Determining the spatial variation of accelerated electron spectra in solar flares

The RHESSI spacecraft images hard X-ray emission from solar flares with an angular resolution down to $sim$ 2" and an energy resolution of 1 keV. In principle, images in different count energy bands may be combined to derive the hard X-ray spectrum for different features in the flare and hence to determine the variation of the (line-of-sight-integrated) electron spectrum with position in the image. However, images in different count energy bands are each subject to an independent level of statistical noise. Because of the inherent ill-posedness of the count $ ightarrow$ electron spectral inversion problem, this noise is considerably amplified upon spectral inversion to obtain the parent electron spectrum for the feature, to the point where unphysical features can emerge. Imaging information is gathered by RHESSI’s Rotating Modulation Collimator (RMC) imagingsystem. For such an instrument, spatial information is gathered not as a set of spatial images, but rather as a set of (energy-dependent) spatial Fourier components (termed visibilities). We report here on a novel technique which uses these spatial Fourier components in count space to derive, via a regularized spectral inversion process, the corresponding spatial Fourier components for the electron distribution, in such a way that the resulting electron visibilities, and so the images that are constructed from them, vary smoothly with electron energy E. "Stacking" such images then results in smooth, physically plausible, electron spectra for prominent features in the flare. Application of visibility-based analysis techniques has also permitted an assessment of the density and volume of the electron acceleration region, and so the number of particles it contains. This, plus information on the rate of particle acceleration to hard-X-ray-producing energies [obtained directly from the hard X-ray spectrum $I(epsilon)$] allows us to deduce the specific acceleration rate (particles $s^{-1}$ per particle). The values of this key quantity are compared with the predictions of variouselectron acceleration scenarios.