Relativistic Bondi accretion for stiff equations of state

Abstract

We revisit Bondi accretion – steady-state, adiabatic, spherical gas flow onto a Schwarzschild black hole at rest in an asymptotically homogeneous medium – for stiff polytropic equations of state (EOSs) with adiabatic indices Γ > 5/3. A general relativistic treatment is required to determine their accretion rates, for which we provide exact expressions. We discuss several qualitative differences between results for soft and stiff EOSs – including the appearance of a minimum steady-state accretion rate for EOSs with Γ ≥ 5/3 – and explore limiting cases in order to examine these differences. As an example we highlight results for Γ = 2, which is often used in numerical simulations to model the EOS of neutron stars. We also discuss a special case with this index, the ultra-relativistic ‘causal’ EOS, P = ρ. The latter serves as a useful limit for the still undetermined neutron-star EOS above nuclear density. The results are useful, for example, to estimate the accretion rate onto a mini-black hole residing at the center of a neutron star.

Self-Interacting Dark Scalar Spikes around Black Holes via Relativistic Bondi Accretion

“…1. This contrasts with the result of [65] in considering the relativistic Bondi accretion of the matter with polytropic EoS, for which the accretion rate remains finite as a ∞ increases. However, there is a trade-off between the accretion rate ( Ṁ ) and accretion range (r B ): The larger the accretion rate, the smaller the accretion range, see Fig.…”

“…By solving the relativistic Bondi accretion problem, we find that the corresponding accretion rate, Ṁ ≥ 96πG 2 M 2 m 4 /λ 3 , is bounded from below, and can become divergently large when the initial sound speed approaches the sound barrier. This is quite different from the one for the polytropic type of matter [65]. Assuming this scalar field dominates the main component of dark matter around the black hole, the shape of the density spike is determined by the model parameters of the dark matter model, i.e., mass and quartic coupling.…”

“…On the other hand, we can fit some particular region over which γ remains constant. In such cases, the result shall take the limiting power-law form obtained in [65] (see (A.8) therein)…”

“…Inspired by the early works [59][60][61], there are recent studies on the spike or cusp profiles around a black hole by quite different approaches for various DM models [62][63][64][65][66][67][68]. Our work can be seen as an extension along the same line but consider a nontrivial SIDM with a closed form of non-polytropic EoS.…”

Constraints on Relic Magnetic Black Holes

“…Some magnetic black holes would be able to cause this collapse because the friction between them and the electron Fermi gas in the neutron star allows them to be captured by the neutron star, while uncharged primordial black holes are much less likely to get trapped in a neutron star they pass through. The minimum accretion rate for a black hole in a degenerate neutron gas with a stiff equation of state, as one might expect in a neutron star core was found in [84] to be: (5.11) A sub-extremal magnetic black hole with a mass above ∼ 10 22 g can easily consume a neutron star within 1 Gyr, causing it to collapse into a black hole below the lower mass limit on a black hole formed from a collapsing star.…”