Relativistic Bondi accretion for stiff equations of state

TL;DR

This paper provides exact relativistic formulas for Bondi accretion onto black holes with stiff equations of state, revealing qualitative differences from softer EOSs and implications for neutron star environments.

Contribution

It introduces exact relativistic expressions for accretion rates with stiff EOSs and discusses qualitative differences from soft EOSs, including a minimum accretion rate for certain stiff EOSs.

Findings

Exact formulas for accretion rates with stiff EOSs

Minimum steady-state accretion rate for $ ext{G}\u2265 5/3$

Differences between soft and stiff EOS accretion behaviors

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 $\Gamma > 5/3$. 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 $\Gamma \geq 5/3$ - and explore limiting cases in order to examine these differences. As an example we highlight results for $\Gamma = 2$, 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, $P = \rho$. 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.