Three-dimensional simulations of stellar core collapse in full general relativity: Nonaxisymmetric dynamical instabilities
Three-dimensional simulations of stellar core collapse in full general relativity: Nonaxisymmetric dynamical instabilities
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DOI：
10.1103/physrevd.71.024014
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发表时间：
2004-12
影响因子：
5
通讯作者：
M. Shibata;Yuichiro Sekiguchi
中科院分区：
文献类型：
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作者：
M. Shibata;Yuichiro Sekiguchi
我们在三个空间维度上进行了旋转恒星核坍塌的完全广义相对论模拟。流体动力学方程采用高分辨率激波捕捉格式进行求解。采用一个参数状态方程来模拟紧随Dimmelmeier等人的恒星核和中子星的崩塌。坍塌的早期阶段之后是轴对称代码。当恒星核变得足够紧凑时，我们开始添加条模非轴对称密度微扰的三维模拟。轴对称模拟是在各种初始条件下进行的，这些初始条件改变了旋转速度分布、状态方程参数和总质量。阐明了在恒星崩塌和反弹过程中所获得的最大密度、致密性的最大值以及动能与引力势能之比的最大值({β}T/W)敏感地依赖于初始核的速度分布和总质量以及状态方程。研究还发现，在中子星形成后，所有具有高度差动自转的模型都围绕着自转轴形成了漏斗结构。对于{beta}的最大值大于{近似}0.27的选定模型，进行了三维数值模拟。结果表明，在满足下列条件的情况下，棒模动力学不稳定性开始出现：(I)恒星核塌缩的前驱星体必须以0.01<；或近似的初值快速自转。{beta}或大约0.02(Ii)初始条件的速度剖面的差动旋转度应该足够高，以及(Iii)崩塌早期的压力损耗因子应该足够大，以引起显著的收缩，以形成一个致密的星核，其有效的自旋可以超越强大的离心力。由于杆模动力学不稳定性的开始，引力波的振幅可以比轴对称坍缩中的振幅大约10倍。结果发现，对于与杆模相反的动力学不稳定情况，也会产生m=1模的动力学不稳定性，但微扰并没有显著增长，因此对引力波的显著放大没有贡献。在弹回后的最初10毫秒内，没有发现质子中子星碎裂的证据。
We perform fully general relativistic simulations of rotating stellar core collapse in three spatial dimensions. The hydrodynamic equations are solved using a high-resolution shock-capturing scheme. A parametric equation of state is adopted to model collapsing stellar cores and neutron stars following Dimmelmeier et al. The early stage of the collapse is followed by an axisymmetric code. When the stellar core becomes compact enough, we start a three-dimensional simulation adding a bar-mode nonaxisymmetric density perturbation. The axisymmetric simulations are performed for a wide variety of initial conditions changing the rotational velocity profile, parameters of the equations of state, and the total mass. It is clarified that the maximum density, the maximum value of the compactness, and the maximum value of the ratio of the kinetic energy T to the gravitational potential energy W ({beta}{identical_to}T/W) achieved during the stellar collapse and bounce depend sensitively on the velocity profile and the total mass of the initial core and equations of state. It is also found that for all the models with a high degree of differential rotation, a funnel structure is formed around the rotational axis after the formation of neutron stars. For selected models in which the maximum value of {beta} ismore » larger than {approx}0.27, three-dimensional numerical simulations are performed. It is found that the bar-mode dynamical instability sets in for the case that the following conditions are satisfied: (i) the progenitor of the stellar core collapse should be rapidly rotating with the initial value of 0.01 < or approx. {beta} < or approx. 0.02 (ii) the degree of differential rotation for the velocity profile of the initial condition should be sufficiently high, and (iii) a depletion factor of pressure in an early stage of collapse should be large enough to induce a significant contraction to form a compact stellar core for which an efficient spin-up can be achieved surmounting the strong centrifugal force. As a result of the onset of the bar-mode dynamical instabilities, the amplitude of gravitational waves can be by a factor of {approx}10 larger than that in the axisymmetric collapse. It is found that a dynamical instability with the m=1 mode is also induced for the dynamically unstable cases against the bar mode, but the perturbation does not grow significantly and, hence, it does not contribute to an outstanding amplification of gravitational waves. No evidence for fragmentation of the protoneutron stars is found in the first few 10 msec after the bounce.« less