Effect of a high-precision semianalytical mass function on the merger rate of primordial black holes in dark matter halos

Abstract

In this work, we study the effect of a high-precision semianalytical mass function on the merger rate of primordial black holes (PBHs) in dark matter halos. For this purpose, we first explain a theoretical framework for dark matter halo models and introduce relevant quantities such as the halo density profile, the concentration parameter, and a high-precision semianalytical function, namely Del Popolo (DP) mass function. In the following, we calculate the merger rate of PBHs in the framework of ellipsoidal-collapse dark matter halo models while considering the DP mass function, and compare it with our previous study for the Sheth-Tormen (ST) mass function. The results show that by taking the mass of PBHs as ${M}_{\mathrm{PBH}}=30{M}_{\ensuremath{\bigodot}}$, the DP mass function can potentially amplify the merger rate of PBHs. Moreover, we calculate the merger rate of PBHs for the DP mass function as a function of their mass and fraction and compare it with the black hole mergers recorded by the Laser Interferometer Gravitational-Wave Observatory (LIGO)-Virgo detectors during the latest observing run. Our findings show that the merger rate of PBHs will fall within the LIGO-Virgo band if ${f}_{\mathrm{PBH}}\ensuremath{\gtrsim}\mathcal{O}({10}^{\ensuremath{-}1})$. This implies that the DP mass function can be used to strengthen constraints on the fraction of PBHs.