Dark matter accretion into supermassive black holes

The relativistic accretion rate of dark matter by a black hole is revisited. Under the assumption that the phase space density indicator, $Q={\rho }_{\infty }/{\sigma }_{\infty }^3$, remains constant during the inflow, the derived accretion rate can be higher up to 5 orders of magnitude than the classical accretion formula, valid for nonrelativistic and noninteracting particles, when typical dark halo conditions are considered. For these typical conditions, the critical point of the flow is located at distances of about 30–150 times the horizon radius. Application of our results to black hole seeds hosted by halos issued from cosmological simulations indicate that dark matter contributes to no more than $\sim 10\%$ of the total accreted mass, confirming that the bolometric quasar luminosity is related to the baryonic accretion history of the black hole.

Figure 1

Evolution of the velocity dispersion (km/s) inside the core of halos 3 and 211 (upper panel). Evolution of the phase density ($M_{\odot }{\mathrm{pc}}^{-3}{\mathrm{km}}^{-3}{\mathrm{s}}^3$) in core for the same halos (lower panel). Time is given in units of $H_0^{-1}$.

Figure 2

In the upper panel it is shown the mass evolution of black holes while in the lower panel the evolution of the fraction of accreted dark matter is shown.

Figure 3

Evolution of the baryonic and dark matter accretion rates for halo 211 (upper panel) and halo 3 (lower panel).