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

Abstract

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 nonuniform/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.

On the Magnetogravitational Instability of a Ferromagnetic Dust Cloud in the Presence of Nonuniform Rotation

“…The inequality (54) implies that the Bel and Schatzman criterion determines the gravitational instability of this general problem, thus we can conclude that the ferromagnetism in the presence of magnetic field has no effect on the gravitational instability on the self-gravitating cloud. Comparing this result with result obtained by Dhiman and Dadwal [10] for the gravitational instability of a homogeneous gaseous medium in the presence of nonuniform magnetic field for nonferromagnetic case, it appears that the effect of magnetic field on the criterion for instability has been marginalized by the magnetic polarizability of ferrofluid. Further, from inequality (54) for ω = 0, we can deduce that gravitational instability is governed by the Jeans criterion, in the absence of nonuniform rotation.…”

“…The cylinder is assumed to be rotating about its axis (z-axis) with nonuniform angular velocity ω. The propagation of wave is taken along the radial direction "r" Following Dhiman and Dadwal [10], the basic equations (1)-(4), (7) and (9) …”

“…Bel and Schatzman [9] studied the effect of nonuniform rotation on the onset of gravitational instability and obtained a modified expression for the Jeans criterion, which is now known as the Bel and Schatzman criterion. Recently, Dhiman and Dadwal [10,11] also studied the simultaneous effect of nonuniform magnetic field and rotation on the gravitational instability of gaseous medium and obtained some general qualitative results.…”

“…Our aim here is to investigate the gravitational instability of an infinite axisymmetric cylinder of a homogenous nonuniformly rotating medium containing the ferromagnetic dust particles in the presence of nonuniform magnetic field. The mathematical analysis followed in this paper is precisely the same as that of [9,10]. Since the system of linearized perturbation equation governing the problem contains variable coefficients, the sufficient condition for GI is derived using the local instability approach as adopted in [9].…”

“…It is found that Bel and Schatzman criterion determines the gravitational instability of this general problem. Thus, it appears that the effect of non-uniform magnetic field on the gravitational instability as discussed by (Dhiman and Dadwal, 2010) is marginalized by the magnetic polarizability of ferrofluid. …”