Magneto-Thermal Instability In Galaxy Clusters I: Theory and
  Two-Dimensional Simulations
  Determining the origin of turbulence in galaxy clusters, and quantifying its
transport of heat, is an outstanding problem, with implications for our
understanding of their thermodynamic history and structure. As the dilute
plasma of the intracluster medium (ICM) is magnetized, heat and momentum travel
preferentially along magnetic field lines. This anisotropy triggers a class of
buoyancy instabilities that destabilize the ICM, and whose turbulent motions
can augment or impede heat transport. We focus on the magneto-thermal
instability (MTI), which may be active in the periphery of galaxy clusters. We
aim to take a fresh look at the problem and construct a general theory that
explains the MTI saturation mechanism and provides scalings and estimates for
the turbulent kinetic energy, magnetic energy, and heat flux. We simulate MTI
turbulence with a Boussinesq code, SNOOPY, which, in contrast to previous work,
allows us to perform an extensive sampling of the parameter space. In two
dimensions the saturation mechanism involves an inverse cascade carrying
kinetic energy from the short MTI injection scales to larger scales, where it
is arrested by the stable entropy stratification; at a characteristic "buoyancy
scale", the energy is dumped into large-scale g-modes, which subsequently
dissipate. Consequently, the entropy stratification sets an upper limit on the
size and strength of turbulent eddies. Meanwhile, the MTI conveys a substantial
fraction of heat, despite the tangled geometry of the magnetic field. In a
companion paper, these results are extended to three-dimensional flows, and
compared to real cluster observations.
