Exploring the effects of pressure on the radial accretion of dark matter by a Schwarzschild supermassive black hole

TL;DR

This study uses numerical simulations to analyze how pressure influences the radial accretion of dark matter onto supermassive black holes, revealing that pressure can significantly limit black hole growth from dark matter accretion.

Contribution

It provides the first detailed numerical analysis of pressure effects on dark matter accretion onto Schwarzschild black holes, exploring steady state conditions and growth implications.

Findings

Zero-pressure dark matter leads to rapid black hole growth.

Non-zero pressure dark matter results in minimal black hole mass increase.

Pressure can suppress dark matter accretion, affecting black hole evolution.

Abstract

Based on the numerical solution of the time-dependent relativistic Euler equations onto a fixed Schwarzschild background space-time, we estimate the accretion rate of radial flow toward the horizon of a test perfect fluid obeying an ideal gas equation of state. We explore the accretion rate in terms of the initial density of the fluid for various values of the inflow velocity in order to investigate whether or not sufficiently arbitrary initial conditions allow a steady state accretion process depending on the values of the pressure. We extrapolate our results to the case where the fluid corresponds to dark matter and the black hole is a supermassive black hole seed. Then we estimate the equation of state parameters that provide a steady state accretion process. We found that when the pressure of the dark matter is zero, the black hole's mass grows up to values that are orders of magnitude above $10^{9}M_{\odot}$ during a lapse of 10Gyr, whereas in the case of the accretion of the ideal gas dark matter with non zero pressure the accreted mass can be of the order of $\sim 1M_{\odot}/10Gyr$ for black holes of $10^{6}M_{\odot}$. This would imply that if dark matter near a supermassive black hole acquires an equation of state with non trivial pressure, the contribution of accreted dark matter to the supermassive black hole growth could be small, even though only radial accretion is considered.