Dynamical Instability of Collapsed Dark Matter Halos

Abstract

A self-interacting dark matter halo can experience gravothermal collapse, resulting in a central core with an ultrahigh density. It can further contract and collapse into a black hole, a mechanism proposed to explain the origin of supermassive black holes. We study dynamical instability of the core in general relativity. We use a truncated Maxwell-Boltzmann distribution to model the dark matter distribution and solve the Tolman-Oppenheimer-Volkoff equation. For given model parameters, we obtain a series of equilibrium configurations and examine their dynamical instability based on considerations of total energy, binding energy, fractional binding energy, and adiabatic index. Our numerical results indicate that the core can collapse into a black hole when the fractional binding energy reaches $0.035$ with a central gravitational redshift of $0.5$. We further show for the instability to occur in the classical regime, the boundary temperature of the core should be at least $10\%$ of the mass of dark matter particles; for a $10^9{\mathrm{M}}_{\odot }$ seed black hole, the particle mass needs to be larger than a few keV. These results can be used to constrain different collapse models, in particular, those with dissipative dark matter interactions.

23 pages, 4 figures, 2 tables, minor typos corrected, new section connecting to the conducting fluid model, version accepted for publication in JCAP

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• Astrophysical Tests of Dark Matter Self-Interactions
• Gravothermal collapse of Self-Interacting Dark Matter halos as the Origin of Intermediate Mass Black Holes in Milky Way satellites
• Dark Black Holes in the Mass Gap
• Testing the parametric model for self-interacting dark matter using matched halos in cosmological simulations
• Discriminating power of milli-lensing observations for dark matter models
• Exploring Self-Interacting Dark Matter Halos with Diverse Baryonic Distributions: A Parametric Approach
• Gravothermalizing into primordial black holes, boson stars, and cannibal stars
• On the Dynamical Instability of Monatomic Fluid Spheres in (N+1)-Dimensional Spacetime
• Diversifying halo structures in two-component self-interacting dark matter models via mass segregation
• A Universal Analytic Model for Gravitational Lensing by Self-Interacting Dark Matter Halos
• Gravothermal Phase Transition, Black Holes and Space Dimensionality
• Black Hole Cold Brew: Fermi Degeneracy Pressure
• Accretion of self-interacting dark matter onto supermassive black holes