ISSI Visiting Scientists Programme
Solar flares emit hard X-ray radiation bursts (photon energy ε>~10 keV) which indicate copious amounts of energy among the (mainly) bremsstrahlung emitting electrons causing them. The process of bremsstrahlung (and recombination) hard X-ray emission by energetic electrons is intrinsically inefficient compared to other energy-consuming processes (such as Coulomb heating of ambient particles in the solar atmosphere). So the observed brightness in hard X-rays implies that electrons are accelerated at a rate of up to 1037 electrons s−1 in large events. If such an electron rate were quite beamed it would correspond to a current of some 1018 Amps, spread over an observed flare area of no more than 1018 cm2, possibly much less. Naive application of the Ampere law implies for this a steady-state magnetic field of order 108 Gauss, some five orders of magnitude higher than observed, and corresponding to a magnetic energy of order 1042 ergs, ten orders of magnitude higher than in the electrons themselves. Similarly, since hard X-ray fluxes are observed to rise on a timescale ~10 s, and since the inductance of a flaring loop of some 109 cm in length is ~10 H, application of the Faraday law implies emfs of order 1018 Volts, some fourteen orders of magnitude higher than the energy of the accelerated particles. While some of these difficulties can be eased by invoking a return current, clearly, such simple “cartoon” models are inadequate to describe the true process of electron acceleration in solar flares. In reality these problems are “solved” by the overall electron distribution being close to “isotropic” (very small vector flux) due to near isotropy of the beam itself and or the oppositely directed slow plasma return current that any intense beam automatically generates when injected in a plasma. The return current is created very rapidly by the E fields generated by the initial rise in beam current and charge in the system. However, the overall isotropy has to be very high and it is essential to have observational diagnostics of the beam anisotropy to understand properly the real solar situation. Understanding the processes of electron acceleration and propagation in solar flares, including such large scale electrodynamic issues, is a paramount challenge, addressing which will lead to an increased understanding of particle acceleration in other astrophysical sites as well as on the sun. Nearly all of space science involves remote sensing, the interpretation of physical conditions in a source through analysis of the radiation emitted by that source. High-energy solar physics is no exception; we must learn about the accelerated particles through the radiation they produce, in this case the hard X-ray bremsstrahlung. Now, the form of the observed X-ray radiation spectrum I(ε, r) from a location r (the “data function”) is basically an integral convolution of the electron spectrum F(E, r) at the point r (the “source function”) and the cross-section Q(ε,E) for hard X-ray production by electrons (the “kernel”):
It follows that extraction of scientifically useful information onF(E,r), and its concomitant implications for our understanding of electron acceleration and propagation in flares, requires not only expertise in solar physics, but also in the solution of integral equations such as (1). Since 2005, a group of researchers have held a series of meetings, generously sponsored by ISSI, to study problems related to the inference of F(E,r) from hard X-ray data. They have comprised experts in electron acceleration and propagation in solar flares (Brown, Emslie, Kontar), data analysis (Hurford, Kašparová) and mathematical inversion techniques (Massone, Piana, Prato). The main source of the data is the NASA Ramaty High Energy Solar Spectroscopic Imager (RHESSI) satellite, launched in early 2002 and tasked with determining information on I(ε,r) with unprecedented quality. The satellite continues to produce data of exceptional quality and quantity. Our main previous accomplishments have been the validation and comparison of different regularization methods in the reconstruction of the mean electron spectrum from X-ray data, the study of the infuence of albedo and electron-electron bremsstrahlung contribution on X-ray solar spectroscopy and the formulation of a reconstruction method for the differential emission measure from X-ray spectra in a thermal interpretation of the bremsstrahlung emission process. We also focused on the integration of 2D spatial imaging with 1D high resolution spectroscopy into an imaging-spectroscopy approach. We developed a new method for imaging spectroscopy that involves regularized inversion of the photon visibility spectra (i.e., the twodimensional spatial Fourier transforms of the spectral image) to obtain smoothed (regularized) forms of the corresponding electron visibility spectra. Application of conventional visibility-based imaging algorithms then yields images of the electron flux that vary smoothly with energy. Both spatially-integrated spectra Itot(ε) = ∫ I(ε,r) dr and, for sufficiently intense events, spatially-imaged spectra I(ε;x,y) have been used in our work.
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