Thermal instability in molecular clouds, including dust particles, Hall effect and ambipolar diffusion

Abstract

In ideal magnetohydrodynamics (MHD), ions and electrons are both tied to the magnetic field. The Hall effect arises in a plasma when electrons are able to drift with the magnetic field but ions cannot. In this case, the generalized Ohm law is modified, and it affects the ideal MHD equations. In this paper, we study thermal instability in molecular clouds, when it is affected by ambipolar and Hall diffusion and charged dust particles. For this purpose, we include their effects in the equations of weakly ionized molecular clouds. By using a linear perturbation method, we investigate the thermal instability of the system. In this way, we obtain a non-dimensional seventh-degree characteristic equation, which, in the absence of a magnetic field, leads to the prior characteristic equations. From a numerical manipulation of the characteristic equation, we conclude that the thermal instability allows compression along the magnetic field when the effects of both ambipolar and Hall diffusion are considered. Moreover, when the effect of Hall diffusion is increased, there is a compression at θ=π/4, where θ is angle between the magnetic field and the wave vector of perturbation. We also derive some new critical wavelengths that separate the spatial ranges of stability and instability.