Self-interacting dark scalar spikes around black holes via relativistic Bondi accretion

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 ? 10(-5) eV and quartic self-coupling lambda ? 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, M-min = 96 pi G(2)M(2)m(4)/lambda h(3). Therefore, for M = 10(6) M? we have M-min ? 1.41 x 10(-9) M-? 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) proportional to r(-1.20) near the sound horizon, rho(0)(r) proportional to r(-1.00) towards the Bondi radius and rho(0)(r) proportional to r(-1.08) for the region in between. This contrasts with more cuspy rho(0)(r) proportional to r(-1.75) for dark matter with Coulomb-like self-interaction.

Automated summary

The article discusses the spike mass density profile of dark matter in a dark halo, by self-consistently solving the relativistic Bondi accretion of dark matter onto a black hole. The research findings show that within the self-gravitating regime, the spike density profile does not fit well with a single-power law but a double-power one.