Exploring the relativistic regime with Newtonian hydrodynamics: an improved effective gravitational potential for supernova simulations
Exploring the relativistic regime with Newtonian hydrodynamics: an improved effective gravitational potential for supernova simulations
复制标题
用牛顿流体动力学探索相对论体系：超新星模拟的改进有效引力势
DOI：
10.1051/0004-6361:20052840
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发表时间：
2005
影响因子：
6.5
通讯作者：
R. Buras
中科院分区：
文献类型：
--
作者：
A. Marek;H. Dimmelmeier;H. Janka;E. Mueller;R. Buras
我们在一个标准的牛顿流体动力学程序中，研究了在恒星核坍塌和反弹后演化的流体动力学模拟中，使用修正的引力势来近似相对论效应的可能性。讨论了对以前引入的有效相对论势的不同修正。将相应的静水压解与TOV方程的解进行了比较，并将两种不同程序的水动力模拟结果与完全相对论结果进行了比较。其中一个程序用于一维和二维的简单状态方程的计算，或者在牛顿框架下使用修正的有效相对论势，或者在三度规的共形平坦度条件(CFC)的假设下求解一般相对论场方程组。第二个代码允许完整的超新星运行，包括基于Boltzmann方程及其矩方程的解的微物理状态方程和中微子输运。我们给出了牛顿程序中使用的自引力流体的有效相对论势能的公式，它与球对称下的完全相对论解非常吻合，与以前发表的近似值相比有了显著的改进。此外，对于具有旋转的模型，它们也定性地很好地逼近相对论解。
We investigate the possibility approximating relativistic effects in hydrodynamical simulations of stellar core collapse and post-bounce evolution by using a modified gravitational potential in an otherwise standard Newtonian hydrodynamic code. Different modifications of a previously introduced effective relativistic potential are discussed. Corresponding hydrostatic solutions are compared with solutions of the TOV equations, and hydrodynamic simulations with two different codes are compared with fully relativistic results. One code is applied for one- and two-dimensional calculations with a simple equation of state and employs either the modified effective relativistic potential in a Newtonian framework or solves the general relativistic field equations under the assumption of the conformal flatness condition (CFC) for the three-metric. The second code allows for full-scale supernova runs including a microphysical equation of state and neutrino transport based on the solution of the Boltzmann equation and its moments equations. We present prescriptions for the effective relativistic potential for self-gravitating fluids to he used in Newtonian codes, which produce excellent agreement with fully relativistic solutions in spherical symmetry, leading to significant improvements compared to previously published approximations. Moreover, they also approximate qualitatively well relativistic solutions for models with rotation.