Does the Black Hole Merger Rate Evolve with Redshift?

TL;DR

This paper investigates how gravitational-wave detectors can determine the redshift distribution of binary black hole mergers, aiming to understand their formation history and evolution, and assesses the potential of future detections to distinguish different astrophysical models.

Contribution

It introduces a joint analysis of mass and redshift distributions to constrain the merger rate density and forecasts the ability to differentiate formation scenarios with upcoming GW detections.

Findings

Current data is consistent with a uniform merger rate in comoving volume.

Mass distribution constraints agree with previous results, showing an upper mass cutoff around 40 solar masses.

Future detections will enable distinguishing between different redshift evolution models and exotic scenarios.

Abstract

We explore the ability of gravitational-wave detectors to extract the redshift distribution of binary black hole (BBH) mergers. The evolution of the merger rate across redshifts $0 < z \lesssim 1$ is directly tied to the formation and evolutionary processes, providing insight regarding the progenitor formation rate together with the distribution of time delays between formation and merger. Because the limiting distance to which BBHs are detected depends on the masses of the binary, the redshift distribution of detected binaries depends on their underlying mass distribution. We therefore consider the mass and redshift distributions simultaneously, and fit the merger rate density, ${dN}/{dm_1\,dm_2\,dz}$. Our constraints on the mass distribution agree with previously published results, including evidence for an upper mass cutoff at $\sim 40 \ M_\odot$. Additionally, we show that the current set of six BBH detections are consistent with a merger rate density that is uniform in comoving volume. Although our constraints on the redshift distribution are not yet tight enough to distinguish between BBH formation channels, we show that it will be possible to distinguish between different astrophysically motivated models of the merger rate evolution with $\sim 100$--$300$ LIGO-Virgo detections (to be expected within 2--5 years). Specifically, we will be able to infer whether the formation rate peaks at higher or lower redshifts than the star formation rate, or the typical time delay between formation and merger. Meanwhile, with $\sim 100$ detections, the inferred redshift distribution will place constraints on more exotic scenarios such as modified gravity.