[Paper Review] Constraining high-redshift stellar-mass primordial black holes with next-generation ground-based gravitational-wave detectors

Ken K. Y. Ng, Gabriele Franciolini+4 more|arXiv (Cornell University)|Apr 25, 2022

Pulsars and Gravitational Waves ResearchPhysics and Astronomy136 references54 citations

TL;DR

This paper proposes using next-generation gravitational-wave detectors, Cosmic Explorer and Einstein Telescope, to constrain the abundance of high-redshift stellar-mass primordial black holes (PBHs) by exploiting the distinct redshift evolution of PBH and Population III binary black hole merger rates. It shows that with four months of data, future observations could set upper limits on PBH abundance as low as fPBH ∼10⁻⁵, improving current constraints by nearly two orders of magnitude if no PBHs exist.

ABSTRACT

The possible existence of primordial black holes in the stellar mass window has received considerable attention because their mergers may contribute to current and future gravitational-wave detections. Primordial black hole mergers, together with mergers of black holes originating from Population~III stars, are expected to dominate at high redshifts ($z\gtrsim 10$). However the primordial black hole merger rate density is expected to rise monotonically with redshift, while Population~III mergers can only occur after the birth of the first stars. Next-generation gravitational-wave detectors such as Cosmic Explorer~(CE) and Einstein Telescope~(ET) can access this distinctive feature in the merger rates as functions of redshift, allowing for a direct measurement of the abundance of the two populations, and hence for robust constraints on the abundance of primordial black holes. We simulate four-months worth of data observed by a CE-ET detector network and perform hierarchical Bayesian analysis to recover the merger rate densities. We find that if the Universe has no primordial black holes with masses of $\mathcal{O}(10M_{\odot})$, the projected upper limit on their abundance $f_{ m PBH}$ as a fraction of dark matter energy density may be as low as $f_{ m PBH}\sim \mathcal{O}({10^{-5}})$, about two orders of magnitude lower than current upper limits in this mass range. If instead $f_{ m PBH}\gtrsim 10^{-4}$, future gravitational wave observations would exclude $f_{ m PBH}=0$ at the 95\% credible interval.

Motivation & Objective

• To distinguish primordial black hole (PBH) mergers from Population III star-originated mergers using their distinct redshift evolution.
• To quantify how well next-generation ground-based GW detectors (Cosmic Explorer and Einstein Telescope) can constrain the PBH abundance fPBH in the 10–50 M⊙ mass range.
• To assess the sensitivity of hierarchical Bayesian inference on simulated CE-ET network data to detect or exclude PBHs.
• To evaluate the robustness of constraints when accretion and other astrophysical effects are neglected.
• To explore how additional features like mass, spin, and eccentricity could further improve separation of PBH and Pop III merger populations.

Proposed method

• Simulate four months of gravitational-wave data from a network of Cosmic Explorer and Einstein Telescope, incorporating realistic redshift uncertainty estimates.
• Use hierarchical Bayesian inference to recover the morphology of merger rate densities as a function of redshift (z ≥ 8) using only redshift measurements.
• Model PBH merger rate density as scaling with cosmic age as ˙nPBH ∝ (t(z)/t₀)⁻³⁴/³⁷, reflecting a monotonically increasing rate with redshift.
• Model Population III merger rate density as declining at high redshift, peaking around z ≲10, due to delayed formation after first stars.
• Assume a lognormal mass function for PBHs and neglect accretion effects to derive conservative, least stringent constraints on fPBH.
• Apply the suppression factor S(M, fPBH) ≈ 33fPBH²¹/³⁷ to account for environmental effects in early and late Universe, reducing merger rates at higher PBH abundances.

Experimental results

Research questions

• RQ1 Can next-generation gravitational-wave detectors distinguish between primordial black hole and Population III binary black hole mergers based on their redshift-dependent merger rate evolution?
• RQ2 What is the projected upper limit on the primordial black hole abundance fPBH as a fraction of dark matter energy density using four months of CE-ET data?
• RQ3 How sensitive are future GW observations to low PBH abundances, and can they detect fPBH ≳10⁻⁴ with high credibility?
• RQ4 How do the constraints change if accretion or other astrophysical effects are included in the PBH evolution model?
• RQ5 Can additional parameters such as mass, spin, or eccentricity further improve the separation of PBH and Pop III merger populations?

Key findings

• In the absence of primordial black holes (fPBH = 0), the projected upper limit on fPBH from four months of CE-ET data could reach fPBH ∼10⁻⁵, approximately two orders of magnitude lower than current observational constraints.
• If the true PBH abundance is fPBH ≳10⁻⁴, future gravitational-wave observations would exclude fPBH = 0 at the 95% credible interval, enabling a robust detection.
• The monotonically increasing merger rate of PBHs with redshift contrasts sharply with the declining rate of Population III mergers, providing a clean discriminant for population inference.
• The constraints are conservative because accretion—known to enhance PBH merger rates—was neglected; including it would allow even tighter bounds on fPBH.
• The method relies only on redshift measurements, demonstrating that the redshift evolution of merger rates alone provides powerful discriminatory power between PBH and Pop III origins.
• The results highlight the unique potential of next-generation detectors to probe the primordial universe and test the PBH dark matter hypothesis in the stellar-mass window.