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 mag-netical field show important differences with respect to those detected in observations or realistic numerical simulations of sunspot umbrae. Aims. In order to elucidate the origin of these discrepancies, here 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 nonmagnetized or weakly magnetized con-vection, 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, reminiscent of the “convectons ” identified in earlier semi-analytic 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 con-vectons dynamically evolve into multiply segmented granular inclusions and back. Conclusions. Our results are in somewhat closer agreement with observed umbral structures than earlier idealized models, as they do reproduce the strong localized, patchy downflows immediately adjacent to the narrow convective columns. Based on recent observa-tions of umbral dots we suggest that the conditions in sunspot umbræ correspond to the newly identified F/S transitional regime. Key words. Sun: sunspots – magnetoconvection – MHD 1