The influence of dark matter halo onto the evolution of a supermassive black hole

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Abstract
The influence of dark matter (DM) on the growth of supermassive black holes (SMBHs) in galaxies is studied. It is shown that gravitational scattering of DM particles on bulge stars leads to diffusion of DM in phase space {m, m_z, I} ('m' denotes the angular momentum and 'I' is the radial action). Appropriate diffusion coefficients are calculated for different bulge models, and it is argued that the diffusion along 'm' axis is the most important effect. It is shown that this process leads to noticeable flow of DM into the black hole (BH), resulting in its power-law growth: M_{bh} ~ t^{9/16}. Comparison with observational data shows that, in principle, this effect may explain observed masses of SMBHs. Special attention is paid to the corrections related to the innermost region of BH gravitational influence and the diffusion along 'I' axis. Their influence on the BH growth law is shown to be negligible in most cases.

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