Numerical analysis for merger of binary neutron stars in full general relativity

由两颗中子星组成的天体物理系统被称为双中子星。这样的近轨双星发射引力波，导致轨道分离减少到合并。根据统计研究，这种合并每年发生一次，发生在距离我们银河系50 Mpc的地方。在合并前的最后15分钟，会发射出超过10Hz的引力波。这种高频引力波是LIGO等引力波探测器最有希望的来源之一。预测引力波是理论天体物理学中的一个问题。双中子星合并后形成黑洞或超大质量中子星（HMNS）。如果一个黑洞被巨大的、热的、密集的环体包围，它可能是伽马射线爆发的中心引擎。虽然这个假设已经提出了大约20年，但没有人知道它是否正确。这是天体物理学中的一个重要问题，以澄清这种情况是否正确。基于这两个动机，我们在完全广义相对论下进行了两年的数值模拟。我们得出了以下结论。(1)双中子星合并后，如果总质量超过临界质量，就会形成黑洞。它取决于中子星的状态方程；对于似是而非的硬核状态方程，临界质量为2.6-2.8太阳质量。(2)当总质量小于临界质量时，形成椭圆形状的HMNS。由于其椭圆形状，HMNS发射引力波并耗散角动量。由于离心力的减少，HMNS在大约100毫秒内坍缩成一个黑洞。(3)双中子星质量比不一致时，黑洞周围形成吸积环。但即使质量比是2/3，环面质量也大约是太阳质量的10%(4)在黑洞形成过程中，引力波是在黑洞形成的最后时刻发出的，引力波与准模环有关。在50 Mpc距离处，振幅约为10^<-23>，频率约为7 kHz。要探测到这种引力波是非常困难的，除非这种并合碰巧发生在我们的银河系周围。(5)在HMNS形成的情况下，准周期引力波是由于椭圆型HMNS的旋转而发射的。在距离为50 Mpc时，有效振幅约为10^<-20>，频率约为3 kHz。这种引力波可能会被下一代探测器探测到。等质量双星合并后，形成一个被大质量环面包围的黑洞。该系统是伽马射线暴中心引擎的候选系统。少

Astrophysical systems of two neutron stars are referred to as binary neutron stars. Such binary of close orbits emits gravitational waves, resulting in decreasing the orbital separation to merger. According to statistical studies, the merger happens once a year in a distance of 50 Mpc around our Galaxy. In the last about 15 minutes just before the merger, gravitational waves of more than 10Hz is emitted. Such high frequency gravitational waves are among the most promising sources of gravitational wave detector such as LIGO. Predicting the gravitational waveforms is an issue in theoretical astrophysics.After merger of binary neutron stars, a black hole or a hypermassive neutron star (HMNS) is formed. If a black hole surrounded by massive, hot, and dense torus is formed, it may be a central engine of gamma-ray burst. Although this hypothesis has been proposed for about 20 years, no one knows if it is correct. It is one of the important issues in astrophysics to clarify whether this scena … More rio is correct or not.By these two motivations, we have performed numerical simulations in full general relativity for two years. We have reached the following conclusion. (1) A black hole is formed after merger of binary neutron stars if the total mass exceeds a critical mass. It depends on the equation of state of neutron stars ; for plausible stiff nuclear equations of state, the critical mass is 2.6-2.8 solar mass. (2) If the total mass is smaller than the critical mass, an HMNS of elliptical shape is formed. Because of its elliptic shape, the HMNS emits gravitational waves and dissipates angular momentum. As a result of the reduced centrifugal force, the HMNS collapses to a black hole in about 100 ms. (3) Accretion torus is formed around a black hole if the mass ratio of binary neutron stars is not unity. But even for the mass ratio 2/3, the torus mass is about 10% of the solar mass. (4) For the black hole formation, gravitational waves associated with the quasinormal mode ringing are emitted in the last moment.The amplitude is about 10^<-23> at a distance of 50 Mpc and the frequency is about 7 kHz. It is very difficult to detect such gravitational waves unless the merger happens around our Galaxy by chance. (5) In the case of HMNS formation, quasiperiodic gravitational waves are emitted due to rotation of elliptic HMNS. The effective amplitude is about 10^<-20> at a distance of 50 Mpc and the frequency is about 3 kHz. Such gravitational waves may be detected by the next-generation detectors. (6) After merger of unequal mass binaries, a black hole surrounded by a massive torus is formed. Such system is a candidate of the central engine of gamma-ray bursts. Less