Collisional Dark Matter and the Origin of Massive Black Holes

If the cosmological dark matter is primarily in the form of an elementary particle which has mass $m_p$ and cross section for self-interaction $\sigma$, then seed black holes (formed in stellar collapse) will grow in a Hubble time $t_H$ due to accretion of the dark matter to a mass, $M_H=\sqrt{{\mathrm{IC}}_A^9{t}_H\left(\sigma {/G}^3{m}_p{c}^2\right)}=7.1\mathrm{}\times {10}^6(\sigma {/m}_p{)}^{1/2}{V}_c^{9/2}{t}_{H,15\mathrm{}}^{1/2}$ solar masses. Here $I$ is a numerical factor, $C_A$ the galactic velocity dispersion, and $V_c$ its rotation velocity. For the same values of ( $\sigma {/m}_p$) that are attractive with respect to other cosmological desiderata, this produces massive black holes in the $({10}^6–{10}^9)M_{\odot }$ range observed, with the same dependence on a $V_c$ seen, and with a time dependence consistent with observations. Other astrophysical consequences of collisional dark matter and tests of the idea are noted.