Eduard P. Kontar

Implications of X-Ray Observations for Electron Acceleration and Propagation in Solar Flares

High-energy X-rays and γ-rays from solar flares were discovered just over fifty years ago. Since that time, the standard for the interpretation of spatially integrated flare X-ray spectra at energies above several tens of keV has been the collisional thick-target model. After the launch of the Reuven Ramaty High Energy Solar Spectroscopic Imager (RHESSI) in early 2002, X-ray spectra and images have been of sufficient quality to allow a greater focus on the energetic electrons responsible for the X-ray emission, including their origin and their interactions with the flare plasma and magnetic field. The result has been new insights into the flaring process, as well as more quantitative models for both electron acceleration and propagation, and for the flare environment with which the electrons interact. In this article we review our current understanding of electron acceleration, energy loss, and propagation in flares. Implications of these new results for the collisional thick-target model, for general flare models, and for future flare studies are discussed.

Differential emission measures from the regularized inversion of Hinode and SDO data

Aims. To demonstrate the capabilities of regularized inversion to recover differential emission measures (DEMs) from multiwavelength observations provided by telescopes such as Hinode and SDO. Methods. We develop and apply an enhanced regularization algorithm, used in RHESSI X-ray spectral analysis, to constrain the ill-posed inverse problem that is determining the DEM from solar observations. We demonstrate this computationally fast technique applied to a range of DEM models simulating broadband imaging data from SDO/AIA and high resolution line spectra from Hinode/EIS, as well as actual active region observations with Hinode/EIS and XRT. As this regularization method naturally provides both vertical and horizontal (temperature resolution) error bars we are able to test the role of uncertainties in the data and response functions. Results. The regularization method is able to successfully recover the DEM from simulated data of a variety of model DEMs (single Gaussian, multiple Gaussians and CHIANTI DEM models). It is able to do this, at best, to over four orders of magnitude in DEM space but typically over two orders of magnitude from peak emission. The combination of horizontal and vertical error bars and the regularized solution matrix allows us to easily determine the accuracy and robustness of the regularized DEM. We find that the typical range for the horizontal errors is ΔlogT ≈ 0.1−0.5 and this is dependent on the observed signal to noise, uncertainty in the response functions as well as the source model and temperature. With Hinode/EIS an uncertainty of 20% greatly broadens the regularized DEMs for both Gaussian and CHIANTI models although information about the underlying DEMs is still recoverable. When applied to real active region observations with Hinode/EIS and XRT the regularization method is able to recover a DEM similar to that found via a MCMC method but in considerably less computational time. Conclusions. Regularized inversion quickly determines the DEM from solar observations and provides reliable error estimates (both horizontal and vertical) which allows the temperature spread of coronal plasma to be robustly quantified.

Recent Advances in Understanding Particle Acceleration Processes in Solar Flares

We review basic theoretical concepts in particle acceleration, with particular emphasis on processes likely to occur in regions of magnetic reconnection. Several new developments are discussed, including detailed studies of reconnection in three-dimensional magnetic field configurations (e.g., current sheets, collapsing traps, separatrix regions) and stochastic acceleration in a turbulent environment. Fluid, test-particle, and particle-in-cell approaches are used and results compared. While these studies show considerable promise in accounting for the various observational manifestations of solar flares, they are limited by a number of factors, mostly relating to available computational power. Not the least of these issues is the need to explicitly incorporate the electrodynamic feedback of the accelerated particles themselves on the environment in which they are accelerated. A brief prognosis for future advancement is offered.

Deducing Electron Properties from Hard X-Ray Observations

X-radiation from energetic electrons is the prime diagnostic of flare-accelerated electrons. The observed X-ray flux (and polarization state) is fundamentally a convolution of the cross-section for the hard X-ray emission process(es) in question with the electron distribution function, which is in turn a function of energy, direction, spatial location and time. To address the problems of particle propagation and acceleration one needs to infer as much information as possible on this electron distribution function, through a deconvolution of this fundamental relationship. This review presents recent progress toward this goal using spectroscopic, imaging and polarization measurements, primarily from the Reuven Ramaty High Energy Solar Spectroscopic Imager (RHESSI). Previous conclusions regarding the energy, angular (pitch angle) and spatial distributions of energetic electrons in solar flares are critically reviewed. We discuss the role and the observational evidence of several radiation processes: free-free electron-ion, free-free electron-electron, free-bound electron-ion, photoelectric absorption and Compton backscatter (albedo), using both spectroscopic and imaging techniques. This unprecedented quality of data allows for the first time inference of the angular distributions of the X-ray-emitting electrons and improved model-independent inference of electron energy spectra and emission measures of thermal plasma. Moreover, imaging spectroscopy has revealed hitherto unknown details of solar flare morphology and detailed spectroscopy of coronal, footpoint and extended sources in flaring regions. Additional attempts to measure hard X-ray polarization were not sufficient to put constraints on the degree of anisotropy of electrons, but point to the importance of obtaining good quality polarization data in the future.

The Determination and Use of Mean Electron Flux Spectra in Solar Flares

Hard X-ray spectra in solar flares provide information on electron acceleration and propagation processes. We here point out that the inference of these processes involves two distinct steps: (1) the model- independent deconvolution of the hard X-ray spectrum to obtain the effective mean electron spectrum in the source and ¯ F(E) (2) the model-dependent interpretation of this mean spectrum in terms of physical processes operating in that source. Thus, the mean electron spectrum is a natural “middle ground” on which to compare the predictions of models with observations, and we urge the presentation of results, both from analysis of photon spectra and from modeling of candidate physical processes, in the form of spectra. We consider the constraints that various ¯ F(E) source models impose on , and we present explicit forms for an illustrative corresponding to the ¯¯ F(E) F(E) injection of a power-law spectrum of electrons into a thick target with a nonuniform ionization level. Subject heading: Sun: flares

Local re-acceleration and a modified thick target model of solar flare electrons

Context. The collisional thick target model (CTTM) of solar hard X-ray (HXR) bursts has become an almost “standard model” of flare impulsive phase energy transport and radiation. However, it faces various problems in the light of recent data, particularly the high electron beam density and anisotropy it involves. Aims. We consider how photon yield per electron can be increased, and hence fast electron beam intensity requirements reduced, by local re-acceleration of fast electrons throughout the HXR source itself, after injection. Methods. We show parametrically that, if net re-acceleration rates due to e.g. waves or local current sheet electric (E) fields are a significant fraction of collisional loss rates, electron lifetimes, and hence the net radiative HXR output per electron can be substantially increased over the CTTM values. In this local re-acceleration thick target model (LRTTM) fast electron number requirements and anisotropy are thus reduced. One specific possible scenario involving such re-acceleration is discussed, viz, a current sheet cascade (CSC) in a randomly stressed magnetic loop. Results. Combined MHD and test particle simulations show that local E fields in CSCs can efficiently accelerate electrons in the corona and and re-accelerate them after injection into the chromosphere. In this HXR source scenario, rapid synchronisation and variability of impulsive footpoint emissions can still occur since primary electron acceleration is in the high Alfven speed corona with fast re-acceleration in chromospheric CSCs. It is also consistent with the energy-dependent time-of-flight delays in HXR features. Conclusions. Including electron re-acceleration in the HXR source allows an LRTTM modification of the CTTM in which beam density and anisotropy are much reduced, and alleviates theoretical problems with the CTTM, while making it more compatible with radio and interplanetary electron numbers. The LRTTM is, however, different in some respects such as spatial distribution of atmospheric heating by fast electrons.

RHESSI Hard X-Ray Imaging Spectroscopy of the Large Gamma-Ray Flare of 2002 July 23

We present Reuven Ramaty High Energy Solar Spectroscopic Imager (RHESSI) hard X-ray images in different energy bands for the large X-class flare of 2002 July 23; these images are used to construct spatially resolved hard X-ray spectra for each of four prominent features: a bright, soft source high in the corona, two localized, hard footpoints in opposite polarity magnetic regions that show highly correlated flux and spectral variations in time, and a third footpoint bounded by the other three sources. The power-law spectral indices of the two correlated footpoints differ by ~0.3-0.4, which may be the result of differing column densities from the electron source.

Compton backscattered and primary X-rays from solar flares: angle dependent Green's function correction for photospheric albedo

The observed hard X-ray (HXR) flux spectrum

Nonlinear development of electron-beam-driven weak turbulence in an inhomogeneous plasma

I(\epsilon)

Regularized electron flux spectra in the 2002 July 23 solar flare

from solar flares is a combination of primary bremsstrahlung photons