Accretion onto black holes inside neutron stars with piecewise-polytropic equations of state: analytic and numerical treatments

TL;DR

This paper develops analytical and numerical models for spherically symmetric accretion onto black holes inside neutron stars, using piecewise-polytropic equations of state, and finds that accretion rates are mainly determined by black hole mass.

Contribution

It generalizes the relativistic Bondi solution for neutron star EOSs approximated by piecewise polytropes and validates the analytical results with hydrodynamical simulations.

Findings

Accretion rates depend primarily on black hole mass.

Excellent agreement between analytical and numerical models.

Accretion rates vary little across different neutron star EOSs.

Abstract

We consider spherically symmetric accretion onto a small, possibly primordial, black hole residing at the center of a neutron star governed by a cold nuclear equation of state (EOS). We generalize the relativistic Bondi solution for such EOSs, approximated by piecewise polytropes, and thereby obtain analytical expressions for the steady-state matter profiles and accretion rates. We compare these rates with those found by time-dependent, general relativistic hydrodynamical simulations upon relaxation and find excellent agreement. We consider several different candidate EOSs, neutron star masses and central densities and find that the accretion rates vary only little, resulting in an accretion rate that depends primarily on the black hole mass, and only weakly on the properties of the neutron star.