  The physical properties of the so-called Ostriker isothermal filament
(Ostriker 1964) have been classically used as benchmark to interpret the
stability of the filaments observed in nearby clouds. However, recent continuum
studies have shown that the internal structure of the filaments depart from the
isothermality, typically exhibiting radially increasing temperature gradients.
The presence of internal temperature gradients within filaments suggests that
the equilibrium configuration of these objects should be therefore revisited.
The main goal of this work is to theoretically explore how the equilibrium
structure of a filament changes in a non-isothermal configuration. We solve the
hydrostatic equilibrium equation assuming temperature gradients similar to
those derived from observations. We obtain a new set of equilibrium solutions
for non-isothermal filaments with both linear and asymptotically constant
temperature gradients. Our results show that, for sufficiently large internal
temperature gradients, a non-isothermal filament could present significantly
larger masses per unit length and shallower density profiles than the
isothermal filament without collapsing by its own gravity. We conclude that
filaments can reach an equilibrium configuration under non-isothermal
conditions. Detailed studies of both the internal mass distribution and
temperature gradients within filaments are then needed in order to judge the
physical state of filaments.
