Improvement of the Mean Field T-Matrix method for scattering by fractal aggregates of identical spheres in astrophysical environments

Aggregated particles and aerosols are common in natural or industrial environments. Analysing their scattering and absorption properties with precise methods may prove useful for gaining information about real particles, using remote sensing or in situ active optical instruments in natural environments. Many methods, with varying complexities, were developed in the past. For aggregates of spheres, the most recent version of the T-Matrix method by Mackowski and Mishchenko (2011) is able to treat the problem almost exactly and can yield all the details of the scattering properties. However, for computational reasons, the T-Matrix method cannot handle large particles. In order to deal with large particles, a mean-field version of the T-Matrix theory was developed by Botet et al. (1997) for aggregates of identical spheres and used in particular to analyse the case of Titan haze. This mean-field T-Matrix method is efficient to quickly calculate accurate approximations of many optical properties of aggregates of Mie spheres, but it is inherently limited by the mean field approximations. It uses crude approximation of the pair-correlation functions (Seignovert et al., 2017) and leads to inaccurate estimations in the geometrical optics limit (Tazaki and Tanaka, 2018). In the present work, we bring improvements that overcome these two limitations. This significantly increases the validity range of the method and its accuracy. We display comparisons with the results obtained with T-Matrix method in order to assess the performance of the new version of the mean field method (MFT-M${}^{+}$).