Press-Schechter primordial black hole mass functions and their observational constraints

TL;DR

This paper develops a modified Press-Schechter formalism to derive primordial black hole mass functions, constraining their role as dark matter and linking to LIGO black hole observations.

Contribution

It introduces an extended PS model with a new parameter for PBH formation, accommodating various physical conditions and enabling constraints from observational data.

Findings

Regions where PBHs could account for all dark matter.

Characteristic PBH mass around 100 solar masses consistent with LIGO detections.

Extended mass functions can be constrained using existing monochromatic PBH constraints.

Abstract

We present a modification of the Press-Schechter (PS) formalism to derive general mass functions for primordial black holes (PBHs), considering their formation as being associated to the amplitude of linear energy density fluctuations. To accommodate a wide range of physical relations between the linear and non-linear conditions for collapse, we introduce an additional parameter to the PS mechanism, and that the collapse occurs at either a given cosmic time, or as fluctuations enter the horizon. We study the case where fluctuations obey Gaussian statistics and follow a primordial power spectrum of broken power-law form with a blue spectral index for small scales. We use the observed abundance of super-massive black holes (SMBH) to constrain the extended mass functions taking into account dynamical friction. We further constrain the modified PS by developing a method for converting existing constraints on the PBH mass fraction, derived assuming monochromatic mass distributions for PBHs, into constraints applicable for extended PBH mass functions. We find that when considering well established monochromatic constraints there are regions in parameter space where all the dark matter can be made of PBHs. Of special interest is the region for the characteristic mass of the distribution ~10^2 M_Sun, for a wide range of blue spectral indices in the scenario where PBHs form as they enter the horizon, where the linear threshold for collapse is of the order of the typical overdensities, as this is close to the black hole masses detected by LIGO which are difficult to explain by stellar collapse.