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 \sim 10 ~ { } { K } and an external pressure p _ { ext } / k in the range 1.5 \times 10 ^ { 4 } ~ { } { K~ { } cm } ^ { -3 } to 5 \times 10 ^ { 4 } ~ { } { K~ { } cm ^ { -3 } } .
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 .