Horizon growth of supermassive black hole seeds fed with collisional dark matter

TL;DR

This study models the accretion of collisional dark matter onto supermassive black hole seeds using full general relativity, finding that dark matter accretion is insufficient for SMBH growth, supporting models where SMBHs form already supermassive.

Contribution

It provides the first fully relativistic simulation of dark matter accretion onto SMBH seeds, comparing results with the Bondi formula, and analyzing density profiles near the event horizon.

Findings

Dark matter accretion does not significantly grow SMBHs.

Results align with the Bondi accretion formula in the studied regime.

SMBHs cause a cuspy density profile near the horizon.

Abstract

We present the accretion of collisional dark matter on a supermassive black hole seed. The analysis is based on the numerical solution of the fully coupled system of Einstein-Euler equations for spherically symmetric flow, where the dark matter is modeled as a perfect fluid that obeys an ideal gas equation of state. As the black hole actually grows, the accretion rate of dark matter corresponds to the black hole apparent horizon growth rate. We analyse cases with infall velocity as high as $0.5c$ and an environment density of $100M_{\odot}/\mathrm{pc}^3$, which are rather extreme conditions. Being the radial flux the maximum accretion case, our results show that the accretion of an ideal gas, eventually collisional dark matter, does not contribute significantly to SMBH masses. This result favors models predicting SMBHs were formed already with supermasses. We show that despite the fact that we are solving the full general relativistic system, for the parameter space studied our results are surprisingly similar to those obtained using the Bondi formula, which somehow certifies its use as a good approximation of a fully evolving space-time with spherical symmetry at short scales at least for dark matter densities. Additionally, we study the density profile of the gas and find that the presence of SMBHs redistributes the gas near the event horizon with a cuspy profile, whereas beyond a small fraction of a parsec it is not-cuspy anymore.