Which Is Which Identification of the Two Compact Objects in Gravitational-Wave Binaries

Compact objects observed in gravitational-wave astronomy so far always come in pairs and never individually. Identifying the two components of a binary system is a delicate operation that is often taken for granted. The labeling procedure (i.e., which is object "1"and which is object "2") effectively acts as systematics, or, equivalently, an unspecified prior, in gravitational-wave data inference. The common approach is to label the objects solely by their masses, on a sample-by-sample basis. We show that object identification can instead be tackled using the posterior distribution as a whole. We frame the problem in terms of constrained clustering - a flavor of semisupervised machine learning - and find that unfolding the labeling systematics can significantly impact, and arguably improve, our interpretation of the data. In particular, the precision of black-hole spin measurements improves by up to 50%, multimodalities and tails tend to disappear, posteriors become closer to Gaussian distributions, and the identification of the nature of the object (i.e., black hole vs neutron star) is facilitated. We estimate that about 10% of the LIGO/Virgo posterior samples are affected by this relabeling, i.e., they might have been attributed to the other compact object in the observed binaries.