Samsuzzaman Afroz, Suvodip Mukherjee

Gravitational wave (GW) observations have significantly advanced our understanding of binary compact object (BCO) formation, yet directly linking these observations to specific formation scenarios remains challenging. The BCO phase space provides a robust and data-driven approach to discover the likely formation scenarios of these binaries. In this study, we expand the previously introduced binary black hole phase-space technique to encompass low-mass compact objects (LMCOs), establishing a novel framework to investigate their diverse formation mechanisms. Applying this approach to selected low-mass events $(\lesssim 5 M_\odot)$ from the GWTC-3 catalog and the recently observed GW230529 event, we show for the first time the phase-space demonstration of the LMCOs and find the associated probabilities for different formation scenarios including neutron stars, astrophysical black holes, or primordial black holes. Our analysis includes the astrophysical modelling uncertainties in and how it causes degeneracy between different formation scenarios. In future, with improvements in GW detector sensitivity and with detection of more GW events, the LMCO phase-space framework will significantly strengthen our capacity to associate more likely formation scenarios over the other, thereby refining our understanding of compact object formation for both astrophysical and primordial scenarios, and its evolution across the cosmic redshift.