非均匀随机性对平均场论可证伪性的影响和来自吸积盘模拟的例子
Influence of inhomogeneous stochasticity on the falsifiability of mean-field theories and examples from accretion disc modeling
摘要：
尽管湍流天体物理系统中存在时空涨落，但平均场论可以用来描述它们的长期演化。然而，在比动力学时间尺度短得多的时间尺度上进行的观测捕获了处于其湍流系综的单一状态的系统。与平均场论相比，只有当该理论被附加以量化的精度时，才能证伪后者。中心极限定理提供了适当的估计，只有当波动线性贡献的可观察性和恒定的相干尺度的精度。在这里，我们引入一个误差传播公式，放宽这两个限制，允许非线性函数形式的观测和非均匀相干尺度和波动幅度。该方法是在吸积盘理论的背景下，其中在表面温度的不均匀波动传播到光盘发射光谱-后者是一个非线性和非本地功能的前者举例说明。导出的精度依赖于非单调的发射频率。使用相同的方法，我们调查如何在望远镜数据的分箱光谱波动的光谱分辨率的变化。我们讨论了平均场论的可证伪性的更广泛的含义。
英文摘要：
Despite spatial and temporal fluctuations in turbulent astrophysical systems, mean-field theories can be used to describe their secular evolution. However, observations taken over time scales much shorter than dynamical time scales capture a system in a single state of its turbulence ensemble. Comparing with mean-field theory can falsify the latter only if the theory is additionally supplied with a quantified precision. The central limit theorem provides appropriate estimates to the precision only when fluctuations contribute linearly to an observable and with constant coherent scales. Here we introduce an error propagation formula that relaxes both limitations, allowing for nonlinear functional forms of observables and inhomogeneous coherent scales and amplitudes of fluctuations. The method is exemplified in the context of accretion disc theories, where inhomogeneous fluctuations in the surface temperature are propagated to the disc emission spectrum--the latter being a nonlinear and non-local function of the former. The derived precision depends non-monotonically on emission frequency. Using the same method, we investigate how binned spectral fluctuations in telescope data change with the spectral resolving power. We discuss the broader implications for falsifiability of a mean-field theory.
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