Magnetothermal instability with generalized Ohm’s law

Abstract

The problem of thermal instability, having bearing on the formation of astrophysical condensations, is investigated for a hydromagnetic fluid obeying generalized Ohm’s law, both for self-gravitating and nongravitating configurations. Effects of finite Larmor frequency, resistivity, and finite plasma frequency on the stability of the system are studied and the condition of instabilities are derived for a temperature-dependent and density-dependent heat-loss function. It is found that the condition of instability for propagation parallel to the ambient magnetic field is independent of finite resistivity, Hall current, and electron inertia effects and also of the magnetic field strength. For transverse propagation, however, the instability criterion involves the field strength, resistivity, and electron inertia terms. The Hall current is found to modify the growth rates for generally inclined propagation only. Both monotonically unstable and overstable modes of instability arise in the system depending on the dependence of the heat-loss function on the local density and temperature.

Effect of Radiative Heat-Loss Function and Finite Larmor Radius Corrections on Jeans Instability of Viscous Thermally Conducting Self-Gravitating Astrophysical Plasma

“…The above condition of instability is independent of FLR corrections, finite electrical conductivity, magnetic field strength, and viscosity. The above inequality (12) is same as obtained by Bora and Talwar [34], and by Kaothekar and Chhajlani [36]. But Kaothekar and Chhajlani [36] have also considered the effect of permeability in their analysis.…”

“…Thus we conclude that FLR corrections and viscosity have no effect on the condition of instability, but presence of these parameters modifies the growth rate of instability in the present case. Hence these are the new findings in our case than that of Bora and Talwar [34]. Also on comparing our dispersion relation (8) with dispersion relation (20) of Vaghela and Chhajlani [19] we find that two factors are the same, but the third factor is different and gets modified because of radiative terms.…”

“…In absence of FLR corrections and radiative heatloss function the general dispersion relation (7) is identical to Shaikh et al [32] neglecting Hall current in their case. In absence of FLR corrections and viscosity dispersion relation (7) is identical to Bora and Talwar [34] neglecting Hall current and electron inertia in their case. Also in absence of FLR corrections, viscosity and finite conductivity dispersion relation (7) reduces to that obtained by Field [24] for nongravitating medium.…”

“…On multiplying all the components of (8), we get the dispersion relation, which is an equation of degree eight in ω, and it is cumbersome to write such a lengthy equation. If we remove the effect of FLR corrections and viscosity in the above relation, then we recover the relation given by Bora and Talwar [34] excluding Hall current and electron inertia in their case. Hence the above dispersion relation is the modified form of equation (21) of Bora and Talwar [34] due to the inclusion of FLR corrections and viscosity in our case and by neglecting Hall current and electron inertia in their case for longitudinal propagation in dimensional form.…”

“…Aggarwal and Talwar [33] have discussed magnetothermal instability in a rotating gravitating fluid, but they neglect the effect of FLR correction on radiative instability. Bora and Talwar [34] have investigated the magnetothermal instability with finite electrical resistivity and Hall current, but they neglect the effect of FLR corrections and viscosity on radiative instability. Recently ElSayed and Mohamed [35] have discussed the gravitational instability of rotating viscoelastic partially ionized plasma in the presence of oblique magnetic field and Hall current.…”