per cent of the current mass in the stellar halo.Comment: To appear in May 2008 issue of MNRAS, 386, L6

The distribution of stars around the Milky Way's central black hole II: Diffuse light from sub-giants and dwarfs

This is the second of three papers that search for the predicted stellar cusp around the Milky Way's central black hole, Sagittarius A*, with new data and methods. We aim to infer the distribution of the faintest stellar population currently accessible through observations around Sagittarius A*. We use adaptive optics assisted high angular resolution images obtained with the NACO instrument at the ESO VLT. Through optimised PSF fitting we remove the light from all detected stars above a given magnitude limit. Subsequently we analyse the remaining, diffuse light density. The analysed diffuse light arises from sub-giant and main-sequence stars with KS ~ 19 - 20 with masses of 1 - 2 Msol . These stars can be old enough to be dynamically relaxed. The observed power-law profile and its slope are consistent with the existence of a relaxed stellar cusp around the Milky Way's central black hole. We find that a Nuker law provides an adequate description of the nuclear cluster's intrinsic shape (assuming spherical symmetry). The 3D power-law slope near Sgr A* is \gamma = 1.23 +- 0.05. At a distance of 0.01 pc from the black hole, we estimate a stellar mass density of 2.3 +- 0.3 x 10^7 Msol pc^-3 and a total enclosed stellar mass of 180 +- 20 Msol. These estimates assume a constant mass-to-light ratio and do not take stellar remnants into account. The fact that no cusp is observed for bright (Ks 16) giant stars at projected distances of roughly 0.1-0.3 pc implies that some mechanism has altered their appearance or distribution.Comment: Accepted for publication A&

The distribution of old stars around the Milky Way's central black hole I: Star counts

(abridged) In this paper we revisit the problem of inferring the innermost structure of the Milky Way's nuclear star cluster via star counts, to clarify whether it displays a core or a cusp around the central black hole. Through image stacking and improved PSF fitting we push the completeness limit about one magnitude deeper than in previous, comparable work. Contrary to previous work, we analyse the stellar density in well-defined magnitude ranges in order to be able to constrain stellar masses and ages. The RC and brighter giant stars display a core-like surface density profile within a projected radius R<0.3 pc of the central black hole, in agreement with previous studies, but show a cusp-like surface density distribution at larger R. The surface density of the fainter stars can be described well by a single power-law at R<2 pc. The cusp-like profile of the faint stars persists even if we take into account the possible contamination of stars in this brightness range by young pre-main sequence stars. The data are inconsistent with a core-profile for the faint stars.Finally, we show that a 3D Nuker law provides a very good description of the cluster structure. We conclude that the observed stellar density at the Galactic Centre, as it can be inferred with current instruments, is consistent with the existence of a stellar cusp around the Milky Way's central black hole, Sgr A*. This cusp is well developed inside the influence radius of about 3 pc of Sgr A* and can be described by a single three-dimensional power-law with an exponent gamma=1.23+-0.05. The apparent lack of RC stars and brighter giants at projected distances of R < 0.3 pc (R<8") of the massive black hole may indicate that some mechanism has altered their distribution or intrinsic luminosity.Comment: Accepted for publication A&

Modeling the dynamical evolution of the M87 globular cluster system

We study the dynamical evolution of the M87 globular cluster system (GCS) with a number of numerical simulations. We explore a range of different initial conditions for the GCS mass function (GCMF), for the GCS spatial distribution and for the GCS velocity distribution. We confirm that an initial power-law GCMF like that observed in young cluster systems can be readily transformed through dynamical processes into a bell-shaped GCMF. However,only models with initial velocity distributions characterized by a strong radial anisotropy increasing with the galactocentric distance are able to reproduce the observed constancy of the GCMF at all radii.We show that such strongly radial orbital distributions are inconsistent with the observed kinematics of the M87 GCS. The evolution of models with a bell-shaped GCMF with a turnover similar to that currently observed in old GCS is also investigated. We show that models with this initial GCMF can satisfy all the observational constraints currently available on the GCS spatial distribution,the GCS velocity distribution and on the GCMF properties.In particular these models successfully reproduce both the lack of a radial gradient of the GCS mean mass recently found in an analysis of HST images of M87 at multiple locations, and the observed kinematics of the M87 GCS.Our simulations also show that evolutionary processes significantly affect the initial GCS properties by leading to the disruption of many clusters and changing the masses of those which survive.The preferential disruption of inner clusters flattens the initial GCS number density profile and it can explain the rising specific frequency with radius; we show that the inner flattening observed in the M87 GCS spatial distribution can be the result of the effects of dynamical evolution on an initially steep density profile. (abridged)Comment: 15 pages,14 figures;accepted for publication in The Astrophysical Journa

A search for an intermediate-mass black hole in the core of the globular cluster NGC 6266

It has long been thought that intermediate-mass black holes (IMBHs) might be located in the cores of globular clusters. However, studies attempting to confirm this possibility have been inconclusive. To refine the search for these objects, Baumgardt et al. completed a series of N-body simulations to determine the observational properties that a host globular cluster should possess. Keys to revealing the presence of an IMBH were found to be the shape of the cluster's core proper motion dispersion profile and its surface density profile. Among the possible host clusters identified by Baumgardt et al., NGC 6266 was found to be the most suitable object to search. Hubble Space Telescope Wide Field Planetary Camera 2 images with an epoch difference of eight years were, therefore, used to measure this cluster's internal proper motion dispersion profile from 0.8 arcsec to 17 arcsec from the cluster center. This profile and the surface density profiles obtained by Noyola & Gebhardt and Trager et al. were then compared to those produced by N-body simulations of NGC 6266 with and without an IMBH. We find that a centrally located IMBH is not required to match these profiles, but that an IMBH with a 1 sigma upper limit mass of less than a few thousand M-circle dot cannot be excluded. To establish the existence of this object, the exact location of the density center and more precise velocity measurements within the inner 1 arcsec of this center are required. Our best-fitting model of NGC 6266 without an IMBH yields a cluster mass of M = 8.22 +/- 0.17 x 10(5) M-circle dot, leading to a mass-to-light ratio of M/L-V = 2.05 +/- 0.04