SOLARNET Conference: The Many Scales of the Magnetic Sun

We will review the recent observational results that show the key role played by the vertical component of the magnetic field (B$_\mathrm{ver}$) in the inhibition of convection in the solar photosphere. In sunspots, only regions with B$_\mathrm{ver}$ stronger than a critical value of approximately 1.8 kG (the critical value is dependent on the data used, definition of the umbral boundary, inversion scheme, etc.) are stable against convection and the intensity boundaries of stable umbrae can be equally outlined by this critical B$_\mathrm{ver}$. In regions with B$_\mathrm{ver}$ weaker than the critical value, more vigorous modes of magneto-convection take over. This behavior is observed during the formation of penumbra and light bridges and during the decay of sunspots and pores. We will compare these observations to analyses of sunspots simulations and to theoretical models describing the stability of overturning convection in the presence of magnetic fields and we will discuss the repercussion in the life cycle of magnetic structures.