Constraint damping of the conformal and covariant formulation of the Z4 system in simulations of binary neutron stars
Constraint damping of the conformal and covariant formulation of the Z4 system in simulations of binary neutron stars
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双中子星模拟中 Z4 系统共形和协变公式的约束阻尼
DOI：
10.1103/physrevd.88.064049
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发表时间：
2013
影响因子：
5
通讯作者：
Luciano Rezzolla
中科院分区：
文献类型：
--
作者：
Daniela Alic;Wolfgang Kastaun;Luciano Rezzolla
在真空时空的前人工作的基础上，我们研究了最近发展起来的爱因斯坦方程的无迹、共形和协变Z4(CCZ4)形式的物质存在下的约束-阻尼性。首先，我们用理想气体状态方程演化了一颗孤立的中子星，并受到一种违反约束的微扰。我们使用CCZ4和Baumgarte-Shibata-Shapiro-Nakamura-Oohara-Kojima(BSSNOK)系统比较了约束的演化。其次，我们研究了一颗不稳定的球星向黑洞的坍缩。最后，我们在几个轨道上演化双中子星系统，直到合并，形成黑洞，直到环下降。我们证明了CCZ4公式在物质存在的情况下是稳定的，并且约束违反比BSSNOK公式小1个数量级或更多。此外，通过比较CCZ4和BSSNOK公式对具有大初始约束违反的中子星双星的影响，我们考察了它们对物理量误差的影响。我们还给出了一个新的、简单而稳健的阻尼参数公式，它消除了使用完全协变版本的CCZ4在黑洞演化中发现的不稳定性。总体而言，我们发现在基本相同的计算成本下，CCZ4公式提供的解是稳定的，并且与BSSNOK公式相比，对哈密顿约束的破坏要小得多。我们还发现，CCZ4公式的性能与Z4系统的另一种共形的、无迹的、但非协变的公式非常相似，即Z4c公式。
Following previous work in vacuum spacetimes, we investigate the constraint-damping properties in the presence of matter of the recently developed traceless, conformal and covariant Z4 (CCZ4) formulation of the Einstein equations. First, we evolve an isolated neutron star with an ideal gas equation of state and subject to a constraint-violating perturbation. We compare the evolution of the constraints using the CCZ4 and Baumgarte-Shibata-Shapiro-Nakamura-Oohara-Kojima (BSSNOK) systems. Second, we study the collapse of an unstable spherical star to a black hole. Finally, we evolve binary neutron star systems over several orbits until the merger, the formation of a black hole, and up to the ringdown. We show that the CCZ4 formulation is stable in the presence of matter and that the constraint violations are 1 or more orders of magnitude smaller than for the BSSNOK formulation. Furthermore, by comparing the CCZ4 and the BSSNOK formulations also for neutron star binaries with large initial constraint violations, we investigate their influence on the errors on physical quantities. We also give a new, simple and robust prescription for the damping parameter that removes the instabilities found when using the fully covariant version of CCZ4 in the evolution of black holes. Overall, we find that at essentially the same computational costs, the CCZ4 formulation provides solutions that are stable and with a considerably smaller violation of the Hamiltonian constraint than the BSSNOK formulation. We also find that the performance of the CCZ4 formulation is very similar to another conformal and traceless, but noncovariant formulation of the Z4 system, i.e., the Z4c formulation.