Recently, two independent groups found very different results when measuring the central velocity dispersion of the galactic globular cluster NGC 6388 with different methods. While Lutzgendorf et al. (2011) found a rising profile and a high central v
elocity dispersion (23.3 km/s), measurements obtained by Lanzoni et al. (2013) showed a value 40% lower. The value of the central velocity dispersion has a serious impact on the mass and possible presence of an intermediate-mass black hole at the center of NGC 6388. We use a photometric catalog of NGC 6388 to create a simulated SINFONI and ARGUS dataset. The construction of the IFU data cube is done with different observing conditions reproducing the conditions reported for the original observations as closely as possible. In addition, we produce an N-body realization of a 10^6 M_SUN stellar cluster with the same photometric properties as NGC 6388 to account for unresolved stars. We find that the individual radial velocities, i.e. the measurements from the simulated SINFONI data, are systematically biased towards lower velocity dispersions. The reason is that due to the wings in the point spread function the velocities get biased towards the mean cluster velocity. This study shows that even with AO supported observations, individual radial velocities in crowded fields are likely to be biased. The ARGUS observations do not show this kind of bias but were found to have larger uncertainties than previously obtained. We find a bias towards higher velocity dispersions in the ARGUS pointing when fixing the extreme velocities of the three brightest stars but find those variations are within the determined uncertainties. We rerun Jeans models and fit the kinematic profile with the new uncertainties. This yields a BH mass of M_BH = (2.8 +- 0.4) x 10^4 M_SUN and M/L ratio M/L = (1.6 +- 0.1) M_SUN/L_SUN, consistent with our previous results.
CONTEXT: The dynamical mass-to-light (M/L) ratios of massive ultra-compact dwarf galaxies (UCDs) are about 50% higher than predicted by stellar population models. AIMS: Here we investigate the possibility that these elevated M/L ratios are caused by
a central black hole (BH), heating up the internal motion of stars. We focus on a sample of ~50 extragalactic UCDs for which velocity dispersions and structural parameters have been measured. METHODS: Using up-to-date distance moduli and a consistent treatment of aperture and seeing effects, we calculate the ratio Psi=(M/L)_{dyn}/(M/L)_{pop} between the dynamical and the stellar population M/L of UCDs. For all UCDs with Psi>1 we estimate the mass of a hypothetical central BH needed to reproduce the observed integrated velocity dispersion. RESULTS: Massive UCDs (M>10^7 M_*) have an average Psi = 1.7 +-0.2, implying notable amounts of dark mass in them. We find that, on average, central BH masses of 10-15% of the UCD mass can explain these elevated dynamical M/L ratios. The implied BH masses in UCDs range from several 10^5 M_* to several 10^7 M_*. In the M_BH-Luminosity plane, UCDs are offset by about two orders of magnitude in luminosity from the relation derived for galaxies. Our findings can be interpreted such that massive UCDs originate from progenitor galaxies with masses around 10^9 M_*, and that those progenitors have SMBH occupation fractions of 60-100%. The suggested UCD progenitor masses agree with predictions from the tidal stripping scenario. Lower-mass UCDs (M<10^7 M_*) exhibit a bimodal distribution in Psi, suggestive of a coexistence of massive globular clusters and tidally stripped galaxies in this mass regime. CONCLUSIONS: Central BHs as relict tracers of tidally stripped progenitor galaxies are a plausible explanation for the elevated dynamical M/L ratios of UCDs.
The evolution of the global stellar mass function (MF) of star clusters is studied based on a large set of N-body simulations of clusters with a range of initial masses, initial concentrations, in circular or elliptical orbits in different tidal envi
ronments. Models with and without initial mass segregation are included. The depletion of low mass stars in initially Roche-volume (tidal) filling clusters starts typically on a time scale of the order of the core collapse time. In clusters that are initially underfilling their Roche-volume it takes longer because the clusters have to expand to their tidal radii before dynamical mass loss becomes important. We introduce the concept of the differential mass function (DMF), which describes the changes with respect to the initial mass function (IMF). We show that the evolution of the DMF can be described by a set of very simple analytic expressions that are valid for a wide range of initial cluster parameters and for different IMFs. The agreement between this description and the models is very good, except for initially Roche-volume underfilling clusters that are severely mass segregated.
We highlight the impact of cluster-mass-dependent evolutionary rates upon the evolution of the cluster mass function during violent relaxation, that is, while clusters dynamically respond to the expulsion of their residual star-forming gas. Mass-depe
ndent evolutionary rates arise when the mean volume density of cluster-forming regions is mass-dependent. In that case, even if the initial conditions are such that the cluster mass function at the end of violent relaxation has the same shape as the embedded-cluster mass function (i.e. infant weight-loss is mass-independent), the shape of the cluster mass function does change transiently {it during} violent relaxation. In contrast, for cluster-forming regions of constant mean volume density, the cluster mass function shape is preserved all through violent relaxation since all clusters then evolve at the same mass-independent rate. On the scale of individual clusters, we model the evolution of the ratio between the dynamical mass and luminous mass of a cluster after gas expulsion. Specifically, we map the radial dependence of the time-scale for a star cluster to return to equilibrium. We stress that fields-of-view a few pc in size only, typical of compact clusters with rapid evolutionary rates, are likely to reveal cluster regions which have returned to equilibrium even if the cluster experienced a major gas expulsion episode a few Myr earlier. We provide models with the aperture and time expressed in units of the initial half-mass radius and initial crossing-time, respectively, so that our results can be applied to clusters with initial densities, sizes, and apertures different from ours.
We obtained precise line-of-sight radial velocities of 23 member stars of the remote halo globular cluster Palomar 4 (Pal 4) using the High Resolution Echelle Spectrograph (HIRES) at the Keck I telescope. We also measured the mass function of the clu
ster down to a limiting magnitude of V~28 mag using archival HST/WFPC2 imaging. We derived the clusters surface brightness profile based on the WFPC2 data and on broad-band imaging with the Low-Resolution Imaging Spectrometer (LRIS) at the Keck II telescope. We find a mean cluster velocity of 72.55+/-0.22 km/s and a velocity dispersion of 0.87+/-0.18 km/s. The global mass function of the cluster, in the mass range 0.55<=M<=0.85 M_solar, is shallower than a Kroupa mass function and the cluster is significantly depleted in low-mass stars in its center compared to its outskirts. Since the relaxation time of Pal 4 is of the order of a Hubble time, this points to primordial mass segregation in this cluster. Extrapolating the measured mass function towards lower-mass stars and including the contribution of compact remnants, we derive a total cluster mass of 29800 M_solar. For this mass, the measured velocity dispersion is consistent with the expectations of Newtonian dynamics and below the prediction of Modified Newtonian Dynamics (MOND). Pal 4 adds to the growing body of evidence that the dynamics of star clusters in the outer Galactic halo can hardly be explained by MOND.
We describe the interplay between stellar evolution and dynamical mass loss of evolving star clusters, based on the principles of stellar evolution and cluster dynamics and on a grid of N-body simulations of cluster models. The cluster models have di
fferent initial masses, different orbits, including elliptical ones, and different initial density profiles. We use two sets of cluster models: initially Roche-lobe filling and Roche-lobe underfilling. We identify four distinct mass loss effects: (1) mass loss by stellar evolution, (2) loss of stars induced by stellar evolution and (3) relaxation-driven mass loss before and (4) after core collapse. Both the evolution-induced loss of stars and the relaxation-driven mass loss need time to build up. This is described by a delay-function of a few crossing times for Roche-lobe filling clusters and a few half mass relaxation times for Roche-lobe underfilling clusters. The relaxation-driven mass loss can be described by a simple power law dependence of the mass dM/dt =-M^{1-gamma}/t0, (with M in Msun) where t0 depends on the orbit and environment of the cluster. Gamma is 0.65 for clusters with a King-parameter W0=5 and 0.80 for more concentrated clusters with W0=7. For initially Roche-lobe underfilling clusters the dissolution is described by the same gamma=0.80. The values of the constant t0 are described by simple formulae that depend on the orbit of the cluster. The mass loss rate increases by about a factor two at core collapse and the mass dependence of the relaxation-driven mass loss changes to gamma=0.70 after core collapse. We also present a simple recipe for predicting the mass evolution of individual star clusters with various metallicities and in different environments, with an accuracy of a few percent in most cases. This can be used to predict the mass evolution of cluster systems.
We investigate the mean velocity dispersion and the velocity dispersion profile of stellar systems in MOND, using the N-body code N-MODY, which is a particle-mesh based code with a numerical MOND potential solver developed by Ciotti, Londrillo and Ni
poti (2006). We have calculated mean velocity dispersions for stellar systems following Plummer density distributions with masses in the range of $10^4 M_odot$ to $10^9 M_odot$ and which are either isolated or immersed in an external field. Our integrations reproduce previous analytic estimates for stellar velocities in systems in the deep MOND regime ($a_i, a_e ll a_0$), where the motion of stars is either dominated by internal accelerations ($a_i gg a_e$) or constant external accelerations ($a_e gg a_i$). In addition, we derive for the first time analytic formulae for the line-of-sight velocity dispersion in the intermediate regime ($a_i sim a_e sim a_0$). This allows for a much improved comparison of MOND with observed velocity dispersions of stellar systems. We finally derive the velocity dispersion of the globular cluster Pal 14 as one of the outer Milky Way halo globular clusters that have recently been proposed as a differentiator between Newtonian and MONDian dynamics.
Over the last 15 years, around a hundred very young stars have been observed in the central parsec of our Galaxy. While the presence of young stars forming one or two stellar disks at approx. 0.1 pc from the supermassive black hole (SMBH) can be unde
rstood through star formation in accretion disks, the origin of the S stars observed a factor of 10 closer to the SMBH has remained a major puzzle. Here we show the S stars to be a natural consequence of dynamical interaction of two stellar disks at larger radii. Due to precession and Kozai interaction, individual stars achieve extremely high eccentricities at random orientation. Stellar binaries on such eccentric orbits are disrupted due to close passages near the SMBH, leaving behind a single S star on a much tighter orbit. The remaining star may be ejected from the vicinity of the SMBH, thus simultaneously providing an explanation for the observed hypervelocity stars in the Milky Way halo.
A novel way of looking at the evolution of star clusters is presented. With a dynamical temperature, given by the mean kinetic energy of the cluster stars, and a dynamical luminosity, which is defined as the kinetic energy of the stars leaving the cl
uster in analogy to the energy of photons emitted by a star, the dissolution of star clusters is studied using a new dynamical temperature-luminosity diagram for star clusters. The investigation contains a parameter-space study of open clusters of up to N = 32768 single-mass stars with different initial density distributions, half-mass radii, tidal conditions and binary fractions. The clusters show a strong correlation between dynamical temperature and dynamical luminosity and most of the investigated cluster families share a common sequence in such a dynamical temperature-luminosity diagram. Deviations from this sequence are analyzed and discussed. After core collapse, the position of a cluster within this diagram can be defined by three parameters: the mass, the tidal conditions and the binary fraction. Due to core collapse all initial conditions are lost and the remaining stars adjust to the given tidal conditions. Binaries as internal energy sources influence this adjustment. A further finding concerns the Lagrange radii of star clusters: Throughout the investigated parameter space nearly all clusters show a constant half-mass radius for the time after core collapse until dissolution. Furthermore, the ratio of half-mass radius to tidal radius evolves onto a common sequence which only depends on the mass left in the cluster.
We have studied the dissolution of initially mass segregated and unsegregated star clusters due to two-body relaxation in external tidal fields, using Aarseths collisional N-body code NBODY4 on GRAPE6 special-purpose computers. When extrapolating res
ults of initially not mass segregated models to globular clusters, we obtain a correlation between the time until destruction and the slope of the mass function, in the sense that globular clusters which are closer to dissolution are more strongly depleted in low-mass stars. This correlation fits observed mass functions of most globular clusters. The mass functions of several globular clusters are however more strongly depleted in low-mass stars than suggested by these models. Such strongly depleted mass functions can be explained if globular clusters started initially mass segregated. Primordial mass segregation also explains the correlation between the slope of the stellar mass function and the cluster concentration which was recently discovered by De Marchi et al. (2007). In this case, it is possible that all globular clusters started with a mass function similar to that seen in young open clusters in the present-day universe, at least for stars below m=0.8 Msun. This argues for a near universality of the mass function for different star formation environments and metallicities in the range -2 < [Fe/H] < 0. We finally describe a novel algorithm which can initialise stationary mass segregated clusters with arbitrary density profile and amount of mass segregation.
