6.2 Comparisons with observations

Numerous investigators have compared flare observations with various types of submerged poles models. On the whole these investigations have shown that flare-related phenomena such as $Ha$ ribbons, HXR footpoints and radio emission sources occur at sites corresponding, at least approximately, to some of the separatrix traces. Moreover, the separatrices involved in a given flare are those which intersect at a single separator across which reconnection appears to have occurred.

Topological studies using submerged poles models were performed on the oft-studied flares of November 5, 1980, first by Gorbachev and Somov (1989 ) and then by Démoulin et al. (1994 ). Gorbachev and Somov (1989 ) reported that locations of both $Ha$ ribbons from the flare at 22:26 UT corresponded with two separatrix curves from their 4-charge potential field model. (A larger flare at 22:33 UT had almost identical flare ribbon locations). The separatrices involved are the dark dashed curves originating in nulls $A1$ and $B2$ in Figure 18 . These separatrix traces lie very close to the spine curves from the same pair of nulls in Figure 20 .

The association of $Ha$ ribbons with these two separatrices corroborates a general topological theory of two ribbon flares put forth by Gorbachev and Somov (1988 ). As interpreted by this theory, the November 5, 1980 event was powered by reconnection across the $A1$ - $B2$ separator converting $P 3$ - $N 1$ and $P 4$ - $N 2$ field lines into $P 3$ - $N 2$ and $P4$ - $N 1$ field lines. The field lines in the vicinity of this reconnection site map back to the dashed separatrix traces, which are in turn close to the spines of the two nulls at the ends of the separator.

Démoulin et al. (1994 ) argued that the agreement between $Ha$ ribbons and separators of the 4-charge potential model was not good enough to be convincing by itself. They developed the more accurate 18-charge model of AR 2776 shown in Figure 18 . Several of their poles were considerably deeper than those of Gorbachev and Somov (1989 ), resulting in separatrices which were not as close to the projections of spines. (Compare the thick dashed curves to the thin solid ones in each panel of Figure 18 .) Even with this adjustment, however, Démoulin et al. (1994 ) found poor correspondence between the ribbons and the separatrices, in this case near the $N 14$ - $N 17$ spine and the $P 15$ - $P8$ spine. A potential dipole model had almost identical separatrices, but a linear force free field with $- 1 a = - 0.019 Mm$ (a value found by comparison to $Ha$ fibrils) showed superior correspondence. Furthermore, a radio sources observed by VLA and two hard X-ray sources ( $16-30 keV$ ) observed by HXIS were also located along the separatrix traces.

The constant- $a$ model field was topologically equivalent to the potential field but had separatrix traces nearer to the PIL. This led to a better correspondence with flare signatures, but basically upheld the topological interpretation of Gorbachev and Somov (1989 ), although this time through the separator at the $P 8$ / $N 17$ / $P 15$ / $N 17$ junction. The model pointed to the need for non-potential models from numerous submerged sources in order to achieve good geometrical correspondence with observation.

The benefit of more sources had first been established by Mandrini et al. (1991 ) and Mandrini et al. (1993 ) in a topological study of a series of homologous flares in AR 2372 between April 6 and 8, 1980. Vector magnetograms from MSFC were modeled as a potential field from submerged dipoles. While the active region could be crudely modeled using 4-6 submerged dipoles, reasonable correspondence with the locations of $Ha$ kernels required 17, 16 and 18 dipoles for flares on April 6, 7 and 8, respectively. In each case the dipoles could be grouped into a smaller number of families (4-6 families) corresponding to the dipoles of the cruder model. From the numerous separatrices present, only those separating different families were considered as possible sites of reconnection. These separatrices were topologically equivalent to separatrices present in the crude 4-6 dipole model, but the larger number of sources permitted better representation of the magnetic field’s geometry. This more accurate modeling proved critical in producing good correspondence between the separatrices and the observed flare signatures.

Each of the flares studied by Mandrini et al. (1991 ) and Mandrini et al. (1993 ) had five distinct kernels in off-band $Ha$ observations. These were widely separated, but all began and reached their peaks in unison, suggesting a common driver. Mandrini et al. (1991 ) showed that 4 of the 5 kernels lay on top of traces of two separatrices which intersected along a common separator. Moreover, there were four magnetic field lines, one from each of the four domains neighboring the separator, whose footpoints were found within the flare kernels, two footpoints in each kernel. This is still more evidence of magnetic reconnection at a separator causing a flare. All 5 $Ha$ kernels of the flares on April 7 and April 8 were found to lie on separatrix traces; all but one associated with field lines in the vicinity of a common separator (Mandrini et al., 1993 ).

Several other applications of this technique provide still further evidence of the role of separator reconnection in solar flares (Démoulin et al., 1993 ; van Driel-Gesztelyi et al., 1994 ; Bagalá et al., 1995 ; Mandrini et al., 1995 ). When taken as a group these modeling efforts provide very strong evidence of the importance of magnetic field line topology in solar flares.