Statistical approach of the effects of roughness on the polarization of light scattered by dust grains

In order to study the effect of shape on the optical properties of dust grains, we statistically analyze the linear polarized scattered light. We start by examining a homogeneous spherical grain using the discrete dipole approximation (DDA) Draine (Astrophys J 1988;333:848). Using a uniform law we remove elements of matter on the surface of the grain to describe a random roughness. Then, for various scattering angles, the linear polarization P_l is calculated. We successively repeat the simulation in order to obtain a sample of random variables constituting the values P_l of the linear polarization. The analysis of the results is then achieved through a Gaussian kernel method which provides the probability density function of P_l for each scattering angle. We present the results for a typical interstellar grain of water–ice with radius a comparable to the incident wavelength λ so that the parameter size x≡2πa/λ1. We apply this method for two wavelengths in the near IR, when water–ice is transparent at 1.9 μm, and, when water–ice is absorbing at 3.1 μm. We find that the shape of the density function of the linear polarization is asymmetric to the mean value of the density function and non-unimodal for several scattering angles. This allows us to separate the effects of roughness from those of volume. When water–ice is absorbing, we also observe a significant shift of the polarization peak toward greater scattering angles.