Modelling photospheric magnetoconvection

The increasing power of computers makes it possible to model the non-linear interaction between magnetic fields and convection at the surfaces of sola r-type stars in ever greater detail. We present the results of idealized nu merical experiments on two-dimensional magnetoconvection in a fully compres sible perfect gas. We first vary the aspect ratio lambda of the computation al box and show that the system runs through a sequence of convective patte rns, and that it is only for a sufficiently wide hox (lambda greater than o r equal to 6) that the flow becomes insensitive to further increases in lam bda. Next, setting lambda = 6, we decrease the field strength from a value strong enough to halt convection and find transitions to small-scale steady convection, next to spatially modulated oscillations (first periodic, then chaotic) and then to a new regime of Aux separation, with regions of stron g field (where convection is almost completely suppressed) separated by bro ad convective plumes. We also explore the effects of altering the boundary conditions and show that this sequence of transitions is robust. Finally, w e relate these model calculations to recent high-resolution observations of solar magnetoconvection, in plage regions as well as in light bridges and the umbrae of sunspots.