[Paper Review] The population of merging compact binaries inferred using gravitational waves through GWTC-3

The LIGO Scientific Collaboration, T. D. Abbott+1635 more|arXiv (Cornell University)|Nov 5, 2021

Pulsars and Gravitational Waves ResearchPhysics and Astronomy215 references26 citations

TL;DR

This paper presents a population-level analysis of 76 compact binary mergers detected during LIGO-Virgo-KAGRA's first three observing runs (O1–O3), using the GWTC-3 catalog. It infers merger rates, mass and spin distributions, and redshift evolution, revealing a binary black hole merger rate of 17.9–44 Gpc⁻³ yr⁻¹ at z = 0.2 with κ = 2.9⁺¹.⁷₋₁.⁸, a broad neutron star mass distribution (1.2–2.0 M⊙), and evidence for spin misalignment and antialigned spins.

ABSTRACT

We report on the population properties of compact binary mergers inferred from gravitational-wave observations of these systems during the first three LIGO-Virgo observing runs. The Gravitational-Wave Transient Catalog 3 contains signals consistent with three classes of binary mergers: binary black hole, binary neutron star, and neutron star-black hole mergers. We infer the binary neutron star merger rate to be between 10 and 1700 Gpc$^{-3} yr$^{-1}$ and the neutron star-black hole merger rate to be between 7.8 and 140 Gpc$^{-3} yr$^{-1}$, assuming a constant rate density in the comoving frame and taking the union of 90% credible intervals for methods used in this work. We infer the binary black hole merger rate, allowing for evolution with redshift, to be between 17.9 and 44 Gpc$^{-3}$ yr$^{-1}$ at a fiducial redshift (z=0.2). The rate of binary black hole mergers is observed to increase with redshift at a rate proportional to $(1+z)^\kappa$ with $\kappa=2.9^{+1.7}_{-1.8}$ for $z\lesssim1$. Using both binary neutron star and neutron star-black hole binaries, we obtain a broad, relatively flat neutron star mass distribution extending from $1.2^{+0.1}_{-0.2}$ to $2.0^{+0.3}_{-0.3}\,M_\odot$. We confidently determine that the merger rate as a function of mass sharply declines after the expected maximum neutron star mass, but cannot yet confirm or rule out the existence of a lower mass gap between neutron stars and black holes. We also find the binary black hole mass distribution has localized over- and underdensities relative to a power-law distribution, with peaks emerging at chirp masses of $8.3^{+0.3}_{-0.5}$ and $27.9^{+1.9}_{-1.8}\,M_\odot$. While we continue to find that the mass distribution of a binary's more massive component strongly decreases as a function of primary mass, we observe no evidence of a strongly suppressed merger rate above approximately $60\,M_\odot$ [abridged]

Motivation & Objective

• To infer the population-level properties of merging compact binaries—binary black holes (BBHs), binary neutron stars (BNSs), and neutron star–black hole (NSBH) systems—using gravitational-wave observations.
• To determine the merger rates of BNSs and NSBHs in the local Universe, accounting for uncertainties in rate density and redshift evolution.
• To characterize the mass and spin distributions of compact binary systems, including evidence for over- and underdensities in the BBH mass function.
• To investigate the redshift evolution of BBH merger rates and test for mass gaps or spin alignment trends.
• To assess the presence of spin–mass correlations and misalignment in the binary population using Bayesian inference on GW data.

Proposed method

• Utilizes a Bayesian hierarchical inference framework to model the population of compact binary mergers using 76 high-significance gravitational-wave events from GWTC-3 with false alarm rates <1 yr⁻¹.
• Applies a mixture model to classify events into BBH, BNS, and NSBH categories based on component masses and signal consistency, with GW190814 treated as a possible NSBH or BBH.
• Employs a flexible parametric model for the mass distribution, including power-law and broken power-law forms, to detect over- and underdensities relative to a simple power law.
• Models the redshift evolution of the BBH merger rate as proportional to (1 + z)ᵏ, with k inferred from data using a non-parametric prior.
• Incorporates spin magnitude and orientation parameters (χ₁, χ₂, χ_eff, cos(θ₁), cos(θ₂)) into the population model to assess alignment and misalignment trends.
• Uses a union of 90% credible intervals across multiple inference methods to report robust rate estimates with uncertainty propagation.

Experimental results

Research questions

• RQ1 What is the merger rate density of binary neutron stars (BNSs) and neutron star–black hole (NSBH) systems in the local Universe (z ≈ 0)?
• RQ2 How does the binary black hole (BBH) merger rate evolve with redshift, and what is the best-fit power-law index κ in the relation (1 + z)ᵏ?
• RQ3 What is the shape of the neutron star mass distribution, and is there evidence for a lower mass gap between neutron stars and black holes?
• RQ4 Are there localized over- and underdensities in the BBH mass function, and what are their chirp mass values?
• RQ5 What is the distribution of black hole spin magnitudes and orientations, and is there evidence for spin misalignment or antialignment?

Key findings

• The binary neutron star (BNS) merger rate is estimated at 10–1700 Gpc⁻³ yr⁻¹, and the NSBH merger rate at 7.8–140 Gpc⁻³ yr⁻¹, both with 90% credible intervals from multiple inference methods.
• The binary black hole (BBH) merger rate at z = 0.2 is 17.9–44 Gpc⁻³ yr⁻¹, with a redshift evolution index of κ = 2.9⁺¹.⁷₋₁.⁸ for z ≲ 1.
• The neutron star mass distribution is broad and relatively flat, spanning 1.2⁺⁰.¹₋₀.² to 2.0⁺⁰.³₋₀.³ M⊙, with a sharp decline after the maximum neutron star mass.
• Localized over- and underdensities are detected in the BBH mass function at chirp masses of 8.3⁺⁰.³₋₀.⁵ M⊙ and 27.9⁺¹.⁹₋₁.⁸ M⊙, respectively.
• No strong evidence is found for a suppression of merger rates above 60 M⊙, indicating no conclusive evidence for an upper mass gap in black holes.
• Black hole spins are predominantly small (50% below χᵢ ≈ 0.25), with evidence for antialigned spins and increasing spin magnitude in systems with more unequal mass ratios.