On tidal capture of primordial black holes by neutron stars
  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.
