自适应伪谱区域分解方法研究黑洞周围的热不稳定吸积盘。II。Kerr黑洞周围吸积盘的极限环行为
Studies of Thermally Unstable Accretion Disks around Black Holes with Adaptive Pseudospectral Domain Decomposition Method. II. Limit-Cycle Behavior in accretion disks around Kerr black holes
摘要：
首次导出了Kerr度规下完全相对论性细长吸积盘的时间演化方程，并数值构造了详细的非定常模型.我们讨论这些一般结果的应用程序的热不稳定磁盘的可能的极限环行为。我们的方程和数值方法适用于广泛的一类可能的粘度处方，但在本文中，我们使用的扩散形式的“标准阿尔法处方”，假设粘性扭矩是成比例的总压力。在这种特殊的情况下，我们发现，控制极限环特性的参数是质量供应率和α粘度参数的值。虽然周期（或爆发）的持续时间并没有表现出任何明显的依赖于黑洞的自旋，最大的爆发光度（在爱丁顿单位）是正相关的自旋值。我们提出了一个简单的方法，根据最大光度和爆发周期持续时间的比值粗略估计黑洞的自旋。我们还讨论了Kerr黑洞吸积盘极限环的温度-光度关系。在此基础上讨论了微类星体GRS 1915+105的极限环行为。我们还将这项研究扩展到几个非标准的粘度处方，包括“延迟加热”处方最近刺激最近的MHD模拟的吸积盘。
英文摘要：
For the first time ever, we derive equations governing the time-evolution of fully relativistic slim accretion disks in the Kerr metric, and numerically construct their detailed non-stationary models. We discuss applications of these general results to a possible limit-cycle behavior of thermally unstable disks. Our equations and numerical method are applicable in a wide class of possible viscosity prescriptions, but in this paper we use a diffusive form of the "standard alpha prescription" that assumes the viscous torque is proportional to the total pressure. In this particular case, we find that the parameters which dominate the limit-cycle properties are the mass-supply rate and the value of the alpha-viscosity parameter. Although the duration of the cycle (or the outburst) does not exhibit any clear dependence on the black hole spin, the maximal outburst luminosity (in the Eddington units) is positively correlated with the spin value. We suggest a simple method for a rough estimate of the black hole spin based on the maximal luminosity and the ratio of outburst to cycle durations. We also discuss a temperature-luminosity relation for the Kerr black hole accretion discs limit-cycle. Based on these results we discuss the limit-cycle behavior observed in microquasar GRS 1915+105. We also extend this study to several non-standard viscosity prescriptions, including a "delayed heating" prescription recently stimulated by the recent MHD simulations of accretion disks.
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