Examining the Gap in the Chirp Mass Distribution of Binary Black Holes

TL;DR

This study investigates a proposed gap in the BBH chirp-mass distribution, focusing on the $9.5$–$12\,M_\odot$ range. Using Vamana, a Bayesian Gaussian mixture population model with three flavours, the authors compare featureless and gap-enabled models and calibrate significance with simulated catalogs via Bayes factors and a conservative $\chi^2$ statistic. They find strong evidence for a chirp-mass feature: BF-based tests exceed all simulations (>$99.5\%$) and $\chi^2$ tests yield $\sim95\%$ confidence under a broader model, though a gap in chirp mass does not necessarily imply a gap in component masses due to a unique $m_1$–$m_2$ pairing. The work highlights how mass-pairing correlations can shape one-dimensional mass inferences and anticipates substantial gains in confidence with larger GW catalogs.

Abstract

The mass distribution of binary black holes inferred from gravitational wave measurements is expected to shed light on their formation scenarios. An emerging structure in the mass distribution indicates the presence of multiple peaks around chirp masses of $8M_\odot$, $14M_\odot$, and $27M_\odot$. In particular, there is a lack of observations between chirp masses of 10 and 12 $M_\odot$. In this article, we report that observations significantly favour the model supporting suppression of the rate in a narrow chirp mass range compared to the model that doesn't include suppression at a confidence greater than 99.5\%. Using another test, which measures the deviation between the inferred chirp mass distributions from the two models, we conservatively estimate a 95\% confidence in the presence of a feature. A lack of confidence has been reported in the presence of a gap around a comparable location in the component mass distribution. The differing conclusions are due to a unique correlation between the primary~(heavier of the two masses) and the secondary~(lighter of the two masses) masses of binary black holes. This correlation results in increased clustering of measured chirp masses around specific values.

Figures (7)

• Figure 1: The measured chirp mass and redshift value of the 69 BBH observed with a false alarm rate of once per year or less. Observations cluster around a chirp mass value of 8$M_\odot$ and 14$M_\odot$, leaving a gap in between.
• Figure 2: The chirp mass distribution inferred from the models $\mathbb{M}_{pl}$ and $\mathbb{M}_{pl+gap}$. The solid line represents the mean distribution, and the shaded region or dashed line indicates the 90% credible interval. As expected, the orange curve does not exhibit features in the chirp mass range of 9.5--20 $M_\odot$. It is used as the fiducial chirp mass distribution for creating simulated catalogs. The models infer almost identical distributions except in the range 9.5--20$M_\odot$.
• Figure 3: The log Bayes factor (left) and $\chi^2$ values (right) between models $\mathbb{M}_{pl+gap}$ and $\mathbb{M}_{pl}$ for the 500 simulated catalog. The red lines indicate the estimated values for the GW observations.
• Figure 4: The chirp mass distribution inferred from the models $\mathbb{M}_{pl+gap}$ and $\mathbb{M}_{pl}$. The solid line represents the mean distribution, and the shaded region or dashed line indicates the 90% credible interval. The models infer a similar distribution except in the range 9.5--20$M_\odot$.
• Figure 5: The log Bayes factor (left) and $\chi^2$ values (right) between models $\mathbb{M}_{pl+gap}$ and $\mathbb{M}_{pl}$ for the 500 simulated catalog. The red lines indicate the estimated values for the GW observations.