Effects of formation channels and gravitational lensing on stochastic gravitational wave background

TL;DR

This paper investigates how different black hole formation channels and gravitational lensing influence the stochastic gravitational wave background, using Bayesian inference and detector sensitivity comparisons.

Contribution

It introduces a method to distinguish astrophysical and primordial black hole origins in the SGWB considering lensing effects, with implications for current and future detectors.

Findings

Both LIGO and ET can differentiate formation channels within certain frequencies.

Lensing effects modify the frequency range for model discrimination.

ET can distinguish black hole origins over a broader parameter space.

Abstract

Two primary formation channels for black holes have been proposed: the astrophysical channel, driven by the collapse of massive stars, and the primordial channel, involving their direct formation from density fluctuations in the early Universe. The key distinction between astrophysical black holes (ABHs) and primordial black holes (PBHs) is that PBHs can form at very high redshifts, before any stars have formed, leading to different stochastic gravitational-wave backgrounds (SGWBs). These SGWBs arise from the superposition of unresolved gravitational-wave signals accumulated over all redshifts. In this work, we employ the Hierarchical Bayesian Inference (HBI) framework and the publicly available GWTC-4 data to infer the population hyperparameters of PBHs. We then compute the SGWBs from ABHs and PBHs separately, accounting for the lensing effect, which can modify the strain amplitude of the SGWBs. By comparing the resulting SGWBs with the power-law integrated (PI) sensitivity curves of ground-based gravitational-wave detectors -- LIGO and the Einstein Telescope (ET) -- we find that both detectors can distinguish between these two black hole formation models within specific frequency ranges. However, LIGO is limited to a single method for distinguishing these models, and the lensing effect alters the frequency range over which discrimination is possible. In contrast, ET is capable of distinguishing ABHs from PBHs across a broader parameter space.