  The conjecture that energy transport in sunspot penumbrae occurs through
convection by an interchange of magnetic flux tubes is used in order to
construct a magnetostatic model for a deep penumbra which is part of a global
sunspot model. The model describes an overall mechanical equilibrium between
the three stratifications: of the umbra, the penumbra, and of the quiet sun,
all of them being treated as stellar like envelopes. Local differences between
the gas pressure in the neighbouring stratifications are balanced by the
magnetic forces confined to two current sheets: the magnetopause and the
peripatopause, whose shapes are determined by the solution of a free boundary
problem. A self consistent coupling between global magnetostatic and thermal
equilibrium is achieved by the assumption of a perfect thermal isolation of the
umbra and a parametrized inflow of the heat into the penumbra. Characteristic
parameters observed in sunspots have been imposed as surface constraints for
the model. Then only models with a total magnetic flux larger than about
3x10^21 Mx turn out to be feasible. Smaller tubes would require more heat flux
than is available in the solar convection zone if they contained an extended
penumbra. The solutions obtained indicate that the penumbra contains 50-60% of
the total magnetic flux of the spot and has a depth comparable with half the
radius of the spot. About 60% of the solar heat flux impinging on the
magnetopause seems to be transmitted into the penumbra and conveyed to the
photosphere by the interchange convection which can be maintained if the
average inclination of the magnetic field exceeds about 30deg. Such a penumbra
forming an extended
