Finding Elementary Ribbon Motions
2006-01-01 by Jeongwoo Lee
 
Introduction
In an earlier nugget, Arnold Benz presented a case for elementary flare (2002 Nov. 9 flare) that, in fact, contradicts the classical behavior of the elementary flares. The elementary nature should be seen in the footpoint motions if the standard 2D reconnection model is right. We, however, thought that a footpoint motion, if really associated with the elementary energy release at all, could be very subtle and we need a much higher time cadence to see it. We here look at the sufficiently high time cadence (40 ms) data of H-alpha filtergram at the Big Bear Solar Observatory to find such elementary footpoint motion.
 
Intermittent Footpoint Motion  

The RHESSI maps (2-50 keV) during the 2002 Sep. 9 event show a single X-ray source sitting in a loop-top (Fig. 1a). In this case, its lightcurve is ideal for representing the primary energy release, but the maps could not be used to measure the footpoint motion. We thus looked at the H-alpha blue wing (-1.3A) images obtained at both high cadence and spatial resolution. Not only for the instrumental capability, but the fact that the flare kernel at this wavelength appears shaper than at any other wavelengths is favorable for our purpose. In Figure 1, the grayscale image with black contours is the longitudinal magnetic fields in the active region, and the colored dots represent the centers-of-mass of the H-alpha ribbon at multiple times. The same color scheme is used throughout all figures to denote the time. The points concentrated within a narrow region means that the ribbon is more or less stationary in that region; the ribbon speeds up between the groups of the concentrated points. The right panel shows the ribbon emission in contours at four time intervals in which the ribbon speed reaches local maxima. The ribbons do not really appear as a neat rectangular shape as in any theoretical models,but nonetheless we treat them as if fitting into the standard 2D model.
 
Many studies on flare ribbon motions have adopted the idea that in the 2D geometry, the reconnecting magnetic flux per unit time is simply determined by the ribbon speed and the local field strength (after Forbes and Priest 1984). It is thus possible that the multiple peaks in X-ray lightcurve could entirely result from a highly varying magnetic field in space, in which case the footpoint motion needs not be elementary. In this event, however, the impulsive X-ray flux at 25-50 keV (repeatedly shown as gray histograms in Figures 3 and 4) does not correlate with the local magnetic field (Fig. 3a) but with the ribbon velocity (Fig. 3b). On this basis, we identify this intermittent footpoint motion (Figure 2) with an elementary motion. The elementary motion implies that the hard X-ray multiple peaks are associated with occasional incoming motion of field lines into the X point or, in other words, multiple fragmented reconnections.
Further Insights into the Magnetic Reconnection  

If the so-called X point is a mere "point," in 2D, the ribbon should have been a line and its apparent area is dynamically not a meaningful quantity. Only the incremental ribbon area per unit time or the ribbon speed is. If we instead postulate the X-point as a current sheet (CS) with finite extent, then the instantaneous ribbon area can meaningfully be related to the CS area. In this sense, the correlation of the ribbon area with the X-ray radiation shown in Fig. 4a implies that the fluctuation of the CS area would also be a factor in the magnetic energy release. We finally display the product of the area, velocity, and the square of the magnetic field strength in Fig. 4b. Arguably, this quantity can be related to the Poynting flux integrated over the CS area, which physically means the electromagnetic energy released per second in the CS. The energy release rate defined in this way shows not only a good temporal correlation with the X-ray lightcurve but the amount of magnetic energy comparable to the electron energy derived from the RHESSI spectra.

 
 
 
 
Conclusion
To close, the elementary motion seems to exist in view of the present high-cadence H-alpha observation, while counter examples (motions parallel to the neutral line) are also frequently observed in other events. The agreement between the magnetic energy released and the energy of the X-ray electrons provides another support for the idea that the above footpoint motion is associated with the magnetic reconnection. We consider the time variation of the ribbon speed and its area most consistent with the Pulsating Current Sheet model as the primary energy release mechanism as suggested by Kliem and his colleages in 2000.  

As a cautionary remark we, however, note that the time scale of these fluctuations is of a few tens of seconds, much longer than usually speculated for the theoretical elementary bursts, a few seconds or shorter. It remains to be seen whether any theoretical model results can be re-scaled to the presently observed time scales.