Self-interacting Dark Scalar Spikes around Black Holes via Relativistic Bondi Accretion

TL;DR

This paper models the density profile of self-interacting scalar dark matter around black holes using relativistic Bondi accretion, revealing a double-power law profile that differs from Coulomb-like interactions.

Contribution

It provides a self-consistent relativistic analysis of scalar dark matter accretion onto black holes, deriving the density profile and accretion rate constraints.

Findings

Accretion rate is bounded from below and subdominant to baryonic Eddington accretion.

Density profile fits a double-power law with specific slopes near the sound horizon and Bondi radius.

Dark matter with scalar self-interaction has a less cuspy density profile compared to Coulomb-like interactions.

Abstract

We consider the spike mass density profile in a dark halo by self-consistently solving the relativistic Bondi accretion of dark matter onto a non-spining black hole of mass $M$. We assume that the dominant component of the dark matter in the halo is a Standard model gauge-singlet scalar. Its mass $m\simeq 10^{-5}{\rm eV}$ and quartic self-coupling $\lambda\lesssim10^{-19}$ are constrained to be compatible with the properties of galactic dark halos. In the hydrodynamic limit, we find that the accretion rate is bounded from below, $\dot{M}_{\rm min}=96\pi G^2M^2 m^4/\lambda\hbar^3$. Therefore, for $M=10^6~{\rm M}_\odot$ we have $\dot{M}_{\rm min}\simeq1.41\times 10^{-9}~{\rm M}_\odot~{\rm yr}^{-1}$, which is subdominant compared to the Eddington accretion of baryons. The spike density profile $\rho_0(r)$ within the self-gravitating regime cannot be fitted well by a single-power law but a double-power one. Despite that, we can fit $\rho_0(r)$ piecewise and find that $\rho_0(r) \propto r^{-1.20}$ near the sound horizon, $\rho_0(r) \propto r^{-1.00}$ towards the Bondi radius and $\rho_0(r) \propto r^{-1.08}$ for the region in between. This contrasts with more cuspy $\rho_0(r) \propto r^{-1.75}$ for dark matter with Coulomb-like self-interaction.