The orientations of the binary black holes in GWTC-3

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 $\pi/2$, with skewness $\mathcal{S}_{\rm{post}}=0.01^{+0.17}_{-0.17}$. Meanwhile, the median of the inferred distribution has a Jensen-Shannon divergence of $1.4\times 10^{-4}$ bits when compared to the expected isotropic distribution.