Local stability of a gravitating filament: a dispersion relation

Abstract

Filamentary structures are ubiquitous in astrophysics and are observed at various scales. On a cosmological scale, matter is usually distributed along filaments, and filaments are also typical features of the interstellar medium. Within a cosmic filament, matter can contract and form galaxies, whereas an interstellar gas filament can clump into a series of bead-like structures that can then turn into stars. To investigate the growth of such instabilities, we derive a local dispersion relation for an idealized self-gravitating filament and study some of its properties. Our idealized picture consists of an infinite self-gravitating and rotating cylinder with pressure and density related by a polytropic equation of state. We assume no specific density distribution, treat matter as a fluid, and use hydrodynamics to derive the linearized equations that govern the local perturbations. We obtain a dispersion relation for axisymmetric perturbations and study its properties in the (k R , k z ) phase space, where k R and k z are the radial and longitudinal wavenumbers, respectively. While the boundary between the stable and unstable regimes is symmetrical in k R and k z and analogous to the Jeans criterion, the most unstable mode displays an asymmetry that could constrain the shape of the structures that form within the filament. Here the results are applied to a fiducial interstellar filament, but could be extended for other astrophysical systems, such as cosmological filaments and tidal tails.

Stability of Filaments in Star-Forming Clouds and the Formation of Prestellar Cores in Them

“…Then in the limit of r → r flat , Equation (14) Freundlich, Jog, & Combes (2014). We also note that a Plummer-like profile (p = 2), fits the radial density distribution of the post-collapse filament very well when gas temperature is calculated by accounting for gascooling.…”

“…Freundlich, Jog, & Combes (2014) derived a dispersion relation for a rotating non-magnetised filamentary cloud idealised as a polytropic cylinder with localised density perturbations. Under these simplifying assumptions, the authors demonstrated that the filament indeed developed Jeans-type instability with propensity to fragment on the scale of the local Jeans length.…”

Baryonic Processes in the Large-Scale Structuring of the Universe

“…Studies that consider deviations from isothermality include Goldreich & Lynden-Bell (1965) who obtained stability criteria for pressure bounded, uniformly rotating polytropic sheets. The fragmentation of cylindrical filaments was first studied by Chandrasekhar & Fermi (1953) in the magnetized, isothermal and incompressible case and has been since then the object of careful attention of many authors including, in addition to those mentioned above, notably Ostriker (1964a), and more recently Breysse et al (2014) and Freundlich et al (2014a) for instance. Most these studies, if not all, approach the problem with the usual procedure of analyzing the system of linearized equations in the so-called primitive variables (see section 7.1.1 below).…”

Filamentary fragmentation in a turbulent medium

“…The recent observations by the Herschel Space Observatory have revealed that filaments are prevalent within molecular clouds and that star-forming cores are often embedded within them (André et al 2010;Arzoumanian et al 2013;Könyves et al 2015;Marsh et al 2016). The ubiquity of filamentary structures has lead to numerous papers studying the effects their geometry has on stability and fragmentation (Ostriker 1964;Larson 1985;Inutsuka & Miyama 1992;Freundlich, Jog & Combes 2014;Clarke, Whitworth & Hubber 2016).…”