ANALYTICAL STUDY OF ADIABATIC BLACK-HOLE GROWTH IN SPHERICAL STELLAR-SYSTEMS

We consider the dynamical effects of adiabatic growth of a black hole at the center of a collisionless spherical stellar system, with or without initial rotation. An analytical description of the resulting density, velocity, and velocity dispersion profiles is obtained and checked against exact numerical calculations. Two regimes can be identified, with black hole mass either smaller or larger than the initial core mass, that are characterized by qualitatively different density cusps. The behavior of these self-consistent adiabatic models is compared to that of some fitting formulae that have been recently used to study light profiles at HST resolution. Such a comparison allows one to identify the black hole mass ranges in which each formula applies, and provides a direct relation between the fitting parameters and the black hole mass.