Journal
PHYSICAL REVIEW D
Volume 89, Issue 2, Pages -Publisher
AMER PHYSICAL SOC
DOI: 10.1103/PhysRevD.89.023506
Keywords
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Funding
- NSF [PHY-0963136, PHY-1300903]
- NASA at the University of Illinois at Urbana-Champaign [NNX11AE11G, NN13AH44G]
- Fortner Fellowship at UIUC
- NASA [NNX11AE11G, 148375] Funding Source: Federal RePORTER
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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 sigma similar to v(-a), the gas again forms a power-law cusp, but now the SIDM density scales as r(-beta), where beta = (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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