Quantitative analysis of hard X-ray ‘footpoint’ flares observed by the Solar Maximum Mission

We describe the instrumental corrections which have to be incorporated for reliable correction and deconvolution of images obtained in the 16–22 keV and 22–30 keV energy bands of the Hard X-Ray Imaging Spectrometer (HXIS) aboard the Solar Maximum Mission (SMM). These corrections include amplifier gain and collimator hole size variations across the field of view, amplifier/filter efficiency, variation in effective collimator hole size and angular response with photon energy, dead-time, and hard X-ray plate transmission. We also emphasise the substantial Poisson noise in these energy bands, and describe the maximum entropy deconvolution/correction routine we have developed to establish the spatial structure which can be reliably inferred from HXIS data.

Next we discuss the results of application of our routine to the three impulsive flare phases reported by Duijveman et al. (1982) as exhibiting hard X-ray ‘footpoints’, namely 1980, April 10, May 21, and November 5. Our main conclusions are:

1. (1)

   Maximum entropy smoothing and Poisson noise data perturbations do not remove the main footpoint features in 16–30 keV nor change their basic morphology. However the results emphasise the asymmetry in footpoint size in the May 21 flare and confirm its possible presence in April 10. They also reveal the 3rd weak distant footpoint in the May 21 flare at an earlier time than found by Duijveman et al.

When the 16–22 and 22–30 keV bands are analysed separately, however, it is found that the footpoints are much less visible above noise in the harder band - i.e. the footpoint spectra are steep. In the April 10 and November 5 flares they are steeper than either the spectrum of intervening pixels or the spectrum at higher energies measured for the whole flare by the SMM Hard X-Ray Burst Spectrometer (HXRBS).

1. (2)

   The footpoint contrast with surroundings is less than found by Duijveman et al., despite image deconvolution, because of the maximum entropy smoothing of noise.

2. (3)

   The 16–30keV HXIS footpoint fluxes in the three flares are respectively 28%, 17%, and 15% of the simultaneous HXRBS flare power-law spectrum extrapolated into this energy range.

3. (4)

   Where Poisson noise is taken into account we find, by cross-correlating pixel count rates, that footpoint synchronism was either not provable at all, or substantially less close than reported by Duijveman et al.

Next we considered the implications of these results for models of the footpoint emission. Contrary to Duijveman et al. we do not consider the HXIS ‘footpoint’ data as supporting a conventional thick target beam interpretation since:

1. (A)

   The footpoint photon (and electron) fluxes are much less than expected from HXRBS extrapolation. This result casts doubt on recent models of chromospheric heating by electron beams which usually assume all of the HXRBS emission to come from HXIS footpoints.

2. (B)

   The footpoint spectra for the April 10 and November 5 flares are much softer than the HXRBS spectrum and than the spectrum of intervening pixels, contrary to thick target predictions.

3. (C)

   Contrary to Duijveman et al. footpoint synchronism does not demand an unreasonable Alfvén speed and so does not require non-thermal particles.

In spite of these objections we also re-considered the constraints placed on the acceleration site conditions in a beam interpretation by return current stability and footpoint contrast in the summed 16–30 keV range. Using the smoothed maximum entropy contrast and taking explicit account of coronal thermal emission, we find maximum densities somewhat larger than Duijveman et al. estimated, and much higher maximum values of T _e /T _i .

Regarding thermal interpretations we found:

1. (a)

   Models involving continuous production of short-lived hot kernels in the arch top with Maxwellian tail electrons escaping to the footpoints could explain the 16–30 keV contrast with a rather higher energetic efficiency than a pure beam model. However, whatever the temperature distribution of hot kernel production, the model predicts footpoints harder than the arch summit, contrary to HXIS data.

2. (b)

   A model with hot kernels produced in one limb of an arch can explain the asymmetry in footpoint size observed in May 21, and probably April 10, and is energetically even more efficient than (a) but is also inconsistent with the spectral data.

3. (c)

   Finally we point out that HXIS footpoint data may be consistent with a purely geometric interpretation in an almost uniform arch filled with hot plasma.