Nonlinear Evolution of the Magnetothermal Instability in Two Dimensions

In weakly magnetized, dilute plasmas in which thermal conduction along magnetic field lines is important, the usual convective stability criterion is modified. Instead of depending on entropy gradients, instability occurs for small wavenumbers when (∂P/∂z)(∂ lnT/∂z) < 0, which we refer to as the Balbus criterion. We refer to the convective instability that results in this regime as the magnetothermal instability (MTI). We use numerical MHD simulations which include anisotropic electron heat conduction to follow the growth and saturation of the MTI in two-dimensional, plane parallel atmospheres that are unstable according to the Balbus criterion. The linear growth rates measured in the simulations agree with the weak field dispersion relation. We investigate the effect of strong fields and isotropic conduction on the linear properties and nonlinear regime of the MTI. In the nonlinear regime, the instability saturates and convection decays away, when the atmosphere becomes isothermal. Sustained convective turbulence can be driven if there is a fixed temperature difference between the top and bottom edges of the simulation domain, and if isotropic conduction is used to create convectively stable layers that prevent the formation of unresolved, thermal boundary layers. The largest component of the time-averaged heat flux is due to advective motions. These results have implications for a variety of astrophysical systems, such as the temperature profile of hot gas in galaxy clusters, and the structure of radiatively inefficient accretion flows. Subject headings: accretion, accretion disks — convection — hydrodynamics — instabilities — MHD — stars: neutron — turbulence Program in Applied and Computational Mathematics, Princeton University, Princeton, NJ, 08544