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Self-interacting dark matter cusps around massive black holes

Stuart L. Shapiro1,* and Vasileios Paschalidis1

  • 1Department of Physics, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA

  • *Also at Department of Astronomy and NCSA, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA.
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Phys. Rev. D 89, 023506 – Published 16 January, 2014

DOI: https://doi.org/10.1103/PhysRevD.89.023506

Abstract

We adopt the conduction fluid approximation to model the steady-state distribution of matter around a massive black hole at the center of a weakly collisional cluster of particles. By “weakly collisional” we mean a cluster in which the mean free time between particle collisions is much longer than the characteristic particle crossing (dynamical) time scale, but shorter than the cluster lifetime. When applied to a star cluster, we reproduce the familiar Bahcall-Wolf power-law cusp solution for the stars bound to the black hole. Here the star density scales with radius as r−7/4 and the velocity dispersion as r−1/2 throughout most of the gravitational well of the black hole. When applied to a relaxed, self-interacting dark matter (SIDM) halo with a velocity-dependent cross section σ∼v−a, the gas again forms a power-law cusp, but now the SIDM density scales as r−β, where β=(a+3)/4, while its velocity dispersion again varies as r−1/2. Results are obtained first in Newtonian theory and then in full general relativity. Although the conduction fluid model is a simplification, it provides a reasonable first approximation to the matter profiles and is much easier to implement than a full Fokker-Planck treatment or an N-body simulation of the Boltzmann equation with collisional perturbations.

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Phys. Rev. D 89, 023506– Published 16 January, 2014
  • Received 15 November 2013

© 2014 American Physical Society

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