The abrupt development of penumbrae in sunspots

A sunspot is distinguished from a pore by having a filamentary penumbra, corresponding to convective motions that carry energy into the spot from the surrounding field-free plasma. A simplified model of energy transport in sunspots is developed in order to model the transition from pores to spots as the magnetic flux is varied. The observed overlap between the radii of large pores and small spots implies that the filamentary convective mode sets in suddenly and rapidly, as in the idealized case where pore solutions lose stability at a bifurcation.