On tidal capture of primordial black holes by neutron stars

TL;DR

This paper compares two methods for estimating the energy loss of primordial black holes passing through neutron stars, concluding that both approaches are consistent when considering realistic supersonic velocities.

Contribution

The study provides an analytical model demonstrating the consistency of dynamical friction and tidal deformation approaches in estimating PBH energy loss in neutron stars.

Findings

Surface wave excitation is suppressed for supersonic PBHs.

Both energy loss estimation methods yield consistent results.

Implications for constraining PBH dark matter fraction.

Abstract

The fraction of primordial black holes (PBHs) of masses $10^{17} - 10^{26}$ g in the total amount of dark matter may be constrained by considering their capture by neutron stars (NSs), which leads to the rapid destruction of the latter. The constraints depend crucially on the capture rate which, in turn, is determined by the energy loss by a PBH passing through a NS. Two alternative approaches to estimate the energy loss have been used in the literature: the one based on the dynamical friction mechanism, and another on tidal deformations of the NS by the PBH. The second mechanism was claimed to be more efficient by several orders of magnitude due to the excitation of particular oscillation modes reminiscent of the surface waves. We address this disagreement by considering a simple analytically solvable model that consists of a flat incompressible fluid in an external gravitational field. In this model, we calculate the energy loss by a PBH traversing the fluid surface. We find that the excitation of modes with the propagation velocity smaller than that of PBH is suppressed, which implies that in a realistic situation of a supersonic PBH the large contributions from the surface waves are absent and the above two approaches lead to consistent expressions for the energy loss.