Non-spherical effects on the mass function of Primordial Black Holes

TL;DR

This study examines how non-spherical effects influence the primordial black hole mass function, revealing that while they can prevent some black hole formation near the threshold, their overall impact on the mass distribution is minimal.

Contribution

It provides the first detailed analysis of non-spherical effects on PBH mass function using relativistic simulations and peak theory, considering different equations of state.

Findings

Non-sphericity can prevent black hole formation near the threshold.

Non-spherical effects slightly reduce the mass function, by a factor of a few.

The mass function's power-law scaling remains unaffected by non-sphericity.

Abstract

In this letter, we investigate the impact of non-spherical effects on the Primordial Black Hole mass function, based on the ellipticity-dependent threshold calculated by performing $3+1$ relativistic numerical simulations. We consider an equation of state of radiation $w:=P/\rho=1/3$ and a softer one $w=1/10$ with $P$ and $\rho$ being the pressure and energy density, respectively. We suppose that the curvature perturbations obey Gaussian statistics with a monochromatic power spectrum and examine the most probable ellipsoidal configurations utilizing peak theory. We also suppose the critical scaling law of the PBH mass near the threshold following the known results. The simulations arXiv:2410.03452 show that the non-sphericity can easily prevent the system from black hole formation when the initial fluctuation amplitude is near the threshold (critical scaling regime). Nevertheless, we show that the non-spherical effects make the mass function just a few times smaller and are insignificant on the mass function distribution, including the power-law scaling in the small mass region.