The scattering order problem in Monte Carlo radiative transfer

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 $\tau_{\rm max}=75$ 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.