2012A&A...542A..77F

We analyze the physical parameters of interstellar filaments that we describe by an idealized model of isothermal self-gravitating infinite cylinder in pressure equilibrium with the ambient medium. Their gravitational state is characterized by the ratio f_cyl of their mass line density to the maximum possible value for a cylinder in a vacuum. Equilibrium solutions exist only for f_cyl<1. This ratio is used in providing analytical expressions for the central density, the radius, the profile of the column density, the column density through the cloud centre, and the FWHM. The dependence of the physical properties on external pressure and temperature is discussed and directly compared to the case of pressure-confined isothermal self-gravitating spheres. Comparison with recent observations of the FWHM and the central column density N_H(0) show good agreement and suggest a filament temperature of ∼10K and an external pressure in the range 1.5x10⁴K/cm3 to 5x10⁴K/cm3. Stability considerations indicate that interstellar filaments become increasingly gravitationally unstable with mass line ratio f_cyl approaching unity. For intermediate f_cyl>0.5 the instabilities should promote core formation through compression, with a separation of about five times the FWHM. We discuss the nature of filaments with high mass line densities and their relevance to gravitational fragmentation and star formation.