Fully convective magneto-rotational turbulence in large aspect-ratio shearing boxes

We present a numerical study of turbulence and dynamo action in stratified shearing boxes with both finite and zero net magnetic flux. We assume that the fluid obeys the perfect gas law and has finite thermal diffusivity. The latter is chosen to be small enough so that vigorous convective states develop. The properties of these convective solutions are analyzed as the aspect ratio of the computational domain is varied and as the value of the mean field is increased. For the cases with zero net flux, we find that a well-defined converged state is obtained for large enough aspect ratios. In the converged state, the dynamo can be extremely efficient and can generate substantial toroidal flux. We identify solutions in which the toroidal field is mostly symmetric about the mid-plane and solutions in which it is mostly anti-symmetric. The symmetric solutions are found to be more efficient at transporting angular momentum and can give rise to a luminosity that is up to an order of magnitude larger than the corresponding value for the anti-symmetric states. In the cases with a finite net flux, the system appears to spend most of the time in the symmetric states.