Paper detail

An upper limit to the central density of dark matter haloes from consistency with the presence of massive central black holes

We study the growth rates of massive black holes in the centres of galaxies from accretion of dark matter from their surrounding haloes. By considering only the accretion due to dark matter particles on orbits unbound to the central black hole, we obtain a firm lower limit to the resulting accretion rate. We find that a runaway accretion regime occurs on a timescale which depends on the three characteristic parameters of the problem: the initial mass of the black hole, and the volume density and velocity dispersion of the dark matter particles in its vicinity. An analytical treatment of the accretion rate yields results implying that for the largest black hole masses inferred from QSO studies ($>10^{9} M_{\odot}$), the runaway regime would be reached on time scales which are shorter than the lifetimes of the haloes in question for central dark matter densities in excess of $250 M_{\odot}$pc$^{-3}$. Since reaching runaway accretion would strongly distort the host dark matter halo, the inferences of QSO black holes in this mass range lead to an upper limit on the central dark matter densities of their host haloes of $ρ_{0} < 250 M_{\odot} $pc$^{-3}$. This limit scales inversely with the assumed central black hole mass. However, thinking of dark matter profiles as universal across galactic populations, as cosmological studies imply, we obtain a firm upper limit for the central density of dark matter in such structures.