Spinning bosonic stars (SBSs) can form from the gravitational collapse of a dilute cloud of scalar/Proca particles with non-zero angular momentum. In a recent work we found that the scalar stars are transient due to a non-axisymmetric instability which triggers the loss of angular momentum. We further study the dynamical formation of SBSs using 3-dimensional numerical-relativity simulations of the Einstein-(massive, complex)Klein-Gordon system and of the Einstein-(complex)Proca system. We incorporate a quartic self-interaction potential in the scalar case to gauge its effect on the instability; we investigate (m=2) Proca stars to assess their stability; we attempt to relate the instability of SBSs to the growth rate of azimuthal density modes and the existence of a corotation point. We show that: the self-interaction potential can only delay the instability in scalar SBSs; m=2 Proca stars always migrate to the stable m=1 spheroidal family; unstable m=2 Proca stars and m=1 scalar boson stars exhibit a corotation point. This establishes a parallelism with rotating neutron stars affected by dynamical bar-mode instabilities. We compute the gravitational waves (GWs) emitted and 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. By assuming that the characteristic damping timescale of the bar-like deformation in SBSs is only set by GWs emission and not by viscosity (unlike in neutron stars), we find that the post-collapse emission could be orders of magnitude more energetic than that of the bar-mode instability itself. Our results indicate that GW 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.

中文翻译：

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旋转玻色子星中的动态棒模不稳定性

旋转玻色子星 (SBS) 可以由具有非零角动量的标量 / Proca 粒子稀云的引力坍缩形成。在最近的一项工作中，我们发现标量恒星是瞬态的，这是由于非轴对称不稳定性导致角动量损失。我们使用爱因斯坦-（大质量、复杂）Klein-Gordon 系统和爱因斯坦-（复杂）Proca 系统的 3 维数值相对论模拟进一步研究了 SBS 的动力学形成。我们在标量情况下加入了四次自相互作用势来衡量它对不稳定性的影响；我们调查 (m=2) Proca 星来评估它们的稳定性；我们试图将 SBS 的不稳定性与方位密度模式的增长率和共转点的存在联系起来。我们证明：自相互作用势只能延迟标量SBSs的不稳定性；m=2 Proca 星总是迁移到稳定的 m=1 球体家族；不稳定的 m=2 Proca 星和 m=1 标量玻色子星表现出共转点。这与受动态棒模不稳定性影响的旋转中子星建立了平行关系。我们计算发射的引力波 (GW) 并研究波形的可探测性，将信号的特征应变与各种探测器的灵敏度曲线进行比较，计算信噪比。通过假设 SBS 中棒状变形的特征阻尼时间尺度仅由 GW 发射而不是由粘度决定（与中子星不同），我们发现坍缩后的发射可能比棒模不稳定性本身的能量高几个数量级。我们的结果表明，对 SBS 的 GW 观测可能在未来实验的范围内，为确定此类恒星的存在和严格限制玻色子粒子的质量提供了一种潜在的手段。