记忆阻尼力作用下非相对论吸积盘的随机共振

摘要

By using a generalized Langevin equation to describe the vertical oscillations of a non-relativistic disk subjected to a memory-damped friction and a stochastic force, we derive the power spectrum density (P(ν)) of accretion disk oscillating luminosity by the method of Laplace transform, and discuss the influence of system parameters on the P(ν) curves. The results show that as the memory timeτof the friction increase, the variation of P(ν) with spectrum frequency ν from monotonous decreasing to occur maximums, and the phenomenon of a general stochastic resonance with single-peak and multi-peaks can be found in P(ν) curves. The viscidity coefficient, mass accretion rate and the mass M of black hole have significant influences on the SR phenomena in system of black hole binaries.%采用受记忆阻尼力和色关联随机力作用下的广义朗之万方程描述黑洞吸积盘的垂向振荡，用拉普拉斯变换的方法推导得到吸积盘随机振荡的光度和功率密度谱，并分析阻尼力的记忆时间和吸积盘系统参数对功率谱曲线的影响。研究结果表明：随着阻尼力记忆时间τ的增大，功率谱P(ν)随频率ν的变化从单调减小到出现极大值，曲线上出现了单峰和多峰的随机共振现象。粘滞系数、吸积率和中心黑洞的质量对曲线上共振峰的强度和位置都有较大的影响。