Curbing PBHs with PTAs

TL;DR

This paper derives bounds on primordial black hole abundance using pulsar timing array data, highlighting how non-Gaussianities and theoretical models influence these constraints and the potential for PBHs to seed supermassive black holes.

Contribution

It provides new conservative bounds on PBH abundance from PTA data, analyzing the impact of non-Gaussianities and different theoretical models on these constraints.

Findings

Constraints on PBH abundance are significant in the 0.1-1000 solar mass range.

Positive non-Gaussianity can relax or eliminate these constraints.

Theoretical uncertainties, like the peak theory, affect the strength of the bounds.

Abstract

Sizeable primordial curvature perturbations needed to seed a population of primordial black holes (PBHs) will be accompanied by a scalar-induced gravitational wave signal that can be detectable by pulsar timing arrays (PTA). We derive conservative bounds on the amplitude of the scalar power spectrum at the PTA frequencies and estimate the implied constraints on the PBH abundance. We show that only a small fraction of dark matter can consist of stellar mass PBHs when the abundance is calculated using threshold statistics. The strength and the shape of the constraint depend on the shape of the power spectrum and the nature of the non-Gaussianities. We find that constraints on the PBH abundance arise in the mass range $0.1-10^3\, M_{\odot}$, with the sub-solar mass range being constrained only for narrow curvature power spectra. These constraints are softened when positive non-Gaussianity is introduced and can be eliminated when $f_{\rm NL} \gtrsim 5$. On the other hand, if the PBH abundance is computed via the theory of peaks, the PTA constraints on PBHs are significantly relaxed, signalling once more the theoretical uncertainties in assessing the PBH abundance. We further discuss how strong positive non-Gaussianites can allow for heavy PBHs to potentially seed supermassive BHs.