Gravitational waves from primordial black holes passing by neutron stars: Observational prospects for the Galactic Center

We investigate the gravitational wave (GW) signals emitted by planetary-mass primordial black holes (PBHs) passing nearby or traversing neutron stars (NSs). While previous studies mainly focused on the detailed waveforms of the signals, we estimate the rate of PBH-NS gravitational-wave events originating from the Galactic center and compute the probability of detecting a signal over 10 years of LIGO-Virgo-KAGRA observations. We examine in detail the case of PBHs bound to NSs, focusing on eccentric orbits that give rise to repeated GW bursts emitted in correlated series, each burst corresponding to a periastron passage. Despite the enhancement from the large number of bursts produced by a single PBH-NS pair, the total number of signals produced in this way remains subdominant to those due to random unbound encounters of PBHs with NSs. We also find that both types of signals have a very small probability $P\lesssim 10^{-8}$ to be detected in a 10 year period.