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Ion-neutral friction and accretion-driven turbulence in self-gravitating filaments

Recent Herschel observations have confirmed that filaments are ubiquitous in molecular clouds and suggest, that irrespective of the column density, there is a characteristic width of about 0.1 pc whose physical origin remains unclear. We develop an analytical model that can be applied to self-gravitating accreting filaments. It is based on the one hand on the virial equilibrium of the central part of the filament and on the other hand on the energy balance between the turbulence driven by accretion onto the filament and dissipation. We consider two dissipation mechanisms, the turbulent cascade and the ion-neutral friction. Our model predicts that the width of the inner part of the filament is almost independent of the column density and leads to values comparable to what is inferred observationally if dissipation is due to ion-neutral friction. On the contrary, turbulent dissipation leads to a structure that is bigger and depends significantly on the column density. Our model provides a reasonable physical explanation which could explain the observed filament width when they are self-gravitating. It predicts the correct order or magnitude though hampered by some uncertainties.