RHESSI hard X-ray imaging spectroscopy of extended sources and the physical properties of electron acceleration regions in solar flares

In this study we present the results of a new approach to studying the acceleration and propagation of bremsstrahlung-producing electrons in solar flares. The method involves an analysis of the size of extended solar flare structures as a function of photon energy. Hard X-ray images from 10 M-class limb events, observed by the Reuven Ramaty High Energy Solar Spectroscopic Imager (RHESSI) to have the general form of a single extended source, were analyzed by forward fitting to the source visibilities in each energy band. On average the source sizes σ increased slowly with photon energy ε as σ ∼ ε^1/2. This behavior is consistent neither with the predictions of a single-loop thermal model nor with a model in which nonthermal electrons are injected into a constant-density structure from a compact acceleration region. While a nonuniform density distribution along the flare loop can in principle reconcile the data with a nonthermal collisional model with point-source injection, the resulting density profiles are highly questionable. On the other hand, the data are consistent with a nonthermal collisional model that incorporates an extended acceleration region, perhaps in combination with a localized thermal source. We present best-fit results on the density and length of this acceleration region. To our knowledge, this is the first quantitative empirical analysis of the physical characteristics of electron acceleration regions in solar flares.