Saturation of the Magnetothermal Instability in Three Dimensions

In dilute astrophysical plasmas, thermal conduction is primarily alongmagnetic field lines, and therefore highly anisotropic. As a result, the usualconvective stability criterion is modified from a condition on entropy to acondition on temperature. For small magnetic fields or small wavenumbers,instability occurs in any atmosphere where the temperature and pressuregradients point in the same direction. We refer to the resulting convectiveinstability as the magnetothermal instability (MTI). We present fullythree-dimensional simulations of the MTI and show that saturation results in anatmosphere with different vertical structure, dependent upon the boundaryconditions. When the temperature at the boundary of the unstable layer isallowed to vary, the temperature gradient relaxes until the unstable region isalmost isothermal. When the temperature at the boundary of the unstable regionis fixed, the magnetic field is reoriented to an almost vertical geometry as aresult of buoyant motions. This case exhibits more vigorous turbulence. In bothcases the resulting saturated heat flux is almost one-half of the valueexpected if the conduction were purely isotropic. The action of the MTI resultsin dynamical processes that lead to significant transport perpendicular to theinitial direction of the magnetic field. The resulting magnetoconvection inboth cases amplifies the magnetic field until it is almost in equipartitionwith sustained subsonic turbulence. These results are relevant to understandingmeasurements of the temperature profiles of the intracluster medium of clustersof galaxies as well as the structure of radiatively inefficient accretionflows.