Identifying Proca-star mergers via consistent ultralight-boson mass estimates across gravitational-wave events

While black hole and neutron star mergers are the most plausible sources of current gravitational-wave observations, mergers of exotic compact objects may mimic these signals. Proca stars---Bose-Einstein condensates of complex vector ultralight bosons---have gained significant attention for their potential to replicate certain gravitational-wave events while yielding consistent estimates of the boson mass ${\ensuremath{\mu}}_{B}$ forming the stars. Using a mixture model within a Bayesian framework, we demonstrate that consistent boson mass estimates across events can be exploited to obtain conclusive evidence for the existence of a number $n$ of Proca-star families characterized by respective boson masses ${\ensuremath{\mu}}_{B}^{i}$, even if no individual event can be conclusively identified as such. Our method provides posterior distributions for $n$ and ${\ensuremath{\mu}}_{B}^{i}$. Applying this framework to the high-mass events GW190521, GW190426_190642, and GW200220_061928, we obtain a Bayes factor ${\mathcal{B}}_{n=1}^{n=0}=2$ against the Proca-star hypothesis, primarily rooted in the limitation of current Proca-star merger signal models to intrinsically weak head-on cases. We show that conclusive evidence $\mathrm{log}{\mathcal{B}}_{n=0}^{n=1}\ensuremath{\ge}5$ could be achieved after five to nine observations of similar event sets, at the 90% credible level. Our framework provides a new way to detect exotic compact objects, somewhat using gravitational-wave detectors as particle detectors.