Absorption of dark matter by a supermassive black hole at the galactic center: Role of boundary conditions

The evolution of the dark matter distribution at the Galactic center is analyzed. It is caused by the combination of gravitational scattering by stars in the Galactic nucleus (bulge) and absorption by a supermassive black hole at the center of the bulge. Attention is focused on the boundary condition on the black hole. It is shown that its form depends on the energy of dark matter particles. The modified flux of dark matter particles onto the black hole is calculated. Estimates of the amount of absorbed dark matter show that the fraction of dark matter in the total mass of the black hole may be significant. The density of dark matter at the central part of the bulge is calculated. It is shown that recently observed γ radiation from the Galactic center can be attributed to the annihilation of dark matter with this density.