Effect of rotation on the growth rate of magnetogravitational instability of a viscoelastic medium

Abstract

In the present paper, we investigate the effect of rotation on the onset of gravitational collapse and the growth rate of magnetogravitational instability of a finitely electrically conducting viscoelastic medium under both strongly and weakly coupled plasma limits for transverse and longitudinal modes of wave propagation. A general dispersion relation, which is uniformly valid for both the transverse and longitudinal mode of wave propagation, is obtained using the normal mode analysis method. It is observed that the rotation has no effect on the instability criterion which governs the onset of gravitational collapse of the viscoelastic medium in the presence of a magnetic field for either the longitudinal or transverse mode of wave propagation in strongly coupled plasma (SCP) or weakly coupled plasma (WCP). Furthermore, the effects of rotation (Coriolis force), finite electrical resistivity and shear viscosity on the growth rate of Jeans instability in both SCP and WCP for transverse modes of propagation have been numerically calculated and the results obtained are depicted graphically. From these results, we concluded that the rotation reduces the growth rate of Jeans instability.

Jeans instability of a rotating partially ionized and strongly coupled plasma with Hall current

“…Equation (4.10) is the modified version of (16) in Dhiman & Sharma (2014) due to the neutral particles. In the hydrodynamic regime the above dispersion relation simplifies as …”

“…Therefore, looking to the importance of the Hall current and neutral particles in strongly coupled plasma systems, in the present work we have extended the study done by Argal et al. (2014) and Dhiman & Sharma (2014) by incorporating the effects of the Hall current and neutral particles. Argal et al.…”

“…2009). Dhiman & Sharma (2014) have investigated the self-gravitational Jeans instability in a rotating, finitely conducting, viscoelastic medium. The effect of rotation on the self-gravitational instability has been studied by Argal, Tiwari & Sharma (2014) in a strongly coupled plasma system using the GH model.…”

“…Argal et al. (2014) and Dhiman & Sharma (2014) both have taken the direction of rotation along the magnetic field, but in our case we are taking the rotation along and across the direction of magnetic field. Thus, in the present work, we have investigated the Jeans instability of partially ionized strongly coupled plasmas considering rotation, Hall current, viscosity and collision frequency in which we have followed the GH model used by Prajapati & Chhajlani (2013).…”

Propagation of waves in a gravitating and rotating anisotropic heat conducting plasma

“…Chandrasekhar (1961) used collision dominated magnetohydrodynamic (MHD) equations to study the effect of magnetic field and rotation on the gravitational instability and found that both magnetic field and rotation leave the Jeans wave number unaltered. The effect of rotation on the onset of gravitational collapse and the growth rate of magnetorotational instability of a finite electrically conducting viscoelastic medium under both strongly and weakly coupled plasma limits for transverse and longitudinal modes of wave propagation is investigated by Dhiman and Sharma (2014) and found that rotation reduces the growth rate of Jeans instability. It has been shown that the magnetorotational instability plays a crucial role in driving plasma turbulence in accretion disks and is believed to be responsible for angular momentum transport, which solves a long standing puzzle how the materials in the accretion disks fall inward to feed the stars or the black holes in the center (Velikhov, 1959;Chandrasekhar, 1960).…”