The Jeans’ criterion and the gravitational instability

2008 ◽  
pp. 151-163
Author(s):  
Serge Bouquet
Keyword(s):  
Gravitational Instability ◽  
Jeans Criterion

Effect of spin-induced magnetization and Hall current on self-gravitational instability of magnetized viscous quantum plasma

2014 ◽  
Vol 81 (2) ◽  
Author(s):  
Prerana Sharma ◽  
R. K. Chhajlani
Keyword(s):  
Gravitational Instability ◽  
Quantum Effect ◽  
Normal Mode Analysis ◽  
Longitudinal Direction ◽  
Transverse Mode ◽  
Mode Analysis ◽  
Quantum Plasma ◽  
Longitudinal Modes ◽  
Jeans Criterion ◽  
Basic Equations

The Jeans self-gravitational instability is studied for dense quantum viscous plasma with Hall term and intrinsic magnetization generated by collective electron spin. The quantum magnetohydrodynamic model is employed to formulate the basic equations of the problem. The dispersion relation is obtained using the normal mode analysis, and further reduced for both transverse and longitudinal modes of propagation. The transverse mode of propagation is found to be unaffected by the Hall term but affected by quantum effect, viscosity, and magnetization parameters. The Jeans criterion of instability in the transverse direction is modified by Alfven velocity, magnetization parameter, and quantum effect. The non-gravitating magnetized mode is obtained in the longitudinal direction, which is modified by Hall parameter and is not affected by quantum term, whereas the gravitational mode is unaffected by the magnetization parameter but affected by viscosity and quantum parameters. It is observed that the Jeans condition of instability is affected by the quantum term. The growth rate of Jeans instability is plotted for various values of magnetization, quantum, and viscosity parameters of the quantum plasma medium.

Effects of collisions and gyroviscosity on gravitational instability in a two-component plasma

1972 ◽  
Vol 8 (3) ◽  
pp. 393-400 ◽  
Author(s):  
F. Herrnegger
Keyword(s):  
Gravitational Instability ◽  
Larmor Radius ◽  
Finite Larmor Radius ◽  
Two Component ◽  
Component Plasma ◽  
Jeans Criterion ◽  
Fluid Theory ◽  
The Magnetic Field ◽  
Two Fluid ◽  
Critical Wavenumber

The dispersion relation for gravitational instability has been given within the framework of a two-fluid theory. It has been shown that the Jeans criterion is changed by finite Larmor radius and by collisions for waves propagating perpendicular to the magnetic field. The critical wavenumber for instability decreases with increasing Alfvén velocity and with increasing gyroviscosity. Instability does not set in with overstabiity.

Gravitational instability with Hall effect in a plasma

1968 ◽  
Vol 46 (22) ◽  
pp. 2553-2556 ◽  
Author(s):  
Amiya K. Sen ◽  
Chih Kang Chou
Keyword(s):  
Growth Rate ◽  
Hall Effect ◽  
Stability Problem ◽  
Hall Current ◽  
Gravitational Instability ◽  
Jeans Criterion ◽  
Gravitational Stability

It is shown that the new modes introduced by the inclusion of the Hall effect in the gravitational stability problem of a plasma are stable. However, an old mode (which is stable in the absence of a Hall current) becomes unstable. We conclude that the Hall current has a destabilizing effect and that the Jeans criterion for stability is adversely affected by its presence. However, the growth rate of the Hall instability is found to be negligible for any astrophysical system.

scholarly journals Effect of Conductivity on Magneto-Gravitational Instability and Suspended Particles

1978 ◽  
Vol 33 (12) ◽  
pp. 1469-1471
Author(s):  
R. K. Chhajlani ◽  
P. Vashistha ◽  
S. C. Bhand
Keyword(s):  
Dispersion Relation ◽  
Gravitational Instability ◽  
Suspended Particles ◽  
The Self ◽  
Sufficient Condition ◽  
Jeans Criterion ◽  
Particle Medium

Abstract The self gravitational instability of an infinite homogeneous magnetized gas-particle medium in the presence of suspended particles is investigated. The conductivity of the medium is assumed to be finite. The dispersion relation is obtained for such a medium. It is found that in the presence of suspended particles a sufficient condition of instability is obtained by Jeans’ criterion for a self gravitating magnetized conducting gas-particle medium.

Jeans’ Gravitational Instability of a Thermally Conducting, Unbounded, Partially Ionized Plasma

2006 ◽  
Vol 61 (5-6) ◽  
pp. 275-280 ◽  
Author(s):  
Shaista Shaikh ◽  
Aiyub Khan ◽  
Prem Kumar Bhatia
Keyword(s):  
Growth Rate ◽  
Gravitational Instability ◽  
The Other ◽  
Wave Number ◽  
Finite Conductivity ◽  
Jeans Criterion ◽  
Partially Ionized ◽  
Thermally Conducting ◽  
Limiting Case ◽  
Oblique Magnetic Field

The gravitational instability of an infinitely extending homogenous, partially ionized plasma, permeated by an oblique magnetic field, has been studied to investigate the effects of Hall currents, finite conductivity, viscosity, collision with neutrals and thermal conductivity on the growth rate of the disturbance. The dispersion relation obtained has been solved numerically, and it has been found that Hall currents and collision with neutrals have a destabilizing influence on the growth rate while the other mechanisms reinforce the gravitational instability. Jeans’ criterion, derived within a purely hydrodynamic framework, has been rediscussed along a nonextensive kinetic theory. A new Jeans’ criterion was deduced, which depends on the nonextensive parameter q and the standard Jeans’ wave number is recovered in the limiting case q = 1

Saturation mechanism and generated viscosity in gravito-turbulent accretion disks

2020 ◽  
Vol 640 ◽  
pp. A53
Author(s):  
L. Löhnert ◽  
S. Krätschmer ◽  
A. G. Peeters
Keyword(s):  
Growth Rate ◽  
Numerical Simulations ◽  
Accretion Disks ◽  
Gravitational Instability ◽  
Turbulent Viscosity ◽  
Radial Distance ◽  
Maximum Growth ◽  
Wave Number ◽  
Radiative Cooling ◽  
Mixing Length

Here, we address the turbulent dynamics of the gravitational instability in accretion disks, retaining both radiative cooling and irradiation. Due to radiative cooling, the disk is unstable for all values of the Toomre parameter, and an accurate estimate of the maximum growth rate is derived analytically. A detailed study of the turbulent spectra shows a rapid decay with an azimuthal wave number stronger than ky−3, whereas the spectrum is more broad in the radial direction and shows a scaling in the range kx−3 to kx−2. The radial component of the radial velocity profile consists of a superposition of shocks of different heights, and is similar to that found in Burgers’ turbulence. Assuming saturation occurs through nonlinear wave steepening leading to shock formation, we developed a mixing-length model in which the typical length scale is related to the average radial distance between shocks. Furthermore, since the numerical simulations show that linear drive is necessary in order to sustain turbulence, we used the growth rate of the most unstable mode to estimate the typical timescale. The mixing-length model that was obtained agrees well with numerical simulations. The model gives an analytic expression for the turbulent viscosity as a function of the Toomre parameter and cooling time. It predicts that relevant values of α = 10−3 can be obtained in disks that have a Toomre parameter as high as Q ≈ 10.

scholarly journals N-BODY SIMULATION OF PLANETESIMAL FORMATION THROUGH GRAVITATIONAL INSTABILITY AND COAGULATION. II. ACCRETION MODEL

2009 ◽  
Vol 703 (2) ◽  
pp. 1363-1373 ◽  
Author(s):  
Shugo Michikoshi ◽  
Eiichiro Kokubo ◽  
Shu-ichiro Inutsuka
Keyword(s):  
Gravitational Instability ◽  
Accretion Model

scholarly journals FORMING PLANETESIMALS BY GRAVITATIONAL INSTABILITY. II. HOW DUST SETTLES TO ITS MARGINALLY STABLE STATE

2010 ◽  
Vol 725 (2) ◽  
pp. 1938-1954 ◽  
Author(s):  
Aaron T. Lee ◽  
Eugene Chiang ◽  
Xylar Asay-Davis ◽  
Joseph Barranco
Keyword(s):  
Gravitational Instability ◽  
Stable State
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