微类星体GRS 1915 + 105 X射线爆发的非线性振子模型
Non-linear oscillator models for the X-ray bursting of the microquasar GRS 1915+105
摘要：
微类星体GRS 1915 + 105，根据其光度、光谱状态和可变性，表现出各种各样的特征状态。最有趣的是所谓的rho态，其光变曲线显示周期性爆发。本文提出了一种基于Fitzhugh-Nagumo方程的模型，该模型包含两个变量：x，与MECS探测到的源光子亮度L相关，y与平均光子能量相关。我们的目标是提供一个简单的数学框架组成的非线性微分方程，用于预测所观察到的光变曲线和能量滞后的ρ状态和可能的其他类的源。我们研究了这个系统的平衡态和稳定性条件，其中包括一个外部参数，J，可以被认为是一个功能的磁盘吸积率。我们的工作是基于BeppoSAX号卫星上的MECS在源分别处于rho和nu模式时进行的观测。通过研究计数率-光子能量平面内的轨迹，得到了平均计数率和光子能量的演化规律。假设J常数，我们找到了一个解决方案，再现的x档案的ρ类爆发，出乎意料的是，我们发现，y表现出类似的平均能量的时间调制。此外，假设一个缓慢调制的J的解决方案，为x非常类似于那些观察到的nu类光变曲线再现。根据这些结果，外质量吸积率可能是负责状态转换，但在ρ类它是常数。这一发现加强了非线性模型的启发意义，并表明变量x和y之间存在简单的关系。然而，如何从吸积盘这一复杂的数学装置中推导出动力学方程组，还有待于进一步探索。
英文摘要：
The microquasar GRS 1915+105, exhibits a large variety of characteristic states, according to its luminosity, spectral state, and variability. The most interesting one is the so-called rho-state, whose light curve shows recurrent bursts. This paper presents a model based on Fitzhugh-Nagumo equations containing two variables: x, linked to the source photon luminosity L detected by the MECS, and y related to the mean photon energy. We aim at providing a simple mathematical framework composed by non-linear differential equations useful to predict the observed light curve and the energy lags for the rho-state and possibly other classes of the source. We studied the equilibrium state and the stability conditions of this system that includes one external parameter, J, that can be considered a function of the disk accretion rate. Our work is based on observations performed with the MECS on board BeppoSAX when the source was in rho and nu mode, respectively. The evolution of the mean count rate and photon energy were derived from a study of the trajectories in the count rate - photon energy plane. Assuming J constant, we found a solution that reproduces the x profile of the rho class bursts and, unexpectedly, we found that y exhibited a time modulation similar to that of the mean energy. Moreover, assuming a slowly modulated J the solutions for x quite similar to those observed in the nu class light curves is reproduced. According these results, the outer mass accretion rate is probably responsible for the state transitions, but within the rho-class it is constant. This finding makes stronger the heuristic meaning of the non-linear model and suggests a simple relation between the variable x and y. However, how a system of dynamical equations can be derived from the complex mathematical apparatus of accretion disks remains to be furtherly explored.
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