Head-on collisions and orbital mergers of Proca stars

Abstract

Proca stars, aka vector boson stars, are self-gravitating Bose-Einstein condensates obtained as numerical stationary solutions of the Einstein-(complex)-Proca system. These solitonic objects can achieve a compactness comparable to that of black holes, thus yielding an example of a black hole mimicker, which, moreover, can be both stable and form dynamically from generic initial data by the mechanism of gravitational cooling. In this paper we further explore the dynamical properties of these solitonic objects by performing both head-on collisions and orbital mergers of equal mass Proca stars, using fully non-linear numerical evolutions. For the head-on collisions, we show that the end point and the gravitational waveform from these collisions depends on the compactness of the Proca star. Proca stars with sufficiently small compactness collide emitting gravitational radiation and leaving a stable Proca star remnant. But more compact Proca stars collide to form a transient hypermassive Proca star, which ends up decaying into a black hole, albeit temporarily surrounded by Proca quasi-bound states. The unstable intermediate stage can leave an imprint in the waveform, making it distinct from that of a head-on collision of black holes. The final quasi-normal ringing matches that of Schwarzschild black hole, even though small deviations may occur, as a signature of sufficiently non-linear and long-lived Proca quasi-bound states. For the orbital mergers, the outcome also depends on the compactness of the stars. For the binaries with the most compact stars, the binary merger forms a Kerr black hole which retains part of the initial orbital angular momentum, being surrounded by a transient Proca field remnant; in cases with lower compactness, the binary merger forms a massive Proca star with angular momentum, but out of equilibrium. As in previous studies of (scalar) boson stars, the angular momentum of such objects appears to converge to zero as a final equilibrium state is approached.

Nonlinear Dynamics of Spinning Bosonic Stars: Formation and Stability

“…The numerical code we have used to evolve the rotating Proca stars has been assessed in [30] for a real Proca field and in [16] for the complex case. In this section we will discuss the convergence analysis of the rotating Proca star stable solution.…”

Gravitational waves from dark boson star binary mergers

“…The merger of binary BSs has already been studied in several works: head-on and orbital collisions of mini-BSs [21,22], head-on collision of oscillatons (a solution of BS with real scalar field) [23,24], head-on collision of Proca stars (a solution modeled by a massive complex vector field) [25] and orbital collision of solitonic BSs [26,27]. All these studies have in common that both stars are represented by the same complex scalar field, a feature typical for classical fluid stars.…”

Probing the nature of black holes: Deep in the mHz gravitational-wave sky

“…The merging of such binaries carries important information on their nature. For example, such objects respond differently to the tidal interaction of their companion [ 79 , 181 , 216 ] and would, in general, lead to a different post-merger signal when compared to the merger of two BHs [ 139 , 191 , 214 ]. Such effects are imprinted in the gravitational waveform and allow the nature of the compact object to be strongly constrained (see Sections 3.4 and 5 ).…”