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

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 $m\simeq 10^{-5}\mathrm{eV}$ and quartic self-coupling $\lambda \lesssim 10^{-19}$ 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, ${\dot{M}}_{\min }=96\pi G^2{M}^2{m}^4/\lambda {\hslash }^3$. Therefore, for $M=10^6{\mathrm{M}}_{\odot }$ we have ${\dot{M}}_{\min }\simeq 1.41\times 10^{-9}{\mathrm{M}}_{\odot }{\mathrm{yr}}^{-1}$, 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.

20 pages, 2 figures, version accepted for publication in JCAP

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