Nonisothermal filaments in equilibrium

Abstract

Context. The physical properties of the so-called Ostriker isothermal filament have been classically used as a 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. Aims. 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 nonisothermal configuration. Methods. We solve the hydrostatic equilibrium equation by assuming temperature gradients similar to those derived from observations. Results. We obtain a new set of equilibrium solutions for nonisothermal filaments with both linear and asymptotically constant temperature gradients. For sufficiently large internal temperature gradients, our results show that a nonisothermal filament could present significantly larger masses per unit length and shallower density profiles than the isothermal filament without collapsing by its own gravity. Conclusions. We conclude that filaments can reach an equilibrium configuration under nonisothermal conditions. Detailed studies of both the internal mass distribution and temperature gradients within filaments are then needed to judge the physical state of filaments.

Local stability of a gravitating filament: a dispersion relation

“…For such filaments with temperature and sound speed increasing with radius, the critical wavenumber k crit falls more rapidly with radius than in the isothermal case. Consequently, such filaments are expected to be more stable than their isothermal counterparts, which was also inferred by Recchi et al (2013) by comparing the equilibrium structure of isothermal and nonisothermal filaments.…”

“…Recent observations have shown that interstellar filaments are not isothermal, finding dust temperatures that tend to increase with radius (Stepnik et al 2003;Palmeirim et al 2013), and theoretical calculations inspired by Ostriker (1964) show that such filaments are more stable than their isothermal counterparts (Recchi et al 2013). This motivates us not to limit ourselves to the isothermal case, but to assume a more general polytropic equation of state, which can result in a temperature varying with radius.…”

Chains of dense cores in the Taurus L1495/B213 complex

“…Palmeirim et al (2013) also found a larger-than-equilibrium mass per unit length in the B213/B211 filament as a whole using dust continuum measurements, although these authors treated the region as a single object and ignored the presence of multiple velocity components. Whether this larger mass per unit length means that the chains are significantly out of equilibrium is unclear, especially considering the uncertainty in the dust opacity and that additional support mechanisms, such as magnetic fields or temperature gradients can increase the equilibrium mass per unit length (Stodólkiewicz 1963;Nakamura et al 1993;Recchi et al 2013). Further understanding of the physical state of the chains requires the analysis of their internal kinematics, which is the topic of the next two sections.…”

SEDIGISM: the kinematics of ATLASGAL filaments

“…Low resolution and signal-to-noise data explain only partially the observed exponents. Therefore, observations suggest that filaments are embedded in a surrounding molecular cloud (Fischera & Martin 2012), not isothermal (Recchi et al 2013) and/or not in hydrostatic equilibrium (Heitsch 2013a,b).…”