Linear Force Free Field Models of Observed Coronal Loops

Although active region magnetic fields have an overall expansion with height, soft X-ray and EUV loops are observed to have nearly constant cross sections. To investigate this apparent discrepancy, we have compared coronal loops observed by TRACE in the 171 A band with corresponding magnetic flux tubes obtained from linear force-free extrapolations (Demoulin et al. 1997) of nearly concurrent MDI magnetograms. The flux tubes were determined using a procedure that varies the force-free parameter alpha and searches for the field line that most closely coincides with the observed loop axis. Once the axis field line is identified, we construct flux tubes from the model field using a variety of assumed footpoint shapes and orientations. Our detailed comparison confirms the mystery of constant loop cross sections. Although the expansion of the extrapolated flux tube as seen projected onto the plane-of-the-sky varies depending on the footpoint shape and orientation, it is always considerably greater than the expansion of the corresponding TRACE loop. Furthermore, the extrapolated flux tubes are often highly asymmetric (with one leg much wider than the other), in stark contast to the TRACE loops. These results imply that the magnetic structure and possibly also the heating of coronal loops are more complex than we currently understand. Extrapolations of observed photospheric fields are very useful, but direct measurement of the coronal field may be necessary to make fundamental progress on this important problem. This work was funded by NASA and the Office of Naval Research.