ANALYTICAL MODEL FOR FLUTED SUNSPOTS AND A NEW INTERPRETATION OF EVERSHED FLOW AND X-RAY ANEMONES

We present a force-free constant-alpha model for the magnetic field in and above so-called ''fluted'' sunspots. This model is motivated by r ecent high-resolution observations of Title et al. at the Swedish Sola r Observatory in La Palma. They observed that the inclination angle of the magnetic field in the penumbra of sunspots oscillates rapidly wit h azimuth, with a period of about 6 degrees and an amplitude of about 18 degrees. They further find that there is little variation in the ra dial direction and in absolute field strength. The resulting phenomeno n of interlocking high- and low-inclination field lines was called ''f lutedness.'' In our model, the parameters are chosen to reproduce the La Palma magnetograms, and an analytical expression is obtained for th e three-dimensional magnetic field emanating from the sunspot's umbra and penumbra. The model correctly reproduces the azimuthal variation i n inclination angle, as well as the mean constancy of the magnetic fie ld strength, and the appearance of a highly corrugated neutral line on the limb side of off-center sunspots. We find that the ''flutedness'' results in a highly complex topology in a boundary layer extending fr om the photosphere into the chromosphere, while the coronal field is u niform.Title et al. demonstrated that the Evershed flow occurs in regi ons of nearly horizontal magnetic field, and tacitly assumed, as is do ne in most of the literature, that the dark filaments in which the flo w is observed form individual magnetic flux tubes. Our magnetic field solution suggests that the regions of nearly horizontal field at the p hotospheric boundary may not form individual magnetic flux tubes, but rather a series of short horizontal loops bridging a neutral line that is stretched in the radial direction along the penumbra, up to the ou ter penumbral boundary. Hence, the Evershed flow could not be a simple siphon flow in the radial direction, but would consist of phase-coord inated flows along the many short loops bridging the neutral line. How ever, the assumption of a force-free field breaks down in this region of the atmosphere, and the topology suggested by it may not materializ e in reality. We further demonstrate that there are large variations i n the photospheric cross sections of coronal loops, due to the complex ity of the field near their photospheric footpoints. Under the assumpt ion of constant energy input per unit surface area into these loops, t he variation in cross section is qualitatively consistent with the var iation in X-ray brightness of loops in penumbral ''anemones'' observed by Yohkoh.