http://arxiv.org/abs/2212.08646
In this work, we study the effect of a high-precision semi-analytical 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 semi-analytical 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 $M_{PBH} = 30M_{\odot}$, the DP mass function predicts the amplification of the merger rate of PBHs to be in the range of $(42\pm 4)\%$. 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 $f_{PBH} \gtrsim 0.1$. This implies that the DP mass function can be used to strengthen constraints on the fraction of PBHs. Moreover, our results demonstrate that for a mass range of $M_{PBH} = (10-100)M_{\odot}$, the relative amplification is predicted to be in the mean range of $(44.3 \pm 4.5)\%$.
S. Fakhry and A. Popolo
Mon, 19 Dec 22
30/62
Comments: 9 pages, 4 figures, 1 table