TY - JOUR

T1 - Self-interacting dark matter cusps around massive black holes

AU - Shapiro, Stuart L.

AU - Paschalidis, Vasileios

PY - 2014/1/16

Y1 - 2014/1/16

N2 - 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.

AB - 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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U2 - 10.1103/PhysRevD.89.023506

DO - 10.1103/PhysRevD.89.023506

M3 - Article

AN - SCOPUS:84894446982

VL - 89

JO - Physical Review D - Particles, Fields, Gravitation and Cosmology

JF - Physical Review D - Particles, Fields, Gravitation and Cosmology

SN - 1550-7998

IS - 2

M1 - 023506

ER -