Source term method for binary neutron stars initial data
Source term method for binary neutron stars initial data
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DOI：
10.1088/1361-6382/abfc29
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发表时间：
2020-10
影响因子：
3.5
通讯作者：
Bing-Jyun Tsao;R. Haas;A. Tsokaros
中科院分区：
文献类型：
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作者：
Bing-Jyun Tsao;R. Haas;A. Tsokaros
双中子星星系统的初始条件问题需要一个求解速度势的Poisson方程，其边界条件为星星表面的Neumann型边界条件。在这个边值问题中出现的困难是：（a）边界不是先验已知的，但构成问题的解决方案的一部分;（B）各种条款成为奇异的边界。在这项工作中，我们提出了一种新的方法来解决流体泊松方程的无旋/自旋双中子星。新方法的优点是它不需要复杂的流体表面拟合坐标，并且可以在笛卡尔网格中实现，这是数值相对论计算的标准选择。这是通过采用Towers提出的源项方法来实现的，其中边界条件被视为跳跃条件，并作为附加源项纳入泊松方程中，然后迭代求解。通过将计算边界转移到星星内部的额外分离，解决了表面密度消失引起的奇异项问题。我们提出了二维测试显示源项方法的收敛性，我们进一步将此求解器应用到一个现实的三维二元中子星星问题。通过将我们的解决方案与来自初始数据求解器cocal的解决方案进行比较，我们证明了约1%的一致性。我们的方法可以用于其他问题的非光滑解决方案，如磁化中子星。
The initial condition problem for a binary neutron star system requires a Poisson equation solver for the velocity potential with a Neumann-like boundary condition on the surface of the star. Difficulties that arise in this boundary value problem are: (a) the boundary is not known a priori, but constitutes part of the solution of the problem; (b) various terms become singular at the boundary. In this work, we present a new method to solve the fluid Poisson equation for irrotational/spinning binary neutron stars. The advantage of the new method is that it does not require complex fluid surface fitted coordinates and it can be implemented in a Cartesian grid, which is a standard choice in numerical relativity calculations. This is accomplished by employing the source term method proposed by Towers, where the boundary condition is treated as a jump condition and is incorporated as additional source terms in the Poisson equation, which is then solved iteratively. The issue of singular terms caused by vanishing density on the surface is resolved with an additional separation that shifts the computation boundary to the interior of the star. We present two-dimensional tests to show the convergence of the source term method, and we further apply this solver to a realistic three-dimensional binary neutron star problem. By comparing our solution with the one coming from the initial data solver cocal, we demonstrate agreement to approximately 1%. Our method can be used in other problems with non-smooth solutions like in magnetized neutron stars.