标题： 关于广义相对论第一次后牛顿近似下双星流体力学不稳定性的数值研究 显示英文标题

标题： Numerical study on the hydrodynamic instability of binary stars in the first post Newtonian approximation of general relativity

摘要： 我们给出了广义相对论第一后牛顿（1PN）近似下合并双星流体力学稳定性的数值结果。 我们特别关注了平衡状态下共转双星的流体力学不稳定性，假设具有刚性多变量方程状态和绝热常数$\Gamma=3$。 在之前关于平衡状态下共转双星的1PN数值研究中发现，沿二元序列作为轨道间距的函数，它们在能量和/或角动量最小值处具有动力学不稳定性，并且随着1PN修正的增加，这些最小值处的轨道间距减小而角速度增加。 本文中，为了了解最内侧稳定圆轨道（ISCO）的位置，我们进行了数值模拟并找到了共转序列上流体力学不稳定性的发生位置。 从数值结果来看，我们发现动态稳定性极限似乎不仅在牛顿情况下，而且在1PN情况下都存在于能量和/或角动量最小值附近。 这意味着广义相对论的1PN效应增加了ISCO处引力波的角频率。 显示英文摘要

摘要： We present numerical results on the hydrodynamic stability of coalescing binary stars in the first post Newtonian(1PN) approximation of general relativity. We pay particular attention to the hydrodynamical instability of corotating binary stars in equilibrium states assuming the stiff polytropic equation of state with the adiabatic constant $\Gamma=3$. In previous 1PN numerical studies on corotating binary stars in equilibrium states, it was found that along the sequence of binary stars as a function of the orbital separation, they have the energy and/or angular momentum minima where the secular instability sets in, and that with increase of the 1PN correction, the orbital separation at these minima decreases while the angular velocity there increases. In this paper, to know the location of the innermost stable circular orbit(ISCO), we perform numerical simulations and find where the hydrodynamical instability along the corotating sequences of binary sets in. From the numerical results, we found that the dynamical stability limit seems to exist near the energy and/or angular momentum minima not only in the Newtonian, but also in the 1PN cases. This means that the 1PN effect of general relativity increases the angular frequency of gravitational waves at the ISCO.