Accretion Onto a Black Hole at the Center of a Neutron Star: Nuclear Equations of State

A recent re-examination of Bondi accretion (see Richards, Baumgarte and Shapiro (2021)) revealed that, for stiff equations of state (EOSs), steady-state accretion can only occur for accretion rates exceeding a certain minimum. To date, this result has been explored only for gamma-law equations of state. Instead, we consider accretion onto a small black hole residing at the center of a neutron star governed by a more realistic nuclear EOS. We generalize the relativistic Bondi solution for such EOSs, approximated by piecewise polytropes, and thereby obtain analytical expressions for the accretion rates which were reflected in our numerical simulations. After taking several different piecewise EOSs at different neutron star densities into account, the accretion rates of the different EOSs were only slightly larger than the previously observed minimum. In other words there appears to be evidence for a nearly universal accretion rate that depends only on the black hole mass. However, we also observed that for certain densities the fluid profiles of several EOSs exhibited superluminal sound speeds outside the horizon of the black hole, suggesting that the EOSs are not appropriate at these densities.