Tidal capture of a primordial black hole by a neutron star: implications for constraints on dark matter

In a close encounter with a neutron star, a primordial black hole can get gravitationally captured by depositing a considerable amount of energy into nonradial stellar modes of very high angular number $l$. If the neutron-star equation of state is sufficiently stiff, we show that the total energy loss in the point-particle approximation is formally divergent. Various mechanisms -including viscosity, finite-size effects and the elasticity of the crust- can damp high-$l$ modes and regularize the total energy loss. Within a short time, the black hole is trapped inside the star and disrupts it by rapid accretion. Estimating these effects, we predict that the existence of old neutron stars in regions where the dark-matter density rho_{DM}>10^2 sigma/(km/s) GeV/cm^3 (where sigma is the dark-matter velocity dispersion) limits the abundance of primordial black holes in the mass range 10^{17} g < m_{PBH} < 10^{24} g, which was previously unconstrained. In combination with existing limits, our results suggest that primordial black holes cannot be the dominant dark matter constituent.