## 5. ConclusionsWe have presented an expansion scheme that allows us to calculate self-consistent force-free solutions of the magnetohydrostatic equations with the basic properties of fluted sunspot penumbrae. The lowest order of the expansion produces equations which are mathematically equivalent to the equations describing laminated force-free solutions in Cartesian coordinates. The magnetic field then has no toroidal component in the lowest order and the magnetic field strength does not vary with azimuth. The field inclination, however, can have an arbitrary variation with azimuth. In comparison with the force-free model by Martens et al. (1996) the scale height of this variation is generally much larger. We have calculated explicit solutions which have a profile of the magnetic field strength in the plane that exactly matches the profile given by Beckers & Schröter (1969). The field lines emerging from the plane extend across the penumbra in the radial direction and for the maximum inclination angle stay relatively shallow. Our model provides for long, low-lying radial loops that return to the photosphere just beyond the boundary of the penumbra, as is required for the Evershed flow, and confirmed by recent observations of Westendorp-Plaza et al. (1997). © European Southern Observatory (ESO) 1998 Online publication: March 30, 1998 |