The Stability of Weakly Collisional Plasmas With Thermal and Composition Gradients

Abstract

Over the last decade, substantial efforts have been devoted to understanding the stability properties, transport phenomena, and long-term evolution of weakly collisional, magnetized plasmas which are stratified in temperature. The insights gained via these studies have led to a significant improvement of our understanding of the processes that determine the physical evolution and observational properties of the intracluster medium (ICM) permeating galaxy clusters. These studies have been carried out under the assumption that the ICM is a homogeneous medium. This, however, might not be a good approximation if heavy elements are able to sediment in the inner region of the galaxy cluster. Motivated by the need to obtain a more complete picture of the dynamical properties of the ICM, we analyze the stability of a weakly collisional, magnetized plane-parallel atmosphere which is stratified in both temperature and composition. This allows us to discuss for the first time the dynamics of weakly collisional environments where heat conduction, momentum transport, and ion-diffusion are anisotropic with respect to the direction of the magnetic field. We show that, depending on the relative signs and magnitudes of the gradients in the temperature and the mean molecular weight, the plasma can be subject to a wide variety of unstable modes which include modifications to the magnetothermal instability (MTI), the heat-flux-driven buoyancy instability (HBI), and overstable gravity modes previously studied in homogeneous media. We also find that there are new modes which are driven by heat conduction and particle diffusion. We discuss the astrophysical implications of our findings for a representative galaxy cluster where helium has sedimented. Our findings suggest that the core insulation that results from the magnetic field configurations that arise as a natural consequence of the HBI, which would be MTI stable in a homogeneous medium, could be alleviated if the mean molecular weight gradient is steep enough, i.e., (∇µ)/µ > (∇T )/T . This study constitutes a first step toward understanding the interaction between magnetic turbulence and the diffusion of heavy elements, and its consequences for the long-term evolution and observational signatures of the ICM in galaxy clusters.

Effect of composition gradient on magnetothermal instability modified by shear and rotation

“…These values indicate, at least for some typical ICM, the instability due to the compositional gradient may be comparable to that due to the unmodified MTI (see also Fig. 5 of Pessah & Chakraborty (2013)).…”

“…Earlier investigations into the effect of the concentration gradient induced instabilities on the MTI (Pessah & Chakraborty 2013;Berlok & Pessah 2015, 2016a do not consider the non-trivial background velocity profile of the ICM. As elaborated in the introduction of this paper, the simulations and the observations support the view that ICM plasma, that is in a sheared state, is most generally and realistically characterized by a differential rotation.…”

“…After the linear stability analyses of the composition gradient modified HBI and MTI have been done by Pessah & Chakraborty (2013) using the standard WKB-type approximations, Sadhukhan, Gupta & Chakraborty (2017)-following Gupta et al (2016)have shown how the problem can also be studied by employing the technique (Chandrashekhar 1981) traditionally used to study the convection problem in a Rayleigh-Bénard set-up. The latter technique has some added advantages, e.g., it connects with the boundary conditions usually adopted in the numerical simulations, it helps one to find critical Rayleigh number corresponding to the HBI and the MTI, it facilitates easier analytical estimation of the contribution from the magnetic tension, and it may help us to come up with low dimensional models for convection, like the Lorenz model (Lorenz 1963).…”

“…We ensure, by construction, B 0 ·∇T 0 = 0, and this implies that the system is capable of sustaining the MTI besides the Kelvin-Helmholtz instability (KHI). Also, we set B 0 ·∇µ 0 = 0 (Pessah & Chakraborty 2013). We recall that the KHI (Helmholtz 1868; Thomson 1871; Chandrashekhar 1981) essentially refers to the finite velocity gradient induced instability witnessed in a freely (g = 0) streaming shear flow.…”

“…This concentration gradient can feed the convective instabilities and thus has an effect on both the MTI and the HBI (Pessah & Chakraborty 2013). Further studies on this interplay between the temperature gradient and the concentration gradient has been well explored both numerically and analytically (Berlok & Pessah 2015, 2016aSadhukhan, Gupta & Chakraborty 2017).…”