中子星中的临界现象I：线性不稳定非旋转模型
Critical Phenomena in Neutron Stars I: Linearly Unstable Nonrotating Models
摘要：
我们考虑一族线性不稳定的孤立球形中子星在截断误差引起的极小扰动作用下在完全广义相对论中的演化。利用一个简单的理想流体状态方程，我们发现该系统表现出I型临界行为，从而证实了Liebling等人[1]对旋转磁化星的结论。利用我们的系统相对简单，我们能够进行更深入的研究，提供坚实的证据，这种现象的临界性，也给一个简单的解释，作为一个球形的解决方案，不稳定的模式是基本的F-模式的假定的临界解。因此，对于多变常数的任何选择，临界解将区分迁移到平衡模型的稳定分支的次临界模型集和坍缩到黑洞的次临界模型集。最后，我们研究了如何动态变化时，数值扰动被替换为一个有限大小，分辨率独立的速度扰动，并表明，在这种情况下，一个近临界的解决方案可以改变成一个子或超临界。本文所报道的工作也为在一篇配套论文中进行的分析奠定了基础，其中考虑了两颗中子星迎头碰撞的临界行为[2]。
英文摘要：
We consider the evolution in full general relativity of a family of linearly unstable isolated spherical neutron stars under the effects of very small, perturbations as induced by the truncation error. Using a simple ideal-fluid equation of state we find that this system exhibits a type-I critical behaviour, thus confirming the conclusions reached by Liebling et al. [1] for rotating magnetized stars. Exploiting the relative simplicity of our system, we are able carry out a more in-depth study providing solid evidences of the criticality of this phenomenon and also to give a simple interpretation of the putative critical solution as a spherical solution with the unstable mode being the fundamental F-mode. Hence for any choice of the polytropic constant, the critical solution will distinguish the set of subcritical models migrating to the stable branch of the models of equilibrium from the set of subcritical models collapsing to a black hole. Finally, we study how the dynamics changes when the numerically perturbation is replaced by a finite-size, resolution independent velocity perturbation and show that in such cases a nearly-critical solution can be changed into either a sub or supercritical. The work reported here also lays the basis for the analysis carried in a companion paper, where the critical behaviour in the the head-on collision of two neutron stars is instead considered [2].
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