Convective stability in the solar photosphere

We summarise the recent observational results that show the importance of the vertical magnetic field component (Bver) as the crucial parameter to inhibit convection in the solar photosphere. To investigate the physical principle of this observationally found stability criterion, we analyse the MURaM simulations of sunspots. We show that also in the simulations Bver is constant along the umbral boundary. However, the critical value of the Bver is dependent on the top boundary conditions of the simulation domain. In the case of a potential field, the Bver value on the umbral boundary is consistent with observations. The more the magnetic field is forced to be horizontal, the more is the Bver value reduced at the umbral boundary. We further investigate the conditions in the simulation domain with respect to the Gough & Taylor (MNRAS, 1966) convection instability criterion that takes into account the role of Bver. First results suggest that penumbral mode of magneto-convection can occur only in regions where this instability criterion is fulfilled.