作为随机过程的吸积盘变率的热点模型- II。功率谱突变频率的数学计算
Hot-spot model for accretion disc variability as random process - II. Mathematics of the power-spectrum break frequency
摘要：
我们研究了平稳随机过程背景下吸积盘变率的一些一般性质。特别是，我们感兴趣的数学约束，可以施加在傅立叶功率谱密度（PSD），表现出多重破碎的形状和几个局部最大值的函数形式。我们开发了一种方法，用于确定模型参数空间的区域，该区域原则上可以再现具有给定数量和位置的局部峰值和PSD斜率的中断的PSD形状。考虑到可能参数的巨大空间，重要的要求是该方法对于模型的给定参数集快速估计PSD形状。我们产生和讨论的理论PSD配置文件的散粒噪声型随机过程的指数衰减耀斑。然后，我们确定的条件下，一个，两个或更多的休息或局部最大值发生在PSD。我们计算了这些特征的位置，并确定了模型PSD的变化斜率。此外，我们考虑了调制的影响，由轨道运动的变化模式，假设从一个轨道点模型。我们建议，我们的一般方法可以用于描述非单调PSD配置文件（如在不同尺度上看到的趋势，在高质量X射线双星天鹅座X-1和窄线塞弗特星系方舟564的示例性情况下）。我们采用了一个模型，这些功率谱再现为几个洛伦兹的叠加与不同的振幅在X射线波段的光变曲线。我们的一般方法可以帮助约束模型参数，并确定在各种情况下参数空间的哪些部分是可访问的。
英文摘要：
We study some general properties of accretion disc variability in the context of stationary random processes. In particular, we are interested in mathematical constraints that can be imposed on the functional form of the Fourier power-spectrum density (PSD) that exhibits a multiply broken shape and several local maxima. We develop a methodology for determining the regions of the model parameter space that can in principle reproduce a PSD shape with a given number and position of local peaks and breaks of the PSD slope. Given the vast space of possible parameters, it is an important requirement that the method is fast in estimating the PSD shape for a given parameter set of the model. We generated and discuss the theoretical PSD profiles of a shot-noise-type random process with exponentially decaying flares. Then we determined conditions under which one, two, or more breaks or local maxima occur in the PSD. We calculated positions of these features and determined the changing slope of the model PSD. Furthermore, we considered the influence of the modulation by the orbital motion for a variability pattern assumed to result from an orbiting-spot model. We suggest that our general methodology can be useful in for describing non-monotonic PSD profiles (such as the trend seen, on different scales, in exemplary cases of the high-mass X-ray binary Cygnus X-1 and the narrow-line Seyfert galaxy Ark 564). We adopt a model where these power spectra are reproduced as a superposition of several Lorentzians with varying amplitudes in the X-ray-band light curve. Our general approach can help in constraining the model parameters and in determining which parts of the parameter space are accessible under various circumstances.
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