用一个新的代码SACRA模拟合并压缩二进制文件
Simulating coalescing compact binaries by a new code SACRA
摘要：
我们报告我们的新代码（名为SACRA）的数值相对论模拟中，自适应网格细化算法的实施。在该程序中，爱因斯坦方程组采用BSSN格式和四阶差分格式求解，流体动力学方程组采用三阶高分辨率中心格式求解。时间积分采用四阶龙格-库塔格式。为了验证该程序的有效性，对黑洞-黑洞（BH-BH）、中子星-中子星（NS-NS）和黑洞-中子星（BH-NS）双星的合并过程进行了模拟，并对合并后黑洞的性质和引力波形进行了比较。对于BH-BH双星的模拟，我们采用了与Buonanno等人相同的初始条件，并比较了数值结果。我们发现合理的协议，除了轻微的分歧可能与不同的规范条件和数值方案的选择。对于NS-NS二进制，我们进行了模拟，采用SACRA和柴田以前的代码，并找到合理的协议。对于BH-NS双星，我们将数值计算结果与前人的结果进行了比较，发现合并后形成的BH的引力波形和性质与前人的结果一致，尽管合并后形成的盘质量小于总静止质量的0.1%，这与前人的结果不一致。我们还报告的长期模拟（与$\sim 4$轨道）的BH-NS二进制的第一次的数值结果。所有这些数值计算结果表明收敛的行为，和外推的数值结果的时间内螺旋相同意后牛顿预测在一个合理的精度。
英文摘要：
We report our new code (named SACRA) for numerical relativity simulations in which an adaptive mesh refinement algorithm is implemented. In this code, the Einstein equations are solved in the BSSN formalism with a fourth-order finite differencing, and the hydrodynamic equations are solved by a third-order high-resolution central scheme. The fourth-order Runge-Kutta scheme is adopted for integration in time. To test the code, simulations for coalescence of black hole-black hole (BH-BH), neutron star-neutron star (NS-NS), and black hole-neutron star (BH-NS) binaries are performed, and also, properties of BHs formed after the merger and gravitational waveforms are compared among those three cases. For the simulations of BH-BH binaries, we adopt the same initial conditions as those by Buonanno et al. and compare numerical results. We find reasonable agreement except for a slight disagreement possibly associated with the difference in choice of gauge conditions and numerical schemes. For an NS-NS binary, we performed simulations employing both SACRA and Shibata's previous code, and find reasonable agreement. For a BH-NS binary, we compare numerical results with our previous ones, and find that gravitational waveforms and properties of the BH formed after the merger agree well with those of our previous ones, although the disk mass formed after the merger is less than 0.1% of the total rest mass, which disagrees with the previous result. We also report numerical results of a longterm simulation (with $\sim 4$ orbits) for a BH-NS binary for the first time. All these numerical results show behavior of convergence, and extrapolated numerical results for time spent in the inspiral phase agree with post-Newtonian predictions in a reasonable accuracy.
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