M. Atakan Gürkan

Formation of Massive Black Holes in Dense Star Clusters. I. Mass Segregation and Core Collapse

We review possible dynamical formation processes for central massive black holes in dense star clusters. We focus on the early dynamical evolution of young clusters containing a few thousand to a few million stars. One natural formation path for a central seed black hole in these systems involves the development of the Spitzer instability, through which the most massive stars can drive the cluster to core collapse in a very short time. The sudden increase in the core density then leads to a runaway collision process and the formation of a very massive merger remnant, which must then collapse to a black hole. Alternatively, if the most massive stars end their lives before core collapse, a central cluster of stellar-mass black holes is formed. This cluster will likely evaporate before reaching the highly relativistic state necessary to drive a runaway merger process through gravitational radiation, thereby avoiding the formation of a central massive black hole. We summarize the conditions under which these different paths will be followed, and present the results of recent numerical simulations demonstrating the process of rapid core collapse and runaway collisions between massive stars.

The Disruption of Stellar Clusters Containing Massive Black Holes near the Galactic Center

We present results from dynamical Monte Carlo simulations of dense star clusters near the Galactic center. These clusters sink toward the center of the Galaxy by dynamical friction. During their in-spiral, they may undergo core collapse and form an intermediate-mass black hole through runaway collisions. Such a cluster can then reach within a parsec of the Galactic center before it completely disrupts, releasing many young stars in this region. This scenario provides a natural explanation for the presence of the young stars observed near the Galactic center. Here we determine the initial conditions for this scenario to work, and we derive the mass distribution of cluster stars as a function of distance from the Galactic center. For reasonable initial conditions, we find that clusters massive enough for rapid in-spiral would include a larger number of massive stars (m* 30 M☉) than currently observed in the in-spiral region. We point out several possible explanations for this apparent discrepancy.

Massive Black Hole Binaries from Collisional Runaways

Recent theoretical work has solidified the viability of the collisional runaway scenario in young dense star clusters for the formation of very massive stars (VMSs), which may be precursors to intermediate-mass black holes (IMBHs). We present first results from a numerical study of the collisional runaway process in dense star clusters containing primordial binaries. Stellar collisions during binary scattering encounters provide an alternate channel for runaway growth, somewhat independent of direct collisions between single stars. We find that clusters with binary fractions 10% yield two VMSs via collisional runaways, presenting the exotic possibility of forming IMBH-IMBH binaries in star clusters. We discuss the implications for gravitational wave observations and the impact on cluster structure.

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 ) 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. 1. Fast core collapse of a stellar cluster We are exploring pathways through which dynamical evolution of a stellar cluster may lead to the formation of an intermediate-mass black hole (IMBH). We consider the evolution of spherical clusters with a broad mass function (M∗ = 0.2− 120M , typically). Using so-called “Monte Carlo” (MC) and “gaseous” simulation techniques, we have shown that core collapse, driven by mass-segregation, occurs very quickly, i.e. within of order 15 % of the central relaxation time (Gürkan, Freitag & Rasio 2004). During core collapse, the central regions of the cluster become completely dominated by the most massive stars. The central density steadily increases until the first stellar collisions occur. However, the central velocity dispersion decreases during most of the evolution, as a result of a tendency toward kinetic energy equipartition between massive stars and lighter ones, see Fig. 1. Hence relative velocities of a few 1000 km s−1 are never reached and one may expect disruptive collisions to be rare. 2. Collisional run-away In recent MC simulations, we have introduced collisions between single MS stars (Rasio, Freitag, & Gürkan 2004; Freitag, Gürkan & Rasio, in preparation). Our prescription for the outcome of collisions is based on ∼ 15 000 SPH simulations (Freitag & Benz 2004). Hence, we do not assume that collisions are perfect mergers but allow for collisional mass loss and fly-bys, a likely outcome for encounters with relative velocities of a few 100 km s−1. However, we observe that, provided core collapse occurs within less than ∼ 3 Myrs (the time needed for massive stars to evolve off the MS), the cluster always enters a run-away phase in which a star more massive than 1000 M grows through repeated mergers (mostly with ∼ 100 M stars). This is shown, for one simulation, in Fig. 2. Such a very massive star (VMS) is a likely progenitor for an IMBH.