Effect of a High-Precision Semi-Analytical 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 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 $M_{\mathrm{PBH}}=30M_{\odot }$, 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 $f_{\mathrm{PBH}}\gtrsim \mathcal{O}(10^{-1})$. This implies that the DP mass function can be used to strengthen constraints on the fraction of PBHs.

11 pages, 4 figures, 1 table, accepted version

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Cited by in corpus (11)

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• Primordial Black Hole Merger Rate in $f(R)$ Gravity
• On the Merger Rate of Primordial Black Holes in Cosmic Voids
• Primordial Black Hole-Neutron Star Merger Rate in Modified Gravity
• Gravitational Lensing in More Realistic Dark Matter Halo Models
• Toward More Realistic Mass Functions For Ultradense Dark Matter Halos
• Compact Binary Merger Rate with Modified Gravity in Dark-Matter Spikes
• Matching JWST UV Luminosity Functions with Refined $\Lambda$CDM Halo Models
• High-redshift Galaxies from JWST Observations in More Realistic Dark Matter Halo Models
• Ultradense Dark Matter Halos with Poisson Noise from Stellar-Mass Primordial Black Holes
• Toward Gravitational Lensing in Modified Theories of Gravity