Atmospheric multiple scattering of fluorescence light from extensive air showers and effect of the aerosol size on the reconstruction of energy and depth of maximum

12 pages, 9 figures, journal paper, submitted to Astroparticle Physics. arXiv admin note: substantial text overlap with arXiv:1310.1702The reconstruction of the energy and the depth of maximum Xmax of an extensive air shower depends on the multiple scattering of fluorescence photons in the atmosphere. In this work, we explain how atmospheric aerosols, and especially their size, scatter the fluorescence photons during their propagation. Using a Monte Carlo simulation for the scattering of light, the dependence on the aerosol conditions of the multiple scattered light contribution to the recorded signal is fully parameterised. A clear dependence on the aerosol size is proposed for the first time. Finally, using this new parameterisation, the effect of atmospheric aerosols on the energy and on the Xmax reconstructions is presented for a typical extensive air shower observed by a ground-based detector: a systematic over-estimation of these two quantities is observed if aerosols of large size are neglected in the estimation of the multiple scattered fraction