[Paper Review] Stochastic gravitational-wave background as a tool to investigate multi-channel astrophysical and primordial black-hole mergers

Simone S. Bavera, Gabriele Franciolini+4 more|arXiv (Cornell University)|Sep 13, 2021

Pulsars and Gravitational Waves Research4 citations

TL;DR

This paper proposes using the stochastic gravitational-wave background (SGWB) as a complementary tool to constrain the relative contributions of multiple astrophysical and primordial black hole formation channels to binary black hole mergers. By normalizing model-selected branching ratios from GWTC-2 to observed merger rates and computing the resulting SGWB energy density, the study finds a predicted amplitude of $\Omega_{\mathrm{GW}}(25\,\mathrm{Hz}) = 1.11^{+0.16}_{-0.05} \times 10^{-10}$, which lies below current LIGO-Virgo upper limits and will be detectable only by third-generation detectors like the Einstein Telescope and LISA.

ABSTRACT

The formation of merging binary black holes can occur through multiple astrophysical channels such as, e.g., isolated binary evolution and dynamical formation or, alternatively, have a primordial origin. Increasingly large gravitational-wave catalogs of binary black-hole mergers have allowed for the first model selection studies between different theoretical predictions to constrain some of their model uncertainties and branching ratios. In this work, we show how one could add an additional and independent constraint to model selection by using the stochastic gravitational-wave background. In contrast to model selection analyses that have discriminating power only up to the gravitational-wave detector horizons (currently at redshifts $z\lesssim 1$ for LIGO-Virgo), the stochastic gravitational-wave background accounts for the redshift integration of all gravitational-wave signals in the Universe. As a working example, we consider the branching ratio results from a model selection study that includes potential contribution from astrophysical and primordial channels. We renormalize the relative contribution of each channel to the detected event rate to compute the total stochastic gravitational-wave background energy density. The predicted amplitude lies below the current observational upper limits of GWTC-2 by LIGO-Virgo, indicating that the results of the model selection analysis are not ruled out by current background limits. Furthermore, given the set of population models and inferred branching ratios, we find that, even though the predicted background will not be detectable by current generation gravitational-wave detectors, it will be accessible by third-generation detectors such as the Einstein Telescope and space-based detectors such as LISA.

Motivation & Objective

• To provide an independent constraint on the relative contributions of multiple formation channels (astrophysical and primordial) to binary black hole mergers.
• To extend model selection analyses beyond the redshift limit of current detectors ($z \lesssim 1$) by leveraging the redshift-integrated nature of the stochastic gravitational-wave background (SGWB).
• To assess the detectability of the predicted SGWB using current and future gravitational-wave observatories.
• To demonstrate that the SGWB can serve as a complementary probe to individual event catalogs for constraining high-redshift and undetected source populations.
• To quantify how model uncertainties in merger rate densities propagate into SGWB predictions and how normalization to observed events mitigates this.

Proposed method

• Utilizes branching ratios from a Bayesian model selection study (Franciolini et al. 2021) based on GWTC-2 data to assign relative contributions of astrophysical and primordial channels to the total binary black hole merger rate.
• Normalizes the event rate of each channel to the 44 confident detections in GWTC-2 to reduce model-dependent uncertainties.
• Computes the total SGWB energy density spectrum $\Omega_{\mathrm{GW}}(\nu)$ using the redshift-integrated merger rate and the standard formula for the SGWB from coalescing compact binaries.
• Applies a power-law spectral index of $2/3$ to the SGWB, consistent with expectations for binary coalescences.
• Compares the predicted SGWB amplitude to the current observational upper limit from LIGO-Virgo (GWTC-3): $\Omega_{\mathrm{GW}}(25\,\mathrm{Hz}) \leq 1.04 \times 10^{-9}$.
• Evaluates detectability prospects using sensitivity curves of third-generation detectors (Einstein Telescope and LISA), considering both ground-based and space-based observatories.

Experimental results

Research questions

• RQ1 Can the stochastic gravitational-wave background (SGWB) provide an independent constraint on the relative contributions of astrophysical and primordial black hole formation channels?
• RQ2 How does the redshift-integrated nature of the SGWB improve upon model selection analyses limited to the detector horizon ($z \lesssim 1$)?
• RQ3 What is the predicted amplitude of the SGWB for a model selection result based on GWTC-2, normalized to observed merger rates?
• RQ4 Is the predicted SGWB amplitude consistent with current observational upper limits from LIGO-Virgo?
• RQ5 Which future gravitational-wave detectors—third-generation Earth-based or space-based—will be capable of detecting this SGWB?

Key findings

• The predicted SGWB amplitude at 25 Hz is $\Omega_{\mathrm{GW}}(25\,\mathrm{Hz}) = 1.11^{+0.16}_{-0.05} \times 10^{-10}$, which lies well below the current LIGO-Virgo upper limit of $1.04 \times 10^{-9}$.
• The SGWB prediction remains consistent with current observational constraints, meaning the model selection results from GWTC-2 are not ruled out by background limits.
• The predicted SGWB will not be detectable by current-generation detectors such as LIGO-Virgo, due to its low amplitude relative to sensitivity thresholds.
• Third-generation ground-based detectors like the Einstein Telescope and space-based detectors like LISA are expected to have sufficient sensitivity to detect this SGWB.
• Combining individual event catalogs with SGWB mapping can provide complementary information on high-redshift and undetected binary black hole populations.
• The SGWB offers a redshift-integrated probe of the full merger history, making it a valuable tool for constraining formation channels beyond the reach of individual event detection.