The population of merging compact binaries inferred using gravitational waves through GWTC-3 (2111.03634v4)

Abstract: We report on the population properties of 76 compact binary mergers detected with gravitational waves below a false alarm rate of 1 per year through GWTC-3. The catalog contains three classes of binary mergers: BBH, BNS, and NSBH mergers. We infer the BNS merger rate to be between 10 $\rm{Gpc^{-3} yr^{-1}}$ and 1700 $\rm{Gpc^{-3} yr^{-1}}$ and the NSBH merger rate to be between 7.8 $\rm{Gpc^{-3}\, yr^{-1}}$ and 140 $\rm{Gpc^{-3} yr^{-1}}$ , assuming a constant rate density versus comoving volume and taking the union of 90% credible intervals for methods used in this work. Accounting for the BBH merger rate to evolve with redshift, we find the BBH merger rate to be between 17.9 $\rm{Gpc^{-3}\, yr^{-1}}$ and 44 $\rm{Gpc^{-3}\, yr^{-1}}$ at a fiducial redshift (z=0.2). We obtain a broad neutron star mass distribution extending from $1.2^{+0.1}_{-0.2} M_\odot$ to $2.0^{+0.3}_{-0.3} M_\odot$. We can confidently identify a rapid decrease in merger rate versus component mass between neutron star-like masses and black-hole-like masses, but there is no evidence that the merger rate increases again before 10 $M_\odot$. We also find the BBH mass distribution has localized over- and under-densities relative to a power law distribution. While we continue to find 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 $\sim 60 M_\odot$. The rate of BBH mergers is observed to increase with redshift at a rate proportional to $(1+z)^{\kappa}$ with $\kappa = 2.9^{+1.7}_{-1.8}$ for $z\lesssim 1$. Observed black hole spins are small, with half of spin magnitudes below $\chi_i \simeq 0.25$. We observe evidence of negative aligned spins in the population, and an increase in spin magnitude for systems with more unequal mass ratio.

• The paper applies Bayesian models like MultiPeak and PowerLawPeak to compare gravitational-wave source hypotheses, highlighting significant Bayes factor evidence.
• It estimates astrophysical merger rates using a Gaussian process approach, providing median values such as 98 BNS events per year with reliable uncertainties.
• The analysis constrains mass and spin distributions, refining model parameters that influence the design and interpretation of future gravitational wave observations.

Analysis of Bayesian Frameworks in Gravitational Wave Data Interpretation

This paper presents a comprehensive paper on Bayesian inference methods applied to gravitational wave data, specifically focusing on the detection and characterization of sources in the Gravitational Wave Transient Catalog (GWTC). The research primarily compares different models and hypotheses to delineate astrophysical parameters critical to our understanding of gravitational wave sources.

Bayesian Inference Outcomes

The paper employs several Bayesian models such as PowerLawPeak, BrokenPowerLaw, MultiPeak, and their variants, leveraging Bayes factors to ascertain model viability. Notably, the MultiPeak model demonstrates a prominent Bayes factor of 10 against the baseline PowerLawPeak model, suggesting a significant preference. The analysis also explores the logarithmic scales of these factors, where such a result implies substantial evidence favoring the complex MultiPeak hypothesis over simpler models.

Estimation of Astrophysical Rates

Astrophysical event rates, such as binary neutron star (BNS), neutron star-black hole (NSBH), and binary black hole (BBH) mergers, are derived using a Gaussian process-based approach. This methodology provides a spectrum of estimates with respective statistical uncertainties. For example, the BNS rate is estimated with a median value of 98 events per year, illustrating the calibration precision possible with current methodologies.

Mass Distribution Descriptions

The paper discusses the mass distribution of compact objects, particularly focusing on the neutron star and black hole populations. Models estimate medians and percentiles of source masses, demonstrating constraints on these astronomical bodies. Notably, the alpha parameter's median value of 2.1 drives the mass distribution's slope, crucial for understanding formation scenarios and population synthesis models.

Spin Characteristics

The analysis further examines spin distributions, using parameters such as mu_chi and sigma_chi to explore effective spin distributions within stellar remnants. The notation signifies the median values and uncertainties for these parameters, reflecting underlying physical processes such as core-collapse dynamics and binary evolution.

Implications and Future Directions

The results have profound implications for both theoretical modeling and observatory design, influencing the parameters used in ongoing and future gravitational wave searches. The computation of robust Bayesian evidences and parameter posteriors informs and refines population models, thereby enhancing the fidelity of gravitational wave interpretations.

Future developments can include expanding models to incorporate alternative scenarios such as modified gravity or dark matter interactions, thereby refining our empirical understanding of gravitational wave phenomena. Further integration of machine learning techniques could also enhance model adaptability and parameter estimation precision.

This paper represents an incremental advance in our comprehension of gravitational waves, demonstrating the utility of Bayesian frameworks in extracting meaningful physical insights from complex astrophysical data. The methodologies and results provide a foundation for extending analysis in future observational runs, potentially uncovering new physics through deeper, more nuanced interpretations of gravitational wave data.