Selfinteracting dark matter cusps around massive black holes
Abstract
We adopt the conduction fluid approximation to model the steadystate 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 BahcallWolf powerlaw 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, selfinteracting dark matter (SIDM) halo with a velocitydependent cross section σ∼v^{a}, the gas again forms a powerlaw cusp, but now the SIDM density scales as r^{β}, where β=(a+3)/4, while its velocity dispersion again varies as ^{r1/2}. 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 FokkerPlanck treatment or an Nbody simulation of the Boltzmann equation with collisional perturbations.
 Publication:

Physical Review D
 Pub Date:
 January 2014
 DOI:
 10.1103/PhysRevD.89.023506
 arXiv:
 arXiv:1402.0005
 Bibcode:
 2014PhRvD..89b3506S
 Keywords:

 95.35.+d;
 98.62.g;
 98.62.Js;
 Dark matter;
 Characteristics and properties of external galaxies and extragalactic objects;
 Galactic nuclei circumnuclear matter and bulges;
 Astrophysics  Cosmology and Extragalactic Astrophysics;
 Astrophysics  Galaxy Astrophysics;
 Astrophysics  High Energy Astrophysical Phenomena;
 General Relativity and Quantum Cosmology
 EPrint:
 11 pages, 2 figures