Hard X-ray footpoint statistics: spectral indices, fluxes, and positions Pascal Saint-Hilaire 1, Marina Battaglia 2, Jana Kasparova 3, Astrid Veronig 4, Yan Xu 5, Säm Krucker 1, and Robert P. Lin 1 1 University of California, Berkeley (USA), 2 ETH Zürich (Switzerland), 3 University of Glasgow (UK), 4 University of Graz (Austria), 5 Oklahoma State University (USA) Introduction: Footpoint hard X-ray (HXR) emission contain much of the quantitative information that can be gathered about particle acceleration in the solar corona. In this work, we were interested in flares with two footpoints, and the spectral characteristics (photon spectral index  and photon flux at 50 keV F 50 ) of the HXR non-thermal emission from each. Previous work (Krucker et al., 2002; Emslie et al., 2003) have found differences in the spectral indices of flare footpoints. Such differences might be attributable to propagation effects (Fig.1). While previous RHESSI work has concentrated on particular events, we did a statistical survey. While similar statistical surveys have been conducted in the past (e.g. Petrosian et al., 2001), they used instruments with much lesser spectral resolution and coverage. Abstract: We analyzed 34 double-footpoint flares using imaging spectroscopy with hard X-ray (HXR) data from the Ramaty High Energy Solar Spectroscopic Imager (RHESSI). We determined spectral indices, fluxes and positions for each HXR footpoint. The work is still underway: ultimately, the sample will contain about 100 flares. Conclusions (preliminary): -Differences in column density, as an explanation to differences in HXR footpoint spectral indices (Fig. 8 left), do not seem to be supported by the data. -About half of all flares with two footpoints exhibit a spectral difference greater than 0.3 at peak HXR flux times. -Footpoints seem to be able to reach greater separation when they are oriented parallel to the solar equator. -The work is still underway. When all RHESSI flares with similar statistics are incorporated, the sample should contain about 100 flares. DATA: Flares were selected according to the following criteria: -Enough flux above 50 keV to make a RHESSI image -During peak flux in the keV band, 2, and only 2, footpoints are observed Imaging spectroscopy with RHESSI (using CLEAN, and collimators 3-8) is used to obtain spectral indices and HXR fluxes at 50 keV for each footpoint (using OSPEX). For each flare, peak time values have been examined. Accumulation over whole HXR peaks (there can be more than one per flare) has also been done. So far, 34 flares (and 71 HXR peaks) have been analyzed by the team. We expect to reach about 100 when this project is completed.. An “outlier” with  1 -  2 ≈ 1 ! Such a difference in spectral index (already reported earlier, e.g. Petrosian et al., 2001), cannot be easily attributed to propagation effects (cf. Fig. 1). Fig. 1: Using partial thick-target modeling, the emission from each footpoint and from the loop (corona) may be characterized, along the same lines as in Emslie et al. (2003): Particles are accelerated at the blue star (inset). Two identical electron power-law distributions of spectral index  leave the acceleration region, one going left, the other going right, along the loop. The leftward leg has column density N1, the right leg N2. N1 may be different than N2 (here, we took N2=2·N1, as derived by Emslie et al., 2003, for the 2002 July 23 flare). All plots have N1 as their abcissa. Top: Difference between power-law spectral index of each footpoint, measured by fitting the emission above 50 keV. Middle: Fraction of the 50 keV flux present in the footpoints to that emitted in the coronal (loop). Bottom: Footpoint ratio of the 50 keV flux (the harder footpoint always exhibits strongest flux). Clearly, a substantial difference in footpoint spectral indices may be achieved in dense loops, with the harder source having the strongest 50 keV flux. Also, a sizable amount of the 50 keV flux will also be found in the corona, along the loop. Fig. 2: Position of our selected flares on the solar disc. Fig. 3: Relative footpoint positions. Footpoint separation seem to have a tendency of being greater when the footpoints are oriented parallel to the solar equator (see Fig. 4). Fig. 4: Footpoint orientation. 0º corresponds to an east-west orientation (parallel to the solar equator), 90º corresponds to a north-south orientation. Footpoints oriented east-west seem to have greater distance between them than those oriented north- south. No correlation of this effect with solar longitude was observed. The lack of footpoint separation below about 15” is due to observational bias: they would be unresolved and catalogued as single-footpoint flares. Fig. 6: Statistics of spectral index differences. Left: spectral indices of both footpoints were determined at peak time. A gaussian fitting to the data is shown in red. 40% of double footpoint flares seem to exhibit a greater than 0.3 difference in their spectral index. Right: spectral indices were determined for individual HXR peak accumulations. In this case, differences greater than 0.3 in spectral indices should occur 55% of the time. In both plots, the green line represents the expected gaussian distribution, had the spectral differences only been due to noise (error) in the data. Fig. 8: Left: Footpoint flux ratio vs. spectral index difference. No clear correlation can be established. As explained in Fig.1, a correlation was expected if a difference in column density was the origin of the difference in spectral index and flux ratio of the footpoints. Observational bias (dynamic range issues) prevent finding events with large flux ratios and spectral index differences. Right: Footpoint separation vs. spectral index difference. Fig. 8: 6 images: RHESSI images of the 2002 April 10 M8.2 flare, in the different energy bands used for spectroscopy. 2 spectra: spectral fitting of both footpoints, using OSPEX. Non-correlations: -Absence of a clear correlation between spectral index difference and average footpoint spectral index (Fig. 7), flux ratio and footpoint separation (Fig. 8). - No dependence of spectral index difference or flux ratios with solar longitude, solar latitude, total flux, or footpoint separation. -The total flux, as well as the footpoint flux ratio, do not seem to correlate with footpoint separation. Fig. 7: Average footpoint spectral index vs. spectral index difference. No clear correlation could be established. The lack of high-  events is due to observational bias. Fig. 5: Left: Images in different energy bands for the 2003 October 24 02:44 M7.7 flare. Top: Spectral fitting for both footpoints.