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 $\mu_{B}$ 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 \cor{of} a number $n$ of Proca-star families characterized by respective boson masses $\mu_{B}^{i}$, even if no individual event can be conclusively identified as such. Our method provides posterior distributions for $n$ and $\mu_{B}^{i}$. Applying this framework to the high-mass events GW190521, GW190426\_190642 \cor{and} GW200220\_061928, we obtain a Bayes Factor ${\cal{B}}^{n=0}_{n=1}=2$ against the Proca-star hypothesis, primarily rooted in the limitation of current Proca-star merger \cor{signal models} to intrinsically weak head-on cases. We show that conclusive evidence $\log{\cal{B}}^{n=1}_{n=0} \geq 5$ could be achieved after 5 to 9 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.