轴对称动力学时空中的GRMHD：X-ECHO代码
GRMHD in axisymmetric dynamical spacetimes: the X-ECHO code
摘要：
本文提出了一种新的动力学时空中广义相对论磁流体力学（GRMHD）的数值计算程序X-ECHO。这是为了研究天体物理的情况下，强引力和磁场都应该发挥重要作用，如磁化中子星的演变或引力坍缩的磁化旋转核心的大质量恒星，这是天体物理的情况下，相信最终会导致（长期）伽玛射线暴事件。该代码基于欧拉保守高阶（ECHO）方案的扩展[Del Zanna等人，A&A 473，11（2007）]，这里耦合到扩展共形平坦条件（XCFC）中的爱因斯坦方程的新求解器。我们充分利用3+1欧拉形式主义，使所有的方程都写在熟悉的三维矢量和张量单独，我们采用球坐标的共形背景度量，我们考虑轴对称时空和流体配置。的GRMHD守恒律通过冲击捕获方法在有限差分离散求解，而在同一数值网格上，爱因斯坦椭圆方程处理诉诸球谐分解和解决，为每个谐波，通过反转带对角矩阵。作为一个副产品，我们建立并提供给社会的代码产生GRMHD轴对称平衡多方相对论性恒星存在的差异旋转和一个纯粹的环形磁场。它使用与主代码相同的XCFC度量求解器，并命名为XNS。XNS和完整的X-ECHO代码都通过几个天体物理学测试进行了验证。
英文摘要：
We present a new numerical code, X-ECHO, for general relativistic magnetohydrodynamics (GRMHD) in dynamical spacetimes. This is aimed at studying astrophysical situations where strong gravity and magnetic fields are both supposed to play an important role, such as for the evolution of magnetized neutron stars or for the gravitational collapse of the magnetized rotating cores of massive stars, which is the astrophysical scenario believed to eventually lead to (long) GRB events. The code is based on the extension of the Eulerian conservative high-order (ECHO) scheme [Del Zanna et al., A&A 473, 11 (2007)] for GRMHD, here coupled to a novel solver for the Einstein equations in the extended conformally flat condition (XCFC). We fully exploit the 3+1 Eulerian formalism, so that all the equations are written in terms of familiar 3D vectors and tensors alone, we adopt spherical coordinates for the conformal background metric, and we consider axisymmetric spacetimes and fluid configurations. The GRMHD conservation laws are solved by means of shock-capturing methods within a finite-difference discretization, whereas, on the same numerical grid, the Einstein elliptic equations are treated by resorting to spherical harmonics decomposition and solved, for each harmonic, by inverting band diagonal matrices. As a side product, we build and make available to the community a code to produce GRMHD axisymmetric equilibria for polytropic relativistic stars in the presence of differential rotation and a purely toroidal magnetic field. This uses the same XCFC metric solver of the main code and has been named XNS. Both XNS and the full X-ECHO codes are validated through several tests of astrophysical interest.
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