Effect of a High-Precision Semi-Analytical Mass Function on the Merger Rate of Primordial Black Holes in Dark Matter Halos

TL;DR

This paper investigates how a high-precision semi-analytical mass function influences the merger rate of primordial black holes in dark matter halos, with implications for gravitational wave observations and PBH abundance constraints.

Contribution

It introduces the Del Popolo (DP) mass function and demonstrates its impact on PBH merger rates compared to previous models, enhancing the understanding of PBH contributions to gravitational wave signals.

Findings

DP mass function can amplify PBH merger rates for 30 solar mass black holes.

Merger rates with DP mass function align with LIGO-Virgo observations for certain PBH fractions.

DP mass function helps tighten constraints on the primordial black hole fraction.

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 halo density profile, 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 $M_{\rm PBH} = 30M_{\odot}$, 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 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 $f_{\rm PBH} \gtrsim \mathcal{O}(10^{-1})$. This implies that the DP mass function can be used to strengthen constraints on the fraction of PBHs.