蒙特卡罗辐射转移中的散射阶数问题
The scattering order problem in Monte Carlo radiative transfer
摘要：
辐射转移模拟是生成各种天体图像的重要工具。在复杂的三维几何形状的情况下，通常使用基于蒙特卡罗的方法来模拟光子包在其环境中移动并与其环境相互作用。以前的研究表明，在高光学深度的制度，所需的模拟光子包的数量大幅上升，估计通量可能会被严重低估。在本文中，我们确定了两个问题，出现的Monte Carlo辐射转移模拟，阻碍了正确的测定通量：第一，之间的不匹配的概率和重量的路径的光子包，第二，模拟范围广泛的高散射订单的必要性。此外，我们认为剥离方法部分解决了这些问题，我们还提出了一个扩展的剥离方法。我们提出的方法改进了它的基本变体的几个缺点，并依赖于利用预先计算的球光谱。然后，我们结合剥离的方法与分裂方法和拉伸方法，并在数值上评估其能力，而不是纯粹的分裂$\,\&\,$拉伸方法在一个无限的平面平行板设置。我们发现，剥离方法大大提高了这些模拟的性能，特别是在横向光学深度的$τ_{\rm max}=75$，我们的方法实现了显着低于以前的方法，同时节省${>}95\%$计算时间的错误。最后，我们讨论了包括偏振和米氏散射的扩展剥离法，并认为它可能是必要的，以装备未来的Monte Carlo辐射转移模拟与额外的先进寻路技术。
英文摘要：
Radiative transfer simulation is an important tool that allows us to generate synthetic images of various astrophysical objects. In the case of complex three-dimensional geometries, a Monte Carlo-based method that simulates photon packages as they move through and interact with their environment is often used. Previous studies have shown, in the regime of high optical depths, that the required number of simulated photon packages strongly rises and estimated fluxes may be severely underestimated. In this paper we identify two problems that arise for Monte Carlo radiative transfer simulations that hinder a proper determination of flux: first, a mismatch between the probability and weight of the path of a photon package and second, the necessity of simulating a wide range of high scattering orders. Furthermore, we argue that the peel-off method partly solves these problems, and we additionally propose an extended peel-off method. Our proposed method improves several shortcomings of its basic variant and relies on the utilization of precalculated sphere spectra. We then combine both peel-off methods with the Split method and the Stretch method and numerically evaluate their capabilities as opposed to the pure Split$\,\&\,$Stretch method in an infinite plane-parallel slab setup. We find that the peel-off method greatly enhances the performance of these simulations; in particular, at a transverse optical depth of $τ_{\rm max}=75$ our method achieved a significantly lower error than previous methods while simultaneously saving ${>}95\%$ computation time. Finally, we discuss the inclusion of polarization and Mie-scattering in the extended peel-off method, and argue that it may be necessary to equip future Monte Carlo radiative transfer simulations with additional advanced pathfinding techniques.
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