**Authors:**

(1) Antonio Riotto, Département de Physique Theorique, Universite de Geneve, 24 quai Ansermet, CH-1211 Geneve 4, Switzerland and Gravitational Wave Science Center (GWSC), Universite de Geneve, CH-1211 Geneva, Switzerland;

(2) Joe Silk, Institut d’Astrophysique, UMR 7095 CNRS, Sorbonne Universite, 98bis Bd Arago, 75014 Paris, France, Department of Physics and Astronomy, The Johns Hopkins University, Baltimore MD 21218, USA, and Beecroft Institute of Particle Astrophysics and Cosmology, Department of Physics, University of Oxford, Oxford OX1 3RH, UK.

## Table of Links

2.1 What is the abundance of PBHs?

2.2 What is the effect of PBH clustering?

2.3 What fraction of the currently observed GW events can be ascribed to PBHs?

3.3 Plugging the pair instability gap with PBH?

3.4 PBH eccentricity, 3.5 PBH spin and 3.6 Future gamma-ray telescopes

## 3.3 Plugging the pair instability gap with PBH?

An equally powerful mass challenge for PBH arises from the pair instability gap. This is generated by the catastrophic core collapse of massive stars that results from pair-instability SNe, and predicts a deficit of astrophysical BH between ∼ 50 M⊙ and ∼ 120 M⊙. The full LIGO-Virgo O3 data set reveals

a definitive decline in merger rates above ∼ 40 M⊙ [55] but with several candidates filling this gap at high credibility [56].

Could PBH populate the pair instability gap? A smoking gun signature would be a feature in the BH mass spectrum, most likely indicative of a new formation mechanism.

## 3.4 PBH eccentricity

Even though PBH binaries are formed with large eccentricity at high redshift, they have enough time to circularize before the GW signal can enter the observation band of current and future detectors. This implies that an observation of a non-zero eccentricity e would rule out the interpretation as a primordial binary formed in the early Universe, while it may still be compatible with a PBH binary formed in the late-time universe [57, 58].

## 3.5 PBH spin

The PBHs form in the early universe through the standard scenario of the collapse of large overdensities inherit a characteristic mass-spin correlations induced by accretion effects [7]. Using this criterion for determining the possible primordial nature of individual GW events would require reducing uncertainties on the accretion model and studied at the population level [59].

Fig. 3 presents a flowchart from Ref. [47] one might follow to assess the primordial nature of a binary merger based on measurements of the redshift z, eccentricity e, tidal deformability Λ, component masses m, and dimensionless spins χ.

This paper is available on arxiv under CC BY 4.0 DEED license.