# On sampling of scattering phase functions

## TL;DR

This paper reviews and improves sampling algorithms for scattering phase functions in Monte Carlo radiative transfer, enabling accurate simulation of complex phase functions and introducing a new phase function for realistic dust modeling.

## Contribution

It introduces enhanced sampling methods, including piecewise linear approximations and Gibbs sampling, for complex phase functions, and proposes a new phase function for dust scattering.

## Key findings

- Improved sampling performance for small scattering angles.
- Accurate sampling of complex analytic phase functions like Fournier-Forand.
- New phase function fits realistic dust scattering data.

## Abstract

Monte Carlo radiative transfer, which has been demonstrated as a successful algorithm for modeling radiation transport through the astrophysical medium, relies on sampling of scattering phase functions. We review several classic sampling algorithms such as the tabulated method and the accept-reject method for sampling the scattering phase function. The tabulated method uses a piecewise constant approximation for the true scattering phase function; we improve its sampling performance on a small scattering angle by using piecewise linear and piecewise log-linear approximations. It has previously been believed that certain complicated analytic phase functions such as the Fournier-Forand phase function cannot be simulated without approximations. We show that the tabulated method combined with the accept-reject method can be applied to sample such complicated scattering phase functions accurately. Furthermore, we introduce the Gibbs sampling method for sampling complicated approximate analytic phase functions. In addition, we propose a new modified Henyey-Greenstein phase function with exponential decay terms for modeling realistic dust scattering. Based on Monte Carlo simulations of radiative transfer through a plane-parallel medium, we also demonstrate that the result simulated with the new phase function can provide a good fit to the result simulated with the realistic dust phase function.