  Recent Herschel observations have confirmed that filaments are ubiquitous in
molecular clouds and suggest that irrespectively 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 one hand on the virial equilibrium of the
central part of the filament and on the other hand on 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 filament inner part 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.
