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.     

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.     

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.     

A note on MHD instability of a compressible gravitational streaming fluid cylinder

The fundamental equations are formulated using cylindrical polar coordinates and then solved in the unperturbed state. The perturbation equations are determined, simplified, integrated and the constants of integrations are identified by applying appropriate boundary conditions across the perturbed fluid interface. A cumbersome stability criterion for MHD inviscid compressible self-gravitating streaming fluid cylinder is derived. The magnetic field is stabilizing, the streaming is destabilizing while both of the self-gravitating and compressibility are stabilizing or not according to restrictions and that the gravitational instability of sufficiently long waves will persist. Several approximations are required to obtain Chandrasekhar's and Fermi's dispersion relation (Chandrasekhar and Fermi, 1953).     

Gravitational Instability of Cylindrical Viscoelastic Medium Permeated with Non Uniform Magnetic Field and Rotation

The self-gravitating instability of an infinitely extending axisymmetric cylinder of viscoelastic medium permeated with non uniform magnetic field and rotation is studied for both the strongly coupled plasma (SCP) and weakly coupled plasma (WCP). The non uniform magnetic field and rotation are considered to act along the axial direction of the cylinder. The normal mode method of perturbations is applied to obtain the dispersion relation. The condition for the onset of gravitational instability has been derived from the dispersion relation under both strongly and weakly coupling limits. It is found that the Jeans criterion for gravitational collapse gets modified due to the presence of shear and bulk viscosities for the SCP, however, the magnetic field and rotation whether uniform or non uniform has no effect on the Jeans criterion of an infinitely extending axisymmetric cylinder of a self-gravitating viscoelastic medium.     

Gravitational instability of a heat-conducting plasma

The gravitational instability of an infinite, anisotropic, heat-conducting plasma is studied in this paper. It is found that, for the case of parallel propagation, the inclusion of heat-conduction terms in the fluid equations, in general, leads to overstability of the system, whereas the transverse propagation remains unaffected. We have solved numerically the dispersion relation corresponding to the parallel propagation and find that except for a range of wave numbers, the system is overstable. We also found that in the limit of vanishing zeroth-order heat flux, the condition for gravitational instability is similar to the Jeans's condition for instability for an isotropic plasma.     

The gravitational instability in the dust layer of a protoplanetary disk:: axisymmetric solutions for nonuniform dust density distributions in the direction vertical to the midplane

The gravitational instability in the dust layer of a protoplanetary disk with nonuniform dust density distributions in the direction vertical to the midplane is investigated. The linear analysis of the gravitational instability is performed. The following assumptions are used: (1) One fluid model is adopted, that is, difference of velocities between dust and gas are neglected. (2) The gas is incompressible. (3) Models are axisymmetric with respect to the rotation axis of the disk. Numerical results show that the critical density at the midplane is higher than the one for the uniform dust density distribution by Sekiya (1983, Prog. Theor. Phys. 69, 1116-1130). For the Gaussian dust density distribution, the critical density is 1.3 times higher, although we do not consider this dust density distribution to be realistic because of the shear instability in the dust layer. For the dust density distribution with a constant Richardson number, which is considered to be realized due to the shear instability, the critical density is 2.85 times higher and is independent of the value of the Richardson number. Further, if a constant Richardson number could decrease to the order of 0.001, the gravitational instability would be realized even for the dust to gas surface density ratio with the solar abundance. Our results give a new restriction on planetesimal formation by the gravitational instability.     

Dynamics of gravitational instability excitation in viscoelastic polytropic fluids

The evolutionary excitation dynamics of the gravitational instability in a self-gravitating viscoelastic non-thermal polytropic complex fluid is semi-analytically explored on the astro-scales of space and time. The polytropic equation of state is well validated for the hydrostatic equilibrium established by a perfect heating-cooling balancing in the uni-component complex fluid. We apply a generalized gravitating hydrodynamic model in the concurrent presence of buoyancy, thermal fluctuations, volumetric expansion, and so forth. A normal mode (local) analysis yields a quadratic linear dispersion relation with a unique set of multi-parametric coefficients. The analytical reliability is checked by comparing with the existing reports on purely ideal inviscid nebular fluids and non-ideal viscoelastic fluids in isolation. It is seen that, unlike the normal instability mechanisms, the instability here remains unaffected due to the thermo-mechanical diffusion processes. The stabilizing (destabilizing) and accelerating (decelerating) factors of the instability are illustratively explored. The instability features are judged in the light of both impure non-ideal viscoelastic fluid and pure ideal inviscid nebular fluid scenarios. The relevancy of our exploration in superdense compact viscoelastic astro-objects and their surrounding atmospheres is summarily outlined.     

Gravitational instability of a non-linear magnetic fluid

The problem of gravitational instability of an infinite homogenous fluid has been considered in the presence of a non-vertical magnetic field. A non-linear relation between the magnetic field and the magnetic induction proposed by P.H. Roberts (1981) in the context of neutron stars has been used. The dispersion relations have been obtained. It has been found that Jeans's criterion for instability is unaffected by this non-linear relationship even if the effect due to rotation is considered in the presence of a non-vertical magnetic field.     

The effects of the tidal force on shear instabilities in the dust layer of the solar nebula

The linear analysis of the instability due to vertical shear in the dust layer of the solar nebula is performed. The following assumptions are adopted throughout this paper: (1) The self-gravity of the dust layer is neglected. (2) One fluid model is adopted, where the dust aggregates have the same velocity with the gas due to strong coupling by the drag force. (3) The gas is incompressible. The calculations with both the Coriolis and the tidal forces show that the tidal force has a stabilizing effect. The tidal force causes the radial shear in the disk. This radial shear changes the wave number of the mode which is at first unstable, and the mode is eventually stabilized. Thus the behavior of the mode is divided into two stages: (1) the first growth of the unstable mode which is similar to the results without the tidal force, and (2) the subsequent stabilization due to an increase of the wave number by the radial shear. If the midplane dust/gas density ratio is smaller than 2, the stabilization occurs before the unstable mode grows largely. On the other hand, the mode grows faster by one hundred orders of magnitude, if this ratio is larger than 20. Because the critical density of the gravitational instability is a few hundreds times as large as the gas density, the hydrodynamic instability investigated in this paper grows largely before the onset of the gravitational instability. It is expected that the hydrodynamic instability develops turbulence in the dust layer and the dust aggregates are stirred up to prevent from settling further. The formation of planetesimals through the gravitational instabilities is difficult to occur as long as the dust/gas surface density ratio is equal to that for the solar abundance. On the other hand, the shear instability is suppressed and the planetesimal formation through the gravitational instability may occur, if dust/gas surface density ratio is hundreds times as large as that for the solar abundance.     

The structure of a shock front in atomic hydrogen

We examine the problem of a shock wave propagating in a gravitational field in the presence of pressure and density gradients by attacking the non-linear equations of fluid flow. Our approach is analytical rather than numerical, and we analyze the characteristic equations of a fluid in the presence of gravity with radiative dissipation. Because the radiation field enters the fluid equations in the form of an integral, radiative dissipation may be considered an inhomogeneity which does not affect the characteristic directions. The fluid equations remain hyperbolic and thus are amenable to solution by the standard techniques of gas analysis.We give an equation of path for a shock wave and we enumerate the physical conditions which lead to stability or instability. We find that shock waves are generally unstable in most stellar atmospheres unless they are very weak. The form of the instability is that of a spicule deformation similar to that observed in the upper solar chromosphere.This work was carried out at the Smithsonian-Harvard Astrophysical Observatory and was presented in a thesis to Brandeis University, May 1963.     

Tilted accretion discs in cataclysmic variables: tidal instabilities and superhumps

We investigate the growth of tidal instabilities in accretion discs in a binary star potential, using three-dimensional numerical simulations. As expected from analytic work, the disc is prone to an eccentric instability provided that it is large enough to extend to the 3:1 resonance. The eccentric disc leads to positive superhumps in the light curve. It has been proposed that negative superhumps might arise from a tilted disc, but we find no evidence that the companion gravitational tilt instability can grow fast enough in a fluid disc to create a measurable inclination. The origin of negative superhumps in the light curves of cataclysmic variables remains a puzzle.     

Gravitational instability of a Hall plasma in the presence of suspended particles

The gravitational instability of an infinite homogeneous and infinitely conducting selfgravitating gas particle medium in the presence of suspended particles of a Hall plasma is considered. The particular cases of the effects of Hall currents and suspended particles on the waves propagated along and perpendicular to magnetic field have been discussed. Jeans's criterion determines the gravitational instability.     

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.     

Comment on ‘note on the stability of parallel magnetic fields’

It is shown that the conclusions arrived at regarding the instability of an incompressible fluid cylinder in the presence of the magnetic field and the streaming velocity in a recent communication easily follow from the study of propagation characteristics of Alfvén surface waves along cylindrical plasma columns made earlier.     

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.     

Magnetohydrodynamic oscillation of a gas jet of zero inertia dispersed in a resistive liquid with energy conservation

The dynamical oscillation and instability of a gas cylinder of zero inertia immersed in a resistive liquid has been developed for symmetric perturbations. In the absence of the magnetic field we have used the conservation of energy to study such problem for all symmetric and asymmetric perturbations. In the latter it is found that the temporal amplification is much lower than that of the full fluid jet. The model is capillary stable for all short and long wavelengths in the asymmetric perturbation while in the symmetric disturbances it is stabilizing or not according the perturbed wavelength is shorter than the gas cylinder circumference or not. The resistivity is stabilizing or destabilizing according to restrictions. The electromagnetic body force is stabilizing for all wavelengths in the rotationally-symmetric disturbances. The Lorentz body force, for high magnetic field intensity, could be suppressing the destabilizing character of the present model. This may be due to the fact that the acting magnetic field is uniform and that the fluid is considered to be incompressible.     

The gravitational instability of flow through porous medium for some systems of astrophysical interest

The gravitational instability of flow through porous medium for some hydrodynamical and hydromagnetical systems of astrophysical interest is investigated. The effects of rotation, magnetic field, viscosity and finite electrical conductivity are studied for the gravitational instability through porous medium. The effect of suspended particles on the instability is also considered. It is found that Jean's criterion remains unchanged in the presence of porosity, viscosity, finite conductivity, rotation, magnetic field and suspended particles in the medium.     

Large-Scale Gravitational Instability in the Formation of GMCS

Two models of molecular cloud in disk galaxies are proposed to investigate the formation of giant molecular clouds (GMCs) under the gravitational instability and random collision using PP(Particle–Particle) simulation. Having analysed simulation outputs of the two models and comparing them with observation, we are able to draw some general conclusions, the most significant ones of which are: 1) Similar to results obtained previously, the gravitational instability can make small clouds form large clouds faster than random collision. 2) The differential rotation in gravitational instability model plays a positive role in agglomeration of molecular clouds. This revised version was published online in July 2006 with corrections to the Cover Date.     

Stability of a compressible fluid cylinder ambient with a bounded conducting medium under general varying magnetic fields

The stability of a compressible fluid cylinder pervaded by a longitudinal uniform magnetic field-ambient with a bounded conducting medium of negligible inertia penetrated with general varying vacuum magnetic fields has been developed. The stability criterion describing the stability characteristics of that model is derived and discussed analytically in general terms. The axial fields have always stabilizing influences. The azimuthal vacuum field has a destabilizing effect, however, it becomes minimal if the perturbed and the unperturbed vacuum fields are not orthogonal. The magnetodynamic instability of the fluid jet is modified in the presence of the fluid compressibility. The stabilizing influence due to the latter may be realized more clearly on utilizing the numerical methods for investigating the eigenvalue relation.Several reported works can be recovered as limiting cases with appropriate simplifications.