Reconnection and field line shrinkage in solar flares

We use images of flare loops taken by the Soft X-ray Telescope (SXT) on Yohkoh to estimate the decrease in height that open field lines undergo after they have reconnected to form closed loops. Following previous practice, we refer to this decrease as field line shrinkage and assume that intensity structures trace out the field lines. For this study, we examine two long-duration events near the limb which have flare loops that continually grow with time. The shrinkage is determined by comparing the height of a field line when it lies at the outermost edge of the flare loop system with the height it has later on when it lies at the innermost edge. We find that the field lines shrink by about 20% of their initial height in one flare and by about 32% in the other. These values are within 5% of the shrinkage predicted by a simple model of the reconnecting field which assumes that the field is potential everywhere except for a current sheet extending upward from the top of the loops. Numerical integration of the model density along the line of sight implies that most of the discrepancy between the observations and the theory is due to projection effects which occur when an arcade of loops is viewed at an arbitrary angle. Both flares have bright regions at the top of the loops, but in one flare the lower part of the region is cooler and denser than the rest of the loop, while in the other flare it is not. Consideration of the mapping of the bright regions to the footpoint of the loops implies that the cool region is formed by a thermal instability downstream of a reconnection outflow in the uppermost part of the loop. The absence of a cool, dense region in the other flare may be caused by the fact that it is a very weak event with temperatures and densities too low to trigger a thermal instability.