Structures in compressible magnetoconvection and the nature of umbral dots

Context. Structures seen in idealized numerical experiments on compressible magnetoconvection in an imposed strong vertical magnetic field show important differences from those detected in observations or realistic numerical simulations of sunspot umbrae. Aims. To elucidate the origin of these discrepancies, we present a series of idealized 3D compressible magnetoconvection experiments that differ from previous such experiments in several details, bringing them closer to realistic solar conditions. Methods. An initially vertical magnetic field B0 is imposed on a time snapshot of fully developed solar-like turbulent convection in a layer bounded by a stable layer from above. Upon relaxation to a statistically steady state, the structure of the flow field and magnetic field is examined. Results. Instead of the vigorous granular convection (GRC) well known to take place in magnetized or weakly magnetized convection, for high values of B0 heat is transported by small-scale convection (SSC) in the form of narrow, persistent convective columns consisting of slender upflows accompanied by adjacent downflow patches, which are reminiscent of the “convectons” identified in earlier semianalytic models. For moderate field strengths, flux separation (FXS) is observed: isolated field-free inclusions of GRC are embedded in a strongly magnetized plasma with SSC. Between the SSC and FXS regimes, a transitional regime (F/S) is identified where convectons dynamically evolve into multiply segmented granular inclusions and back. Conclusions. Our results agree in some aspects more closely with observed umbral structures than earlier idealized models, because they do reproduce the strong localized, patchy downflows immediately adjacent to the narrow convective columns. Based on recent observations of umbral dots, we suggest that in some cases the conditions in sunspot umbræ correspond to the newly identified F/S transitional regime