The penetration of Far-UV radiation into molecular clouds

Context. FUV radiation strongly affects the physical and chemical state of molecular clouds, from protoplanetary disks to entire galaxies. Aims. The solution of the FUV radiative transfer equation can be complicated if the most relevant radiative processes such us dust scattering and gas line absorption are included, and have realistic (non-uniform) properties, i.e. if optical properties are depth dependent. Methods. We have extended the spherical harmonics method to solve for the FUV radiation field in externally or internally illuminated clouds taking into account gas absorption and coherent, nonconservative and anisotropic scattering by dust grains. The new formulation has been implemented in the Meudon PDR code and thus it will be publicly available. Results. Our formalism allows us to consistently include: (i) varying dust populations and (ii) gas lines in the FUV radiative transfer. The FUV penetration depth rises for increasing dust albedo and anisotropy of the scattered radiation ( e. g. when grains grow towards cloud interiors). Conclusions. Illustrative models of illuminated clouds where only the dust populations are varied confirm earlier predictions for the FUV penetration in diffuse clouds (A(V) < 1). For denser and more embedded sources (A(V) > 1) we show that the FUV radiation field inside the cloud can differ by orders of magnitude depending on the grain properties and growth. Our models reveal significant differences regarding the resulting physical and chemical structures for steep vs. flat extinction curves towards molecular clouds. In particular, we show that the photochemical and thermal gradients can be very different depending on grain growth. Therefore, the assumption of uniform dust properties and averaged extinction curves can be a crude approximation to determine the resulting scattering properties, prevailing chemistry and atomic/molecular abundances in ISM clouds or protoplanetary disks.