[Paper Review] Who Ordered That? Unequal-Mass Binary Black Hole Mergers Have Larger Effective Spins

T. A. Callister, C.‐J. Haster+3 more|arXiv (Cornell University)|Jun 1, 2021

Black Holes and Theoretical PhysicsPhysics and Astronomy113 references126 citations

TL;DR

This study uses hierarchical Bayesian inference on LIGO-Virgo gravitational wave data to reveal a significant anti-correlation between mass ratio (q) and effective spin (χeff) in binary black hole mergers: more unequal-mass systems exhibit systematically larger positive χeff. With 98.7% credibility, the analysis finds Bayesian odds of 10.5 in favor of this correlation, which contradicts predictions from standard formation models and is robust to measurement degeneracies between q and χeff.

ABSTRACT

Hierarchical analysis of the binary black hole (BBH) detections by the Advanced LIGO and Virgo detectors has offered an increasingly clear picture of their mass, spin, and redshift distributions. Fully understanding the formation and evolution of BBH mergers will require not just the characterization of these marginal distributions, though, but the discovery of any correlations that exist between the properties of BBHs. Here, we hierarchically analyze the ensemble of BBHs discovered by the LIGO and Virgo with a model that allows for intrinsic correlations between their mass ratios $q$ and effective inspiral spins $\chi_\mathrm{eff}$. At $98.7\%$ credibility, we find that the mean of the $\chi_\mathrm{eff}$ distribution varies as a function of $q$, such that more unequal-mass BBHs exhibit systematically larger $\chi_\mathrm{eff}$. We find Bayesian odds ratio of $10.5$ in favor of a model that allows for such a correlation over one that does not. Finally, we use simulated signals to verify that our results are robust against degeneracies in the measurements of $q$ and $\chi_\mathrm{eff}$ for individual events. While many proposed astrophysical formation channels predict some degree correlation between spins and mass ratio, these predicted correlations typically act in an opposite sense to the trend we observationally identify in the data.

Motivation & Objective

• To investigate whether correlations exist between mass ratio (q) and effective inspiral spin (χeff) in binary black hole mergers.
• To determine if observed trends in χeff are driven by selection effects or intrinsic population correlations.
• To test the robustness of the correlation detection against measurement degeneracies between q and χeff.
• To compare the observed correlation with predictions from astrophysical formation models.

Proposed method

• Hierarchical Bayesian inference is applied to 44 BBH events from GWTC-2, modeling joint distributions of mass ratio q and effective spin χeff.
• A flexible population model allows the mean of the χeff distribution to vary as a function of q, parameterized by slope α.
• The analysis incorporates selection effects using software injections from LIGO-Virgo, enabling correction for detection biases in the observed sample.
• Parameter estimation is performed using Bilby with the IMRPhenomD waveform model and non-informative priors on χeff and q.
• A mock injection study is conducted to verify that measurement degeneracies between q and χeff do not bias the detection of the q–χeff correlation.
• Posterior samples are reweighted to align with isotropic spin priors for consistent comparison with published results.

Experimental results

Research questions

• RQ1 Is there a statistically significant correlation between mass ratio q and effective spin χeff in the binary black hole population?
• RQ2 Does the observed trend—larger χeff in unequal-mass systems—arise from measurement degeneracies or intrinsic population structure?
• RQ3 How robust is the correlation detection to systematic effects such as selection biases and waveform modeling?
• RQ4 Do the observed correlations align with predictions from standard astrophysical formation channels?

Key findings

• At 98.7% credibility, the mean of the effective spin distribution (χeff) varies with mass ratio q, showing a systematic increase in χeff for more unequal-mass systems.
• The Bayesian odds ratio in favor of a q–χeff correlation model over a no-correlation model is 10.5, indicating strong statistical support for the correlation.
• The observed anti-correlation between q and χeff is inconsistent with predictions from standard formation models, which typically predict the opposite trend.
• The injection study confirms that measurement degeneracies between q and χeff do not generate a spurious correlation, validating the robustness of the result.
• The correlation is robust to changes in priors and does not significantly alter inferences about primary mass or redshift distributions.
• GW190412 and GW190517 are key contributors to the observed trend, with GW190814 excluded due to uncertain nature and outlier status.