The growth of supermassive black holes in the centers of galaxies: absorption of stars and activity of galactic nuclei

The evolution of a supermassive black hole in the center of galaxy is considered. We analyze the kinetic equation describing relaxation processes associated with stellar encounters. The initial distribution function of stars is assumed to be isothermal, and it changes in accordance with consumption of stars by the black hole. We calculate the consumption rate and obtain the law of growth of supermassive black hole, i.e. the dependence of the black hole mass on time and on the velocity dispersion of stars. The obtained values of mean black hole mass and mean rate of stars consumption by a black hole are in reasonable agreement with observational data.