Dynamics and Stability of Black Hole Star Clusters

INTRODUCTION The stellar evolution inevitably produces remnant stars such as white dwarfs, neutron stars and black holes. In old stellar systems dominated by low mass stars, these remnant stars can play important roles in dynamical evolution. For example, the concentrated dark mass indicated by spectroscopic observations in some nearby galaxies are interpreted as central black holes, but a compact cluster of remnant stars can be an alternative explanation [1]. The dynamical evolution of spherical stellar systems have been studied in great detail using various numerical techniques. The core collapse is a natural consequence of the gravothermal instability existing in collisionless stellar systems. The time to reach the core collapse is a several multiple of initial half-mass relaxation time. The relaxation time scale is difficult to define for star clusters at galactic nuclei since there is no clear boundary. The central relaxation time scale can be a well define a quantity, b