Spinning bosonic stars (SBSs) can form from the gravitational collapse of a dilute cloud of scalar/Proca particles with nonzero angular momentum, via gravitational cooling. The scalar stars are, however, transient due to a nonaxisymmetric instability which triggers the loss of angular momentum. By contrast, no such instability was observed for the fundamental ($m=1$) Proca stars. In [N. Sanchis-Gual et al., Phys. Rev. Lett. 123, 221101 (2019)] we tentatively related the different stability properties to the different toroidal/spheroidal morphology of the scalar/Proca models. Here, we continue this investigation, using three-dimensional numerical-relativity simulations of the Einstein-(massive, complex)Klein-Gordon system and of the Einstein-(complex)Proca system. First, we incorporate a quartic self-interaction potential in the scalar case to gauge its effect on the instability. Second, we investigate toroidal ($m=2$) Proca stars to assess their stability. Third, we attempt to relate the instability of SBSs to the growth rate of azimuthal density modes and the existence of a corotation point in the unstable models. Our results indicate that: (a) the self-interaction potential can only delay the instability in scalar SBSs but cannot quench it completely; (b) $m=2$ Proca stars always migrate to the stable $m=1$ spheroidal family; (c) unstable $m=2$ Proca stars and $m=1$ scalar boson stars exhibit a pattern of frequencies for the azimuthal density modes which crosses the angular velocity profile of the stars in the corotation point. This establishes a parallelism with rotating neutron stars affected by dynamical bar-mode instabilities. Finally, we compute the gravitational waves emitted by SBSs due to the nonaxisymmetric instability. We investigate the detectability of the waveforms comparing the characteristic strain of the signal with the sensitivity curves of a variety of detectors, computing the signal-to-noise ratio for different ranges of masses and for different source distances. Moreover, by assuming that the characteristic damping timescale of the bar-like deformation in SBSs is only set by gravitational-wave emission and not by viscosity (unlike in neutron stars), we find that the postcollapse emission could be orders of magnitude more energetic than that of the bar-mode instability itself. Our results indicate that gravitational-wave observations of SBSs might be within the reach of future experiments, offering a potential means to establish the existence of such stars and to place tight constraints on the mass of the bosonic particle.

• Received 16 October 2020
• Accepted 1 November 2020

DOI:https://doi.org/10.1103/PhysRevD.102.124009