The Equilibrium and Stability of Uniformly Rotating, Isothermal Gas Cylinders

Hansen, Carl J.; Aizenman, M. L.; Ross, Randy L.

doi:10.1086/154542

Cited by 18 publications

(17 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…We infer that the equilibrium model of a critically rotating isothermal cylinder is a nonrotating isothermal cylinder. This is in agreement with the results of Hansen et al (1976, Fig. 1), showing that no hydrostatic equilibrium models of complete, rotating isothermal cylinders are possible, because their rotating hydrostatic models exhibit huge density inversions…”

Section: Critically Rotating Isothermal Cylinder (N ¼ 1)supporting

confidence: 92%

Critically Rotating Polytropic Cylinders

Oproiu¹,

Horedt²

2008

Astrophysical Journal

View full text Add to dashboard Cite

Observations indicate that interstellar molecular clouds can often be approximated by rotating (polytropic) cylinders. The two limiting configurations -the homogeneous and the isothermal cylinder-are used to obtain analytical solutions valid, at least qualitatively, for the whole range 0 n 1 of permitted polytropic indices. The radius of critically rotating, infinitely long polytropic cylinders has a flat minimum at polytropic index n ¼ 0:854, becoming infinite in the two limiting cases n ¼ 0 and 1. The ratio between the radii of critically rotating and nonrotating polytropic cylinders decreases strongly from 1 if n ¼ 0 to 1.52 if n ¼ 2:04, afterward increasing slowly to exp (1/2) ¼ 1:65 if n ¼ 1. Natural polytropic variables are presented in the Appendix. Subject headingg s: equation of state -hydrodynamics -ISM: kinematics and dynamics

show abstract

Section: Critically Rotating Isothermal Cylinder (N ¼ 1)supporting

confidence: 92%

Critically Rotating Polytropic Cylinders

Oproiu¹,

Horedt²

2008

Astrophysical Journal

View full text Add to dashboard Cite

show abstract

“…Studies of the structure and stability of self-gravitating filaments have a long history, mostly in the context of star-formation in ISM filaments. Early analytic work investigated the stability of an infinite incompressible cylinder with and without an axial magnetic field (Chandrasekhar & Fermi 1953), a compressible yet still homogeneous infinite cylinder (Ostriker 1964b), a homogeneous stream of finite radius (Mikhaǐlovskiǐ & Fridman 1972;Fridman & Poliachenko 1984), and a uniformly rotating isothermal cylinder (Hansen et al 1976). Hydrostatic equilibrium of a self-gravitating isothermal cylinder is only possible if its mass per unit length (hereafter line-mass) is less than a critical value which depends only on its temperature (Ostriker 1964a; see eq.…”

Section: Introductionmentioning

confidence: 99%

Kelvin–Helmholtz instability in self-gravitating streams

Aung

Mandelker

Nagai

et al. 2019

Monthly Notices of the Royal Astronomical Society

View full text Add to dashboard Cite

Self-gravitating gaseous filaments exist on many astrophysical scales, from sub-pc filaments in the interstellar medium to Mpc scale streams feeding galaxies from the cosmic web. These filaments are often subject to Kelvin-Helmholtz Instability (KHI) due to shearing against a confining background medium. We study the nonlinear evolution of KHI in pressure-confined self-gravitating gas streams initially in hydrostatic equilibrium, using analytic models and hydrodynamic simulations, not including radiative cooling. We derive a critical line-mass, or mass per unit length, as a function of the stream Mach number and density contrast with respect to the background, µ cr (M b , δ c ) ≤ 1, where µ = 1 is normalized to the maximal line mass for which initial hydrostatic equilibrium is possible. For µ < µ cr , KHI dominates the stream evolution. A turbulent shear layer expands into the background and leads to stream deceleration at a similar rate to the non-gravitating case. However, with gravity, penetration of the shear layer into the stream is halted at roughly half the initial stream radius by stabilizing buoyancy forces, significantly delaying total stream disruption. Streams with µ cr < µ ≤ 1 fragment and form round, long-lived clumps by gravitational instability (GI), with typical separations roughly 8 times the stream radius, similar to the case without KHI. When KHI is still somewhat effective, these clumps are below the spherical Jeans mass and are partially confined by external pressure, but they approach the Jeans mass as µ → 1 and GI dominates. We discuss potential applications of our results to streams feeding galaxies at high redshift, filaments in the ISM, and streams resulting from tidal disruption of stars near the centres of massive galaxies.

show abstract

“…The calculation should ideally be applicable to any type of density profile and equation of state. Hansen et al (1976) examined the case of an infinite, isothermal, and uniformly rotating cylinder of finite radius, whereas more complex situations were investigated from a numerical perspective (Bastien & Mitalas 1979;Bastien 1983;Arcoragi et al 1991;Bastien et al 1991;Nakamura et al 1993Nakamura et al , 1995Matsumoto et al 1994;Tomisaka 1995Tomisaka , 1996. Nagasawa (1987) numerically obtained a dispersion relation in the case of an isothermal gas cylinder with an axial magnetic field, and found that such a cylinder was unstable to axisymmetric perturbations of wavelength higher than a particular one.…”

Section: Introductionmentioning

confidence: 99%

Local stability of a gravitating filament: a dispersion relation

Freundlich¹,

Jog²,

Combes³

2014

A&A

View full text Add to dashboard Cite

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.

show abstract

The Equilibrium and Stability of Uniformly Rotating, Isothermal Gas Cylinders

Cited by 18 publications

References 0 publications

Critically Rotating Polytropic Cylinders

Critically Rotating Polytropic Cylinders

Kelvin–Helmholtz instability in self-gravitating streams

Local stability of a gravitating filament: a dispersion relation

Contact Info

Product

Resources

About