Dynamical evolution of black hole subsystems in idealized star clusters

Abstract

In this paper, globular star clusters which contain a sub-system of stellar-mass black holes (BH) are investigated. This is done by considering two-component models, as these are the simplest approximation of more realistic multi-mass systems, where one component represents the BH population and the other represents all the other stars. These systems are found to undergo a long phase of evolution where the centre of the system is dominated by a dense BH sub-system. After mass segregation has driven most of the BH into a compact sub-system, the evolution of the BH sub-system is found to be influenced by the cluster in which it is contained. The BH sub-system evolves in such a way as to satisfy the energy demands of the whole cluster, just as the core of a one component system must satisfy the energy demands of the whole cluster. The BH sub-system is found to exist for a significant amount of time. It takes approximately 10t rh,i , where t rh,i is the initial half-mass relaxation time, from the formation of the compact BH sub-system up until the time when 90% of the sub-system total mass is lost (which is of order 10 3 times the half-mass relaxation time of the BH subsystem at its time of formation). Based on theoretical arguments the rate of mass loss from the BH sub-system (Ṁ 2 ) is predicted to be −βζM/(αt rh ), where M is the total mass, t rh is the half-mass relaxation time, and α, β, ζ are three dimensionless parameters (see Section 2 for details). An interesting consequence of this is that the rate of mass loss from the BH sub-system is approximately independent of the stellar mass ratio (m 2 /m 1 ) and the total mass ratio (M 2 /M 1 ) (in the range m 2 /m 1 10 and M 2 /M 1 ∼ 10 −2 , where m 1 , m 2 are the masses of individual low-mass and high-mass particles respectively, and M 1 , M 2 are the corresponding total masses). The theory is found to be in reasonable agreement with most of the results of a series of N-body simulations, and with all of the models if the value of ζ is suitable adjusted. Predictions based on theoretical arguments are also made about the structure of BH sub-systems. Other aspects of the evolution are also considered such as the conditions for the onset of gravothermal oscillation. out any supernova explosion (Fryer 1999). Uncertainty in the natal kicks leads to uncertainty in the initial size of the BH population. As the BH are more massive than the other stars in the system, any retained BH will undergo mass segregation and almost all are likely to become concentrated in the centre of the system, eventually forming a compact sub-system.The mass of the BH sub-system decreases over time because BH binaries form in the dense core of the BH subsystem, causing the ejection of single BH and ultimately the binaries themselves through super-elastic encounters (see

Binary Black Holes in Dense Star Clusters: Exploring the Theoretical Uncertainties

“…The process and timescale for energy production from BH dynamics depend critically on the mass segregation timescale (t S ) in a cluster (e.g., Breen & Heggie 2013;Morscher et al 2013Morscher et al , 2015. The mass segregation timescale of a massive object depends on the relaxation timescale (t r ), and the ratio of its mass to the average stellar mass (〈m〉) in its neighborhood, (e.g., Gürkan et al 2004).…”

Black hole binaries dynamically formed in globular clusters

“…BHs segregate into the cluster core due to dynamical friction then form a dense BH subsystems in time-scale rather quickly (e.g. Lee 1995Lee , 2001aBreen & Heggie 2013). The BH subsystem in the central part then undergoes core collapse rapidly, further increasing the core density composed of BHs.…”

A Dynamical Gravitational Wave Source in a Dense Cluster

“…This lends credence to the validity of their relationship and means that we can assume that the BH subsystem is in the energy balance phase at this time. We note that m 2 /m 1 , the ratio of the average BH mass to the average stellar mass, is about 15 for our model at 7 Gyr compared to m 2 /m 1 = 10 used by Breen & Heggie (2013) …”