Runaway collisions in young star clusters. II. Numerical results

We present a new study of the collisional runaway scenario to form an intermediate-mass black hole (IMBH, MBH > 100 Msun) at the centre of a young, compact stellar cluster. The first phase is the formation of a very dense central core of massive stars (Mstar =~ 30-120 Msun) through mass segregation and gravothermal collapse. Previous work established the conditions for this to happen before the massive stars evolve off the main sequence (MS). In this and a companion paper, we investigate the next stage by implementing direct collisions between stars. Using a Monte Carlo stellar dynamics code, we follow the core collapse and subsequent collisional phase in more than 100 models with varying cluster mass, size, and initial concentration. Collisions are treated either as ideal, ``sticky-sphere'' mergers or using realistic prescriptions derived from 3-D hydrodynamics computations. In all cases for which the core collapse happens in less than the MS lifetime of massive stars (~3 Myr), we obtain the growth of a single very massive star (VMS, Mstar =~ 400-4000 Msun) through a runaway sequence of mergers. Mass loss from collisions, even for velocity dispersions as high as sigma1D ~ 1000 km/s, does not prevent the runaway. The region of cluster parameter space leading to runaway is even more extended than predicted in previous work because, in clusters with sigma1D > 300 km/s, collisions accelerate (and, in extreme cases, drive) core collapse. Although the VMS grows rapidly to > 1000 Msun in models exhibiting runaway, we cannot predict accurately its final mass. This is because the termination of the runaway process must eventually be determined by a complex interplay between stellar dynamics, hydrodynamics, and the stellar evolution of the VMS. [abridged]Comment: 23 pages, 24 figures. For publication in MNRAS. Paper revised to follow requests and suggestions of referee. Companion paper to Freitag, Rasio & Baumgardt 200

The present day mass function in the central region of the Arches cluster

We study the evolution of the mass function in young and dense star clusters by means of direct N-body simulations. Our main aim is to explain the recent observations of the relatively flat mass function observed near the centre of the Arches star cluster. In this region, the power law index of the mass function for stars more massive than about 5-6 solar mass, is larger than the Salpeter value by about unity; whereas further out, and for the lower mass stars, the mass function resembles the Salpeter distribution. We show that the peculiarities in the Arches mass function can be explained satisfactorily without primordial mass segregation. We draw two conclusions from our simulations: 1) The Arches initial mass function is consistent with a Salpeter slope down to ~1 solar mass, 2) The cluster is about half way towards core collapse. The cores of other star clusters with characteristics similar to those of the Arches are expected to show similar flattening in the mass functions for the high mass (>5 solar mass) stars.Comment: 6 pages with 6 figures and 1 table. Submitted to the letters section of MNRAS. Incorporates changes following suggestions by the refere

Resonant relaxation near a massive black hole: the dependence on eccentricity

It is now commonly accepted that many galaxies contain massive black holes (MBHs) at their centres (e.g., Gebhardt et al. 2003; Miller 2006), with masses 10 6 M ⊙ � M • � 10 9 M⊙. The proximity of our own galactic centre, at a distance of 7.62

Formation of massive black holes in dense star clusters. I. Mass segregation and core collapse

We study the early dynamical evolution of young dense star clusters by using Monte Carlo simulations for systems with up to N = 10(7) stars. Rapid mass segregation of massive main-sequence stars and the development of the Spitzer instability can drive these systems to core collapse in a small fraction of the initial half-mass relaxation time. If the core-collapse time is less than the lifetime of the massive stars, all stars in the collapsing core may then undergo a runaway collision process leading to the formation of a massive black hole. Here we study in detail the first step in this process, up to the occurrence of core collapse. We have performed about 100 simulations for clusters with a wide variety of initial conditions, varying systematically the cluster density profile, stellar initial mass function ( IMF), and number of stars. We also considered the effects of initial mass segregation and stellar evolution mass loss. Our results show that, for clusters with a moderate initial central concentration and any realistic IMF, the ratio of core-collapse time to initial half-mass relaxation time is typically similar to0.1, in agreement with the value previously found by direct N-body simulations for much smaller systems. Models with even higher central concentration initially, or with initial mass segregation ( from star formation) have even shorter core collapse times. Remarkably, we find that, for all realistic initial conditions, the mass of the collapsing core is always close to similar to 10(-3) of the total cluster mass, very similar to the observed correlation between central black hole mass and total cluster mass in a variety of environments. We discuss the implications of our results for the formation of intermediate-mass black holes in globular clusters and super star clusters, ultraluminous X-ray sources, and seed black holes in proto - galactic nuclei

Run-away IMBH formation in dense star clusters

We have established under which conditions core collapse of a spherical cluster occurs before massive stars have time to evolve off the main sequence (MS). We consider cluster central velocity dispersions of 100 km s(-1) and higher, appropriate for galactic nuclei. At such high velocities, binary stars play little dynamical role and are therefore neglected. On the other hand whether collisions allow the growth of very massive stars (VMS, with M-* >> 100 M-circle dot) or, on the contrary, grind them down is a central unknown addressed in this work. We find that, in spite of the high relative velocities, run-away growth of a VMS, a likely progenitor for an intermediate-mass BH (IMBH), occurs in all clusters with short enough a core collapse time