[Paper Review] The orientations of the binary black holes in GWTC-3

S. Vitale, S. Biscoveanu+1 more|arXiv (Cornell University)|Apr 3, 2022

Pulsars and Gravitational Waves Research4 citations

TL;DR

This study extends the LIGO-Virgo-KAGRA GWTC-3 population analysis to infer the astrophysical distribution of binary black hole orbital inclinations, modeling it with a non-singular beta distribution. The results show strong consistency with isotropy: skewness is $\mathcal{S}_{\rm{post}}=0.01^{+0.17}_{-0.17}$ and Jensen–Shannon divergence from isotropy is only $1.4\times 10^{-4}$ bits, supporting general relativity and robust selection effects.

ABSTRACT

It is expected that the orbital planes of gravitational-wave (GW) sources are isotropically distributed. However, both physical and technical factors, such as alternate theories of gravity with birefringence, catalog contamination, and search algorithm limitations, could result in inferring a non-isotropic distribution. Showing that the inferred astrophysical distribution of the orbital orientations is indeed isotropic can thus be used to rule out some violations of general relativity, as a null test about the purity of the GW catalog sample, and as a check that selection effects are being properly accounted for. We augment the default mass/spins/redshift model used by the LIGO-Virgo-KAGRA Collaboration in their most recent analysis to also measure the astrophysical distribution of orbital orientations. We show that the 69 binary black holes in GWTC-3 are consistent with having random orbital orientations. The inferred distribution is highly symmetric around $π/2$, with skewness $\mathcal{S}_{ m{post}}=0.01^{+0.17}_{-0.17}$. Meanwhile, the median of the inferred distribution has a Jensen-Shannon divergence of $1.4 imes 10^{-4}$ bits when compared to the expected isotropic distribution.

Motivation & Objective

• To measure the astrophysical distribution of orbital inclination angles $\theta_{\rm{JN}}$ for 69 binary black holes in GWTC-3.
• To test whether the observed distribution of $\theta_{\rm{JN}}$ is isotropic, as expected in general relativity.
• To use the inclination distribution as a null test for violations of general relativity, selection effect inaccuracies, or glitch contamination in the catalog.
• To assess whether the data favors symmetric distributions around $\pi/2$, indicating no preferred orientation.
• To provide a foundation for future tests of anisotropy with improved data from upcoming observing runs.

Proposed method

• Augment the standard GWTC-3 population model to include the orbital inclination distribution as a hyper-parameterized non-singular beta distribution.
• Use hierarchical Bayesian inference to estimate the hyper-parameters $\alpha_{\theta_{\rm{JN}}}$ and $\beta_{\theta_{\rm{JN}}}$ governing the inclination distribution.
• Model selection effects using the full prior and likelihood, ensuring accurate accounting for detection sensitivity as a function of inclination.
• Compare the inferred distribution to a perfectly isotropic one using Jensen–Shannon divergence to quantify deviation.
• Perform posterior predictive checks by sampling from priors with enforced symmetry around $\pi/2$ to test if data is informative about symmetry.
• Use the full posterior to compute credible intervals and medians for the inclination distribution, with comparison to isotropic expectations.

Experimental results

Research questions

• RQ1 Is the astrophysical distribution of binary black hole orbital inclinations in GWTC-3 consistent with isotropy?
• RQ2 Does the data prefer a distribution symmetric around $\pi/2$, indicating no preferred line-of-sight orientation?
• RQ3 To what extent does the observed inclination distribution deviate from isotropy, as quantified by Jensen–Shannon divergence?
• RQ4 Can the inferred inclination distribution serve as a null test for general relativity violations, such as birefringence or higher-order mode effects?
• RQ5 How informative is the data about the shape of the inclination distribution, compared to the prior?

Key findings

• The inferred distribution of orbital inclinations is highly symmetric around $\pi/2$, with posterior skewness $\mathcal{S}_{\rm{post}}=0.01^{\pm 0.17}$, indicating no significant asymmetry.
• The median of the inferred inclination distribution has a Jensen–Shannon divergence of $1.4\times 10^{-4}$ bits from a perfectly isotropic distribution, indicating near-perfect isotropy.
• The data strongly excludes large deviations from symmetry, as shown by a 288-fold reduction in JS divergence between the posterior and a symmetric prior compared to the isotropic reference.
• The posterior is informative and excludes large regions of the prior space, even when enforcing symmetry, confirming that the data constrains the distribution beyond the prior.
• The results support that selection effects are properly modeled and that the catalog is free from significant contamination by glitches or systematic biases.
• The analysis demonstrates the feasibility of using inclination distributions as a null test for general relativity and analysis pipeline integrity, with potential for stronger constraints in future observing runs.