Does the Black Hole Merger Rate Evolve with Redshift?

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.

• The paper tests two models for redshift evolution of BBH merger rates using a parametrized framework that mirrors star formation trends and potential extreme scenarios.
• It employs LIGO-Virgo data from six BBH detections to constrain mass and redshift distributions, finding results consistent with a uniform merger rate in comoving volume.
• The findings suggest that several hundred detections are needed to clearly differentiate between astrophysical formation channels and refine current cosmic merger rate models.

Analysis of the Redshift Evolution of Binary Black Hole Merger Rates

The paper "Does the Black Hole Merger Rate Evolve with Redshift?" investigates the capacity of gravitational-wave detectors, such as LIGO-Virgo, to elucidate the redshift dependence of binary black hole (BBH) merger rates. The redshift evolution is a crucial parameter as it informs the astrophysical processes influencing BBH evolution and merging, including formation rates and the distribution of time delays between formation and merger. The analysis hinges on a parametrized model that simultaneously addresses the mass and redshift distributions of BBHs.

The central thrust of the work is the formulation and testing of two models that explore the redshift evolution of BBH merger rates. Model A assumes a simple power-law form which approximates the specific star formation rate (SFR) at low redshifts. Model B allows for deviations from constant in comoving volume, which can capture more extreme evolutionary scenarios, such as gravitational leakage or lensing-related effects. By integrating these models, the authors seek to discern whether the current generation of detected BBHs reflects underlying distributions appropriately indicative of specific formation channels or underlying cosmological models.

The paper leverages existing LIGO-Virgo data from six observed BBH sources to establish preliminary constraints on the mass-redshift parameter space. The derived constraints provide a Bayesian framework which assesses the likelihood of various scenarios. Importantly, it reports compatibility with a non-evolving rate density, indicating the current observations do not significantly deviate from rates uniform in comoving volume. However, variations in mass distribution noticeably impact the observed redshift distribution, reaffirming that disentangling these effects requires more comprehensive data.

Predictions highlight that several hundred detections could significantly sharpen constraints on redshift evolution, sufficient to differentiate between distinct astrophysical models with respective formation channels. Intriguingly, with improved sensitivities and detection capabilities anticipated in future observing runs (e.g., post 2020), it is expected that these bounds will either validate or negate hypotheses tied to rapid BBH formation and merging patterns associated with short delay times or unique cosmological factors.

The broader implications of this study extend into the elucidation of BBH progenitor pathways, fundamentally tied to high-redshift astrophysical activity and pinpointing points of time-delay distribution divergences. Future research directions may leverage enhanced gravitational-wave datasets to revisit the constraints on maximum black hole mass and resolve prevailing ambiguities associated with the upper-mass cutoff.

In conclusion, the research provides valuable insights into gravitational-wave cosmology and BBH astrophysics, indicating how current observations align with theoretical frameworks and forecasting the pathways for refining these models with enhanced detection datasets. This effort is part of a groundbreaking thrust into understanding black hole populations, their genesis, and their role in broader cosmic architecture. Future work that integrates more sophisticated models, potentially addressing parameter interdependencies and leveraging extensive detection runs, will indeed propel our comprehension of BBH formation rates and evolutionary characteristics.