Characterization of magneto-convection in sunspots

We analyse a sunspot simulation in an effort to understand the origin of convective instabilities giving rise penumbral and umbral distinct regimes. applied criterion from Gough \& Tayler (1966), accounting for stabilising effect vertical magnetic field investigate MURaM simulation. find: (1) highly unstable shallow layer right beneath surface extending all over box which convection is triggered by radiative cooling photosphere; (2) deep core (beneath -5 Mm) stabilised against overturning that underlies region with stable background values permeated slender coupled dots; (3) filamentary below penumbra nearly parallel undulating originate layers. These deep-rooted result vigorous magneto-convection regime characteristic penumbra; (4) downdrafts granulation, penumbra, umbra develop at about 2 km/s, 1 0.1 respectively, indicating granular more than which, turn, close-to-steady umbra; (5) GT outlines both magnetopause peripatopause, highlighting tripartite nature sub-photospheric layers magnetohydrodynamic (MHD) models; and, finally, (6) Jur\v{c}\'ak photospheric counterpart The as diagnostic tool reveals structure regimes umbra, granulation operating realistic MHD simulations.