A new analytical scattering phase function for interstellar dust
  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)
