On the gravitational instability of a medium in non-uniform rotation and magnetic field

The effect of a non-uniform magnetic field on the gravitational instability for a non-uniformly rotating, infinitely extending axisymmetric cylinder in a homogeneous medium has been studied. The Bel and Schatzman criterion of gravitational instability for a non-uniformly rotating medium is modified under the effect of a non-uniform/uniform magnetic field acting along the tangential and axial directions. As a consequence the stabilizing and destabilizing effect of the non-uniform magnetic field is obtained, a new criterion for the magneto-gravitational instability is deduced in terms of Alfven’s wave velocity; and it is also found that the Jeans criterion determines the gravitational instability in the absence of rotation and when the non-uniform/uniform magnetic field acts along the axis of the cylinder.     

Self-gravitational instability in magnetized finitely conducting viscoelastic fluid

The linear self-gravitational instability of finitely conducting, magnetized viscoelastic fluid is investigated using the modified generalized hydrodynamic (GH) model. A general dispersion relation is obtained with the help of linearized perturbation equations using the normal mode analysis and it is discussed for longitudinal and transverse modes of propagation. In longitudinal propagation, we find that Alfven mode is uncoupled with the gravitating mode. The Jeans criterion of instability is determined which depends upon shear viscosity and bulk viscosity while it is independent of magnetic field. The viscoelastic effects modify the fundamental Jeans criterion of gravitational instability. In transverse mode of propagation, the Alfven mode couples with the acoustic mode, compressional viscoelastic mode and gravitating mode. The growth rate of Jeans instability is compared in weakly coupled plasma (WCP) and strongly coupled plasma (SCP) which is larger for SCP in both the modes of propagations. The presence of finite electrical resistivity removes the effect of magnetic field in the condition of Jeans instability and expression of critical Jeans wavenumber. It is found that Mach number and shear viscosity has stabilizing while finite electrical resistivity has destabilizing influence on the growth rate of Jeans instability.     

Effect of quantum corrections on the Jeans instability of self-gravitating viscoelastic dusty fluid

In this paper we investigate the effects of quantum correction on the Jeans instability of self-gravitating viscoelastic dusty electron-ion quantum fluids. The massive self-gravitating dust grains are assumed to be strongly coupled and non-degenerate having both viscous and elastic behavior while the inertialess electrons and ions are considered as weakly coupled and Fermi degenerate. The hydrodynamic model is modified and a linear dispersion relation is derived employing the plane wave solutions on the linearized perturbation equations for the considered system. It is observed that the dispersion properties are affected due to the presence of viscoelastic effects and quantum statistical corrections. The modified condition of Jeans instability and expression of critical Jeans wavenumber are obtained. Numerically it is shown that viscoelastic effects, dust plasma frequency and quantum statistical effects all have stabilizing influence on the growth rate of gravitationally Jeans mode. The growth rates are also compared in kinetic and hydrodynamic limits and it is found that decay in the growth of unstable Jeans mode is larger under the kinetic limits than the hydrodynamic limits. The results are discussed for the understanding of formation of dense degenerate dwarf star through gravitational collapsing which is assumed to be strongly coupled dusty quantum fluid where the strongly coupled dust provides inertia and Fermi degenerate electron and ions provide quantum statistical effects.     

Studies on some properties of coronal mass ejections based on angular width

The paper investigates the effects of thermal conductivity and non-uniform magnetic field on the gravitational instability of a non-uniformly rotating infinitely extending axisymmetric cylinder in a homogeneous heat conducting medium. The non-uniform rotation and magnetic field are supposed to act along θ and z directions of the cylinder. It is found that the gravitational instability of this general problem is determined by the same criterion as obtained by Dhiman and Dadwal (Astrophys. Space Sci. 325(2):195–200, 2010) for the self-gravitating isothermal medium in the presence of non-uniform rotation and magnetic field with the only difference that adiabatic sound velocity is now replaced by the isothermal sound velocity. It is found that the thermal conductivity has stabilizing effect on the onset of gravitational instability. Further, the stabilizing/destabilizing effect of the non-uniform magnetic field on the gravitational instability of heat conducting medium has been discussed and is illustrated by considering some special forms of the basic magnetic fields.     

On the Jeans Criterion of a Stratified Heat Conducting Gaseous Medium in the Presence of Non-uniform Rotation and Magnetic Field

The problem of self-gravitational instability of an infinite, homogeneous stratified gaseous medium with finite thermal conductivity and infinite electrical conductivity, in the presence of non-uniform rotation and magnetic field in the Chandrasekhar’s frame of reference, is studied. It is found that the magnetic field, whether uniform or non-uniform, has no effect on the Jeans’ criterion for gravitational instability and remains essentially unaffected. However, the thermal conductivity has the usual stabilizing effect on the criterion that the adiabatic sound velocity occurring in the Jeans criterion is replaced by the isothermal sound velocity. Thus, the present analysis extends the results of Chandrasekhar for the case of heat conducting medium and for non-uniform rotation and magnetic field.     

Gravitational instability in isotropic MHD plasma waves

The effect of compressive viscosity, thermal conductivity and radiative heat-loss functions on the gravitational instability of infinitely extended homogeneous MHD plasma has been investigated. By taking in account these parameters we developed the six-order dispersion relation for magnetohydrodynamic (MHD) waves propagating in a homogeneous and isotropic plasma. The general dispersion relation has been developed from set of linearized basic equations and solved analytically to analyse the conditions of instability and instability of self-gravitating plasma embedded in a constant magnetic field. Our result shows that the presence of viscosity and thermal conductivity in a strong magnetic field substantially modifies the fundamental Jeans criterion of gravitational instability.     

Hydromagnetic gravitational instability of an infinite cylinder of a compressible fluid

The gravitational instability of an infinite cylinder of a self-gravitating, perfectly-conducting, compressible fluid subjected to a uniform axial magnetic field is investigated. A generalised dispersion relation describing the stability characteristics of the configuration is given. The gravitational instability of the cylinder is found to be worsened in the presence of the compressibility effects in the fluid.     

Gravitational instability of a rotating partially-ionized plasma carrying a uniform magnetic field with hall effect

The problem of gravitational instability of an infinite homogeneous self-gravitating medium carrying a uniform magnetic field in the presence of Hall effect has been investigated to include the effect due to rotation. The dispersion relation has been obtained. It has been found that the Jeans's criterion for the instability remains unaffected even when the effect due to rotation is considered in the presence of Hall effect carrying a uniform magnetic.     

Magneto-gravitational instability of a fluid through porous medium including finite ion Larmor radius

The magneto-gravitational instability of an infinite, homogenous, and infinitely conducting plasma flowing through a porous medium is studied. The finite ion Larmor radius (FLR) effects and viscosity are also incorporated in the analysis. The prevalent magnetic field is assumed to be uniform and acting in the vertical direction. A general dispersion relation has been obtained from the relevant linearized perturbation equations of the problem. The wave propagation parallel and perpendicular to the direction of the magnetic field have been discussed. It is found that the condition of the instability is determined by the Jeans criterion for a self-gravitating, infinitely conducting, magnetized fluid through a porous medium. Furthermore, for transverse perturbation FLR is found to have stabilizing influence when the medium is considered inviscid.     

Effect of rotation and finite Larmor radius on magneto-gravitational instability of Hall plasma in the presence of suspended particles

The effect of rotation on the self-gravitational instability of an infinite homogeneous magnetized Hall plasma is considered with the inclusion of finite Larmor radius corrections and the effect of suspended particles. A general dispersion relation is obtained from the linearized set of equations. The particular cases of the effect of rotation along and perpendicular to the direction of the magnetic field are considered. The effects of Hall current, finite Larmor radius, and suspended particles on the waves propagated parallel and perpendicular to the uniform magnetic field are investigated along with the uniform rotation of the medium. It is found that in the presence of suspended particles, magnetic field, Hall current, rotation and finite Larmor radius, the Jeans criterion determines the condition of gravitational instability of a gas-particle medium.     

Axisymmetry vs. nonaxisymmetry of a Taylor‐Couette flow with azimuthal magnetic fields

The instability of a supercritical Taylor‐Couette flow of a conducting fluid with resting outer cylinder under the influence of a uniform axial electric current is investigated for magnetic Prandtl number Pm = 1. In the linear theory the critical Reynolds number for axisymmetric perturbations is not influenced by the current‐induced axisymmetric magnetic field but all axisymmetric magnetic perturbations decay. The nonaxisymmetric perturbations with m = 1 are excited even without rotation for large enough Hartmann numbers (“Tayler instability”). For slow rotation their growth rates scale with the Alfvén frequency of the magnetic field but for fast rotation they scale with the rotation rate of the inner cylinder. In the nonlinear regime the ratio of the energy of the magnetic m = 1 modes and the toroidal background field is very low for the non‐rotating Tayler instability but it strongly grows if differential rotation is present. For super‐Alfv´enic rotation the energies in the m = 1 modes of flow and field do not depend on the molecular viscosity, they are almost in equipartition and contain only 1.5 % of the centrifugal energy of the inner cylinder. The geometry of the excited magnetic field pattern is strictly nonaxisymmetric for slow rotation but it is of the mixed‐mode type for fast rotation – contrary to the situation which has been observed at the surface of Ap stars. (© 2015 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Magneto-gravitational instability and suspended particles

The gravitational instability of an infinite homogeneous and infinitely conducting self-gravitating gas-particle medium in the presence of a vertical magnetic field and suspended particles is considered. It is found that in the presence of suspended particles and magnetic field, Jeans' criterion determines the gravitational instability.     

Effect of a helical magnetic field on the stability of a gravitating cylinder

The effect of a helical magnetic field on the stability of an infinitely conducting, inviscid, incompressible and infinitely long self-gravitating cylinder is studied for axisymmetric perturbations. The effect of helicity is also examined.     

Gravitational instability of a rotating plasma

The gravitational instability of an infinite homogeneous self-gravitating rotating plasma in the presence of a uniform vertical magnetic field has been studied to include the FLR effects. It has been found that the Jeans' criterion of instability remains unaffected even if rotation and FLR effects are included. The effect of rotation is to decrease the Larmor radius by an amount-depending upon the wavenumber of perturbation. The particular cases of the effect of FLR and rotation on the waves propagated along and perpendicular to the magnetic field have been discussed.     

Nonaxisymmetric magnetogravitational instability of a streaming fluid cylinder ambient with a tenuous medium pervaded by transverse varying fields

The stability of a self-gravitating streaming fluid cylinder acting upon the electromagnetic force ambient with a tenuous medium of negligible inertia but pervaded by a transverse varying fields, has been developed. The stability criterion is derived, discussed analytically and the results are verified numerically. The cylinder is purely self-gravitating unstable in small axisymmetric domain and stable in all the rest states. modes while the transverse field exterior the cylinder is stabilizing or destabilizing according to restrictions in the asymmetric modes and purely destabilizing in the symmetric one. The streaming has a strong destabilizing influence and that influence is independent of the kind of the perturbation and wavelengths. Both the streaming and the electromagnetic influences increase the gravitational axisymmetric unstable domain and shrink those of stability in the axisymmetric and non-axisymmetric perturbations. Moreover, the stabilizing character of the Lorentz force of some states, is physicaly interpreted, will not be able to suppress the gravitational instability because the gravitational instability of sufficiently long waves will persist.     

Gravitational instability of a composite and rotating plasma in the presence of a variable magnetic field through a porous medium

The gravitational instability of an infinite homogeneous self-gravitating plasma through porous medium is considered to include, separately, the effects due to rotation and collisions between ionized and neutral components. The dispersion relations are obtained in both cases. It is found that the gravitational instability of a composite and rotating plasma in the presence of a variable horizontal magnetic field through porous medium is determined by the Jeans's criterion.     

Suspended particles and the gravitational instability of a rotating plasma

The gravitational instability of an infinite homogeneous self-gravitating and finitely conducting, rotating gas-particle medium, in the presence of a uniform vertical magnetic field, is studied to include finite Larmor radius and suspended particles effects. The particular cases of the effects of rotation, finite conductivity, finite Larmor radius and suspended particles on the waves propagated along and perpendicular to magnetic field have been discussed. Jeans's criterion determines the gravitational instability.     

Modification of the Jeans and Toomre instability criteria for astrophysical fractal objects within nonextensive statistics

Within the formalism of Tsallis nonextensive statistics designed to describe the behavior of anomalous systems, systems with a strong gravitational interaction between their individual parts and the fractal nature of phase space, we have obtained linearized equations for the oscillations of a rigidly rotating disk by taking into account dissipative effects and give a derivation of the dispersion equation in the WKB approximation. Based on the previously derived modified Navier—Stokes hydrodynamic equations (the so-called equations of q-hydrodynamics), we have analyzed the axisymmetric oscillations of an astrophysical, differentially rotating gas—dust cosmic object and obtained modified Jeans and Toomre gravitational instability criteria for disks with a fractal phase-space structure.     

Gravitational instability in the presence of suspended particles and variable magnetic field

The gravitational instability of an infinite homogeneous self-gravitating and infinitely conducting gas-particle medium is considered in the presence of suspended particles and a variable horizontal magnetic field varying in vertical direction. It is found that the Jeans's criterion of instability remains unaffected even if the effects due to suspended particles and variable horizontal magnetic field are included.     

Self-gravitational instability of rotating viscous Hall plasma with arbitrary radiative heat-loss functions and electron inertia

The effects of arbitrary radiative heat-loss functions and Hall current on the self-gravitational instability of a homogeneous, viscous, rotating plasma has been investigated incorporating the effects of finite electrical resistivity, finite electron inertia and thermal conductivity. A general dispersion relation is obtained using the normal mode analysis with the help of relevant linearized perturbation equations of the problem, and a modified Jeans criterion of instability is obtained. The conditions of modified Jeans instabilities and stabilities are discussed in the different cases of our interest. We find that the presence of arbitrary radiative heat-loss functions and thermal conductivity modifies the fundamental Jeans criterion of gravitational instability into a radiative instability criterion. The Hall parameter affects only the longitudinal mode of propagation and it has no effect on the transverse mode of propagation. For longitudinal propagation, it is found that the condition of radiative instability is independent of the magnetic field, Hall parameter, finite electron inertia, finite electrical resistivity, viscosity and rotation; but for the transverse mode of propagation it depends on the finite electrical resistivity, the strength of the magnetic field, and it is independent of rotation, electron inertia and viscosity. From the curves we find that the presence of thermal conductivity, finite electrical resistivity and density-dependent heat-loss function has a destabilizing influence, while viscosity and magnetic field have a stabilizing effect on the growth rate of an instability. The effect of arbitrary heat-loss functions is also studied on the growth rate of a radiative instability.