A new analytical scattering phase function for interstellar dust

TL;DR

This paper introduces the TTU2 analytical phase function as a simple yet accurate model for interstellar dust scattering, outperforming the traditional Henyey-Greenstein function across UV to NIR wavelengths.

Contribution

The paper proposes the TTU2 phase function, offering a balance of realism and simplicity for modeling dust scattering, improving upon existing functions like Henyey-Greenstein and Reynolds-McCormick.

Findings

Henyey-Greenstein poorly fits dust scattering, especially in UV.

Reynolds-McCormick fits well but has degenerate parameters.

TTU2 provides an excellent fit across UV-NIR wavelengths.

Abstract

Context: Properly modelling scattering by interstellar dust grains requires a good characterisation of the scattering phase function. The Henyey-Greenstein phase function has become the standard for describing anisotropic scattering by dust grains, but it is a poor representation of the real scattering phase function outside the optical range. Aims: We investigate alternatives for the Henyey-Greenstein phase function that would allow the scattering properties of dust grains to be described. Our goal is to find a balance between realism and complexity: the scattering phase function should be flexible enough to provide an accurate fit to the scattering properties of dust grains over a wide wavelength range, and it should be simple enough to be easy to handle, especially in the context of radiative transfer calculations. Methods: We fit various analytical phase functions to the scattering phase function corresponding to the BARE-GR-S model, one of the most popular and commonly adopted models for interstellar dust. We weigh the accuracy of the fit against the number of free parameters in the analytical phase functions. Results: We confirm that the Henyey-Greenstein phase functions poorly describe scattering by dust grains, particularly at ultraviolet (UV) wavelengths, with relative differences of up to 50%. The Draine phase function alleviates this problem at near-infrared (NIR) wavelengths, but not in the UV. The two-term Reynolds-McCormick phase function, recently advocated in the context of light scattering in nanoscale materials and aquatic media, describes the BARE-GR-S data very well, but its five free parameters are degenerate. We propose a simpler phase function, the two-term ultraspherical-2 (TTU2) phase function, that also provides an excellent fit to the BARE-GR-S phase function over the entire UV-NIR wavelength range. (Abridged)