Observations show that supermassive black holes (SMBHs) with a mass of ∼109 M ⊙ exist when the universe is just 6% of its current age. We propose a scenario where a self-interacting dark matter halo experiences gravothermal instability and its central region collapses into a seed black hole. The presence of baryons in protogalaxies could significantly accelerate the gravothermal evolution of the halo and shorten collapse timescales. The central halo could dissipate its angular momentum remnant via viscosity induced by the self-interactions. The host halo must be on high tails of density fluctuations, implying that high-z SMBHs are expected to be rare in this scenario. We further derive conditions for triggering general relativistic instability of the collapsed region. Our results indicate that self-interacting dark matter can provide a unified explanation for diverse dark matter distributions in galaxies today and the origin of SMBHs at redshifts z ∼ 6–7.

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 109 M⊙ 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. https://github.com/michaelwxfeng/truncated-Maxwell-Boltzmann.

We study the Starobinsky or R 2 model of f (R) = R + αR 2 for neutron stars with the structure equations represented by the coupled differential equations and the polytropic type of the matter equation of state. The junction conditions of f (R) gravity are used as the boundary conditions to match the Schwarschild solution at the surface of the star. Based on these the conditions, we demonstrate that the coupled differential equations can be solved directly. In particular, from the dimensionless equation of stateρ =kp γ withk ∼ 5.0 and γ ∼ 0.75 and the constraint of α 1.47722 × 10 7 m 2 , we obtain the minimal mass of the NS to be around 1.44 M ⊙ . In addition, ifk is larger than 5.0, the mass and radius of the NS would be smaller.