http://arxiv.org/abs/2112.05160

We consider the spike mass density profile in a dark halo by self-consinstently solving the relativisitic 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 with mass $m\simeq 10^{-5}{\rm eV}$ and quartic self-coupling $\lambda\gtrsim10^{-20}$ to be compatible with the properties of a typical dark halo. 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 $\dot{M}{\rm min}\simeq1.41\times 10^{-10}~{\rm M}\odot~{\rm yr}^{-1}$, 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 the dark matter with Coulomb-like self-interaction.

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W. Feng, A. Parisi, C. Chen, et. al.
Mon, 13 Dec 21
4/70

Comments: 20 pages, 2 figures