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.
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