Models of Galaxies with Central Black Holes: Adiabatic Growth in Spherical Galaxies

We add black holes to nonrotating, spherical galaxy models, with the assumption that the black-hole growth is slow compared with the dynamical time but fast compared with the relaxation time. The outcome differs depending on whether the core of the initial galaxy does or does not resemble that of an isothermal sphere. For the isothermal case the previously-known results are confirmed and sharpened: the black hole induces cusps in the density ($\rho\sim r^{-3/2}$) and velocity dispersion ($v^2\sim r^{-1}$), and a tangential anisotropy in the velocity distribution away from the center. For the non-isothermal case the induced density cusp is steeper, and the induced anisotropy is larger and penetrates right to the center. The cusp around the black hole is insensitive to anisotropy in the initial velocity distribution, and also to the origin of the black hole, unless its mass comes exclusively from the stars of lowest angular momentum, in which case the cusp is suppressed. We discuss the implications for the interpretation of evidence for massive black holes in galactic nuclei.