The Umbral-penumbral Boundary in Sunspots in the Context of Magnetoconvection

Jurcak et al. have reported that, in a sample of more than 100 umbral cores in sunspots, the umbral-penumbral boundary (UPB) is characterized by a remarkably narrowly defined numerical value (1867 G) of the vertical component of the magnetic field. Gough & Tayler, in their study of magnetoconvection, showed that the onset of convection in the presence of a magnetic field is controlled by a parameter δ, which also depends on the vertical component of the field. Combining the Jurcak et al. result with various empirical models of sunspots leads us to propose the following hypothesis: the UPB occurs where the vertical field is strong enough to increase the effective adiabatic temperature gradient by ≥100% over its non-magnetic value.