  After a dynamically active emergence phase, magnetic flux at the solar
surface soon ceases to show strong signs of the subsurface dynamics of its
parent magnetic structure. This indicates that some kind of disconnection of
the emerged flux from its roots in the deep convection zone should take place.
We propose a mechanism for the dynamical disconnection of the surface flux
based upon the buoyant upflow of plasma along the field lines. Such flows arise
in the upper part of a rising flux loop during the final phases of its buoyant
ascent towards the surface. The combination of the pressure buildup by the
upflow and the cooling of the upper layers of an emerged flux tube by radiative
losses at the surface lead to a progressive weakening of the magnetic field in
several Mm depth. When the field strength has become sufficiently low,
convective motions and the fluting instability disrupt the flux tube into thin,
passively advected flux fragments, thus providing a dynamical disconnection of
the emerged part from its roots. We substantiate this scenario by considering
the quasi-static evolution of a sunspot model under the effects of radiative
cooling, convective energy transport, and pressure buildup by a prescribed
inflow at the bottom of the model. For inflow speeds in the range shown by
simulations of thin flux tubes, we find that the disconnection takes place in a
depth between 2 and 6 Mm for disconnection times up to 3 days.
