标题： 使用频率分布调整的蒙特卡罗辐射传输中的辐射平衡 显示英文标题

标题： Radiative equilibrium in Monte Carlo radiative transfer using frequency distribution adjustment

摘要： 蒙特卡罗方法是一种强大的工具，可用于进行辐射平衡计算，即使在复杂的几何形状下也是如此。 标准蒙特卡罗辐射平衡方法的主要缺点是它们需要迭代，这使得它们在数值上非常耗时。 Bjorkman 和 Wood 最近提出了一种频率分布调整方案，该方案允许通过选择每次再发射光子的频率来纠正之前再发射光子的不正确光谱，从而无需迭代即可完成辐射平衡蒙特卡罗计算。 尽管该方法似乎能得出正确的结果，但我们认为其理论基础并不完全透明，并且尚不清楚该技术是否是一种精确的严谨方法，或者它是否仅仅是一种良好的便捷近似。 我们批判性地研究了已采样分布如何通过添加从调整分布中采样的数据点来调整到新分布的一般问题。 我们证明这种调整并非总是可行的，它取决于原始分布和期望分布的形状，以及可以添加的数据点的相对数量。 将此定理应用于辐射平衡蒙特卡罗计算，我们为 Bjorkman 和 Wood 的频率分布调整方法提供了坚实的理论基础，并证明这种方法通过额外的辐射平衡要求提供了正确的频率分布。 我们讨论了这种方法的优点和局限性，并表明它可以轻松与附加加热源的存在和光子加权的概念相结合。 然而，如果包含小尘粒，该方法可能会失效……（摘要） 显示英文摘要

摘要： The Monte Carlo method is a powerful tool for performing radiative equilibrium calculations, even in complex geometries. The main drawback of the standard Monte Carlo radiative equilibrium methods is that they require iteration, which makes them numerically very demanding. Bjorkman & Wood recently proposed a frequency distribution adjustment scheme, which allows radiative equilibrium Monte Carlo calculations to be performed without iteration, by choosing the frequency of each re-emitted photon such that it corrects for the incorrect spectrum of the previously re-emitted photons. Although the method appears to yield correct results, we argue that its theoretical basis is not completely transparent, and that it is not completely clear whether this technique is an exact rigorous method, or whether it is just a good and convenient approximation. We critically study the general problem of how an already sampled distribution can be adjusted to a new distribution by adding data points sampled from an adjustment distribution. We show that this adjustment is not always possible, and that it depends on the shape of the original and desired distributions, as well as on the relative number of data points that can be added. Applying this theorem to radiative equilibrium Monte Carlo calculations, we provide a firm theoretical basis for the frequency distribution adjustment method of Bjorkman & Wood, and we demonstrate that this method provides the correct frequency distribution through the additional requirement of radiative equilibrium. We discuss the advantages and limitations of this approach, and show that it can easily be combined with the presence of additional heating sources and the concept of photon weighting. However, the method may fail if small dust grains are included... (abridged)