The Merger Rate of Primordial Black Hole-Neutron Star Binaries in Ellipsoidal-Collapse Dark Matter Halo Models

Abstract: Primordial black holes (PBHs), as a potential macroscopic candidate for dark matter, can encounter other compact objects in dark matter halos because of their random distribution. Besides, the detection of gravitational waves (GWs) related to the stellar-mass black hole-neutron star (BH-NS) mergers raises the possibility that the BHs involved in such events may have a primordial origin. In this work, we calculate the merger rate of PBH-NS binaries within the framework of ellipsoidal-collapse dark matter halo models and compare it with the corresponding results derived from spherical-collapse dark matter halo models. Our results exhibit that ellipsoidal-collapse dark matter halo models can potentially amplify the merger rate of PBH-NS binaries in such a way that it is very close to the range estimated by the LIGO-Virgo observations. While spherical-collapse dark matter halo models cannot justify PBH-NS merger events as consistent results with the latest GW data reported by the LIGO-Virgo collaboration. In addition, we calculate the merger rate of PBH-NS binaries as a function of PBH mass and fraction within the context of ellipsoidal-collapse dark matter halo models. The results indicate that PBH-NS merger events with the mass of $(M_{PBH}\le 5 M_{\odot}, M_{NS}\simeq 1.4 M_{\odot})$ will be consistent with the LIGO-Virgo observations if $f_{PBH}\simeq 1$. We also show that to have at least on $(M_{PBH}\simeq 5 M_{\odot}, M_{NS}\simeq 1.4 M_{\odot})$ event in the comoving volume $1 Gpc^{3}$ annually, ellipsoidal-collapse dark matter halo models constrain the abundance of PBHs as $f_{PBH} \geq 0.1$.