The dust-to-gas ratio in the gravitational collapse of filamentary clouds

The aim of this study is to investigate the evolution of the dust-to-gas ratio in the self-similar collapse of a filamentary molecular cloud. For this purpose, we use single fluid dusty-gas model in our study, which describes a single fluid moving with the barycentric velocity of the mixture instead of two-fluid method. The self-similar technique is used to consider the problem in two phases of the collapse, i.e. isothermal and polytropic collapse phases. Regarding the analytical methods, we obtain a semi-analytical solution for the dust-to-gas ratio as a function of the barycentric velocity at large radii of the filament. Furthermore, the polytropic collapse is solved numerically at large radii of a collapsing filamentary cloud. The results show that the profile of dust-to-gas ratio is very different for the isothermal and polytropic cases. This issue suggests that thermodynamic processes during the collapse have the most significant effect on the evolution of the dust-to-gas ratio. It was also proved that the intrinsic density and the grain size play important roles on the values of the dust-to-gas ratio during the self-similar collapse. Finally, the results address some outstanding issues about the dust distribution during the gravitational collapse (either the isothermal and adiabatic collapse) which has not received much attention before.