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

Abstract

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 ≃ 10 -5 eV and quartic self-coupling λ ≲ 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 πG 2 M 2 m 4 / λħ 3 . Therefore, for M = 10 6 M ⊙ we have M min ≃ 1.41 × 10 -9 M ⊙ yr -1 , which is subdominant compared to the Eddington accretion of baryons. The spike density profile ρ 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 ρ 0 ( r ) piecewise and find that ρ 0 ( r ) ∝ r -1.20 near the sound horizon, ρ 0 ( r ) ∝ r -1.00 towards the Bondi radius and ρ 0 ( r ) ∝ r -1.08 for the region in between. This contrasts with more cuspy ρ 0 ( r ) ∝ r -1.75 for dark matter with Coulomb-like self-interaction.