利用随机吸积盘数值模型研究传播涨落理论
Investigating the Theory of Propagating Fluctuations with Numerical Models of Stochastic Accretion Discs
AI总结：
本研究通过一组随机驱动的一维α盘数值模拟，验证了吸积盘中传播涨落现象的广泛存在，发现粘滞涨落时标是核心参数，且其与光度功率谱拐折频率密切相关，还给出了相应的拟合公式。
摘要：
在极大的尺度范围内，吸积源均表现出极为相似的变异性模式，其中最显著的是光度分布的对数正态性以及均方根（rms）与流量的线性关系。这些结果通常用传播涨落理论来解释：粘滞性中的涨落会在所有半径处引发吸积率扰动，这些扰动向内传播并以乘法方式叠加。尽管这一观点已在线性区域内得到了大量解析研究，但针对其非线性行为的数值研究仍相对较少。本文中，我们提出了一组随机驱动的一维α盘模拟，以探究这类吸积盘的行为。我们发现，在广泛的模型参数范围内，所有模拟中均存在同名的传播涨落现象，这与此前的研究结论相矛盾。在所有模型参数中，我们发现迄今为止最重要的是粘滞涨落发生的时标。从物理层面看，该时标取决于底层的物理机制，目前认为这一机制是磁旋转不稳定性（MRI）。我们发现，该涨落时标与光度功率谱密度（PSD）中的拐折频率之间存在密切关联，这一特性可用于对MRI发电机的行为进行观测探测。我们还给出了拐折频率作为涨落时标、盘厚度以及中心天体质量函数的拟合公式。
英文摘要：
Across a large range of scales, accreting sources show remarkably similar patterns of variability, most notably the log-normality of the luminosity distribution and the linear root-mean square (rms)-flux relationship. These results are often explained using the theory of propagating fluctuations in which fluctuations in the viscosity create perturbations in the accretion rate at all radii, propagate inwards and combine multiplicatively. While this idea has been extensively studied analytically in a linear regime, there has been relatively little numerical work investigating the non-linear behaviour. In this paper, we present a suite of stochastically driven 1-d $α$-disc simulations, exploring the behaviour of these discs. We find that the eponymous propagating fluctuations are present in all simulations across a wide range of model parameters, in contradiction to previous work. Of the model parameters, we find by far the most important to be the timescale on which the viscosity fluctuations occur. Physically, this timescale will depend on the underlying physical mechanism, thought to be the magnetorotational instability (MRI). We find a close relationship between this fluctuation timescale and the break frequency in the power spectral density (PSD) of the luminosity, a fact which could allow observational probes of the behaviour of the MRI dynamo. We report a fitting formula for the break frequency as a function of the fluctuation timescale, the disc thickness and the mass of the central object.
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