Dark matter dynamics in the galactic center

The evolution of dark matter in central areas of galaxies is considered (the Milky Way is taken as an example). It is driven by the scattering off of dark matter particles by bulge stars, their absorption by the supermassive black hole, and self-annihilation. This process is described by the diffusion equation in the phase space of energy and angular momentum. The equation was integrated for several different models of initial dark matter distribution and using various assumptions about the dynamical factors. It turns out that because the Milky Way center is rather dynamically old (similar to 4 relaxation times t(r)), the difference in initial conditions almost vanishes. The density attains a nearly universal profile, and the gamma-ray flux from dark matter annihilation lies in a rather narrow range, which enables a more robust determination of the dark matter parameters. By presenting the mass of dark matter inside the black hole, the sphere of influence (r < 2 pc) has been reduced approximately twice, mostly because of heating by stars. It is shown that the dynamics of dark matter for t greater than or similar to t(r) is determined mainly by stars outside the sphere of influence.