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In this paper, globular star clusters which contain a sub-system ofstellar-mass black holes (BH) are investigated. This is done by consideringtwo-component models, as these are the simplest approximation of more realisticmulti-mass systems, where one component represents the BH population and theother represents all the other stars. These systems are found to undergo a longphase of evolution where the centre of the system is dominated by a dense BHsub-system. After mass segregation has driven most of the BH into a compactsub-system, the evolution of the BH sub-system is found to be influenced by thecluster in which it is contained. The BH sub-system evolves in such a way as tosatisfy the energy demands of the whole cluster, just as the core of a onecomponent system must satisfy the energy demands of the whole cluster. The BHsub-system is found to exist for a significant amount of time. It takesapproximately 10t_{rh,i}, where t_{rh,i} is the initial half-mass relaxationtime, from the formation of the compact BH sub-system up until the time when90% of the sub-system total mass is lost (which is of order 10^{3} times thehalf-mass relaxation time of the BH sub-system at its time of formation). Basedon theoretical arguments the rate of mass loss from the BH sub-system(\dot{M}_2) is predicted to be -(beta*zeta*M)/(alpha*t_{rh}), where M is thetotal mass, t_{rh} is the half-mass relaxation time, and alpha, beta, zeta arethree dimensionless parameters (see Section 2 for details). An interestingconsequence of this is that the rate of mass loss from the BH sub-system isapproximately independent of the stellar mass ratio (m_2/m_1) and the totalmass ratio (M_2/M_1) (in the range m_2/m_1 >~ 10 and M_2/M_1 ~ 10^{-2}, wherem_1, m_2 are the masses of individual low-mass and high-mass particlesrespectively, and M_1, M_2 are the corresponding total masses).

Dynamical evolution of black hole sub-systems in idealised star clusters