Impact of the wavelike nature of Proca stars on their gravitational-wave emission

We present a systematic study of the dynamics and gravitational-wave emission of head-on collisions of spinning vector boson stars, known as Proca stars. To this aim we build a catalog of about 800 numerical-relativity simulations of such systems. We find that the wavelike nature of bosonic stars has a large impact on the gravitational-wave emission. In particular, we show that the initial relative phase Δε=ε₁-ε₂ of the two complex fields forming the stars (or, equivalently, the relative phase at merger) strongly impacts both the emitted gravitational-wave energy and the corresponding mode structure. This leads to a nonmonotonic dependence of the emission on the frequency of the secondary star ω₂, for fixed frequency ω₁ of the primary. This phenomenology, which has not been found for the case of black-hole mergers, reflects the distinct ability of the Proca field to interact with itself in both constructive and destructive manners. We postulate this may serve as a smoking gun to shed light on the possible existence of these objects.