## 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} = 96πG ^{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.

Original language | English |
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Article number | 032 |

Journal | Journal of Cosmology and Astroparticle Physics |

Volume | 2022 |

Issue number | 8 |

DOIs | |

Publication status | Published - 2022 Aug 1 |

## Keywords

- accretion
- astrophysical fluid dynamics
- dark matter theory
- massive black holes

## ASJC Scopus subject areas

- Astronomy and Astrophysics