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

TL;DR

This work tackles identifying Proca-star mergers by exploiting cross-event consistency in the ultralight boson mass $μ_B$ across gravitational-wave observations. The authors develop a Bayesian mixture-model framework that can (i) test a single Proca-star family with a common $μ_B$, or (ii) accommodate multiple boson masses $μ_B^j$ with corresponding event-frac­tion parameters $ζ_j$, using Bayesian evidences to compare $n$-boson hypotheses. On real events GW190521, GW190426_190642, GW200220_061928 and the S200114 trigger, the data are consistent with BBH explanations under realistic priors, but the framework reveals that a population with a single $μ_B$ could be decisively identified with 5–9 similar observations, while two distinct boson masses may require more data or better modeling due to degeneracies and Occam penalties. Overall, the method provides a principled way to search for exotic compact objects with gravitational waves, effectively using GW detectors as particle detectors to probe sub-populations of Proca-star mergers.

Abstract

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 $μ_{B}$ 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 $μ_{B}^{i}$, even if no individual event can be conclusively identified as such. Our method provides posterior distributions for $n$ and $μ_{B}^{i}$. 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.

Figures (6)

• Figure 1: Boson-mass estimates for the events we consider in this work. Posterior distributions for the boson mass for the four events we consider, obtained under the assumption that these are sourced by head-on Proca-star mergers. Details on the corresponding analysis can be found in Psi4_obs_PRD.
• Figure 2: Posterior probability for the number $N_{\rm bosons}$ of ultra-light bosons given the Advanced LIGO - Virgo events we consider. Solid (dashed) lines ignore (include) the event S200114 in the analysis. Blue and green lines respectively make use of distance priors uniform in co-moving volume and on luminosity distance. Note that, in order to alleaviate notation, in the main text we denote the variable $N_{\rm bosons}$ simply by $n$.
• Figure 3: Posterior distributions for the boson-mass and Proca-star fraction obtained when we only allow for a single ultralight boson. Blue and orange curves and contours denote results obtained by respectively including and excluding and including the S200114 trigger. The results are obtained assuming a distance prior uniform in co-moving volume. The posterior distribution for the boson mass has non-zero support for all the prior range because the posterior distribution for $\zeta$ is non-null at $\zeta = 0$, in which case all values of $\mu_B$ are allowed.
• Figure 4: Posterior distributions for boson-mass (right) and Proca-star fractions (left) for the 2-boson model. Solid and dashed curves denote results respectively excluding and including the S200114 trigger. Blue and orange curves respectively denote the value of the primary and secondary boson-mass $\mu_B^{1,2}$ and the corresponding fraction $\zeta_{1,2}$. Black curves denote the posterior distribution for $\zeta_1+\zeta_2$.
• Figure 5: Accumulated evidence for Proca-star mergers as a function of the number of observations. Left: $90\%$ credible intervals for the natural log Bayes Factor for the $N_{\rm bosons} = 1$ (red) and $N_{\rm bosons} = 2$ (green) bosons v.s.$N_{\rm bosons} = 0$ as a function of the number of times that event sets like GW190521+GW190426+GW200220 are observed. The blue contour shows the evidence for non-zero v.s. zero Proca-star mergers when potential boson-mass coincidences across events are ignored. The magenta contour shows the log Bayes Factor for $N_{\rm bosons} = 1$v.s.$N_{\rm bosons} = 2$. Right: Same as in the right panel, including the event S200114 in the event sets. Here, the magenta contour denotes the log Bayes factor for $N_{\rm bosons} = 2$v.s.$N_{\rm bosons} = 1$.