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Register a new userThe formation of massive black holes through collision runaway in dense young star clusters
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Simon Portegies Zwart
Publication date
2004
fields
Physics
and research's language is
English
Authors
Simon Portegies Zwart
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A luminous X-ray source is associated with a cluster (MGG-11) of young stars ~200pc from the center of the starburst galaxy M82. The properties of the X-ray source are best explained by a black hole with a mass of at least 350Msun, which is intermediate between stellar-mass and supermassive black holes. A nearby but somewhat more massive star cluster (MGG-9) shows no evidence of such an intermediate mass black hole, raising the issue of just what physical characteristics of the clusters can account for this difference. Here we report numerical simulations of the evolution and the motions of stars within the clusters, where stars are allowed to mergers with each other. We find that for MGG-11 dynamical friction leads to the massive stars sinking rapidly to the center of the cluster to participate in a runaway collision, thereby producing a star of 800-3000Msun, which ultimately collapses to an black hole of intermediate mass. No such runaway occurs in the cluster MGG-9 because the larger cluster radius leads to a mass-segregation timescale a factor of five longer than for MGG-11.
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A promising mechanism to form intermediate-mass black holes (IMBHs) is the runaway merger in dense star clusters, where main-sequence stars collide and form a very massive star (VMS), which then collapses to a black hole. In this paper we study the effects of primordial mass segregation and the importance of the stellar initial mass function (IMF) on the runaway growth of VMSs using a dynamical Monte Carlo code for N-body systems with N as high as 10^6 stars. Our code now includes an explicit treatment of all stellar collisions. We place special emphasis on the possibility of top-heavy IMFs, as observed in some very young massive clusters. We find that both primordial mass segregation and the shape of the IMF affect the rate of core collapse of star clusters and thus the time of the runaway. When we include primordial mass segregation we generally see a decrease in core collapse time (tcc). Moreover, primordial mass segregation increases the average mass in the core, thus reducing the central relaxation time, which also decreases tcc. The final mass of the VMS formed is always close to sim 10^-3 of the total cluster mass, in agreement with the previous studies and is reminiscent of the observed correlation between the central black hole mass and the bulge mass of the galaxies. As the degree of primordial mass segregation is increased, the mass of the VMS increases at most by a factor of 3. Flatter IMFs generally increase the average mass in the whole cluster, which increases tcc. For the range of IMFs investigated in this paper, this increase in tcc is to some degree balanced by stellar collisions, which accelerate core collapse. Thus there is no significant change in tcc for the somewhat flatter global IMFs observed in very young massive clusters.
We study the early dynamical evolution of young, dense star clusters 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 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 ~0.1, 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 ~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.
We consider spherical stellar clusters with a broad mass function and a relaxation time short enough so that the segregation of massive stars toward the centre occurs before they have time to evolve off the main sequence. The relaxational and collisional dynamics of model clusters is followed with a high-resolution Monte Carlo code. Stellar collisions are treated in a realistic way, through the use of a outcome of a very large set of SPH simulations. We find that, even in proto-galactic nuclei models with high velocity dispersions, run-away growth of a very massive star (VMS, M>100 M_sun) occurs in all cases when the core collapse time is shorter than the MS life time of massive stars, i.e. 3 Myrs. The VMS is a likely progenitor for an intermediate-mass or massive black hole (IMBH/MBH).
Black holes formed in dense star clusters, where dynamical interactions are frequent, may have fundamentally different properties than those formed through isolated stellar evolution. Theoretical models for single star evolution predict a gap in the black hole mass spectrum from roughly $40-120,M_{odot}$ caused by (pulsational) pair-instability supernovae. Motivated by the recent LIGO/Virgo event GW190521, we investigate whether black holes with masses within or in excess of this upper-mass gap can be formed dynamically in young star clusters through strong interactions of massive stars in binaries. We perform a set of $N$-body simulations using the CMC cluster-dynamics code to study the effects of the high-mass binary fraction on the formation and collision histories of the most massive stars and their remnants. We find that typical young star clusters with low metallicities and high binary fractions in massive stars can form several black holes in the upper-mass gap and often form at least one intermediate-mass black hole. These results provide strong evidence that dynamical interactions in young star clusters naturally lead to the formation of more massive black hole remnants.
Using Monte Carlo codes, we follow the collisional evolution of clusters in a variety of scenarios. We consider the conditions under which a cluster of main sequence stars may undergo rapid core collapse due to mass segregation, thus entering a phase of runaway collisions, forming a very massive star (VMS, M >= 1000 Msun) through repeated collisions between single stars. Although collisional mass loss is accounted for realistically, we find that a VMS forms even in proto-galactic nuclei models with a high velocity dispersion (many 100 km/s). Such a VMS may be a progenitor for an intermediate-mass black hole (M >= 100 Msun). In contrast, in galactic nuclei hosting a central massive black hole, collisions are found to be disruptive. The stars which are subject to collisions are progressively ground down by high-velocity collisions and a merger sequence appears impossible.
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