Spectral Hardening of Large Solar Flares

RHESSI observations are used to quantitatively study the hard X-ray evolution in 5 large solar flares selected for spectral hardening in the course of the event. The X-ray bremsstrahlung emission from non-thermal electrons is characterized by two spectroscopically distinct phases: impulsive and gradual. The impulsive phase usually consists of several emission spikes following a soft-hard-soft spectral pattern, whereas the gradual stage manifests itself as spectral hardening while the flux slowly decreases. Both the soft-hard-soft (impulsive) phase and the hardening (gradual) phase are well described by piecewise linear dependence of the photon spectral index on the logarithm of the hard X-ray flux. The different linear parts of this relation correspond to different rise and decay phases of emission spikes. The temporal evolution of the spectra is compared with the configuration and motion of the hard X-ray sources in RHESSI images. These observations reveal that the two stages of electron acceleration causing these two different behaviors are closely related in space and time. The transition between the impulsive and gradual phase is found to be smooth and progressive rather than abrupt. This suggests that they arise because of a slow change in a common accelerator rather than being caused by two independent and distinct acceleration processes. We propose that the hardening during the decay phase is caused by continuing particle acceleration with longer trapping in the accelerator before escape.Comment: accepted by Ap

The spectral evolution of impulsive solar X-ray flares. II.Comparison of observations with models

We study the evolution of the spectral index and the normalization (flux) of the non-thermal component of the electron spectra observed by RHESSI during 24 solar hard X-ray flares. The quantitative evolution is confronted with the predictions of simple electron acceleration models featuring the soft-hard-soft behaviour. The comparison is general in scope and can be applied to different acceleration models, provided that they make predictions for the behavior of the spectral index as a function of the normalization. A simple stochastic acceleration model yields plausible best-fit model parameters for about 77% of the 141 events consisting of rise and decay phases of individual hard X-ray peaks. However, it implies unphysically high electron acceleration rates and total energies for the others. Other simple acceleration models such as constant rate of accelerated electrons or constant input power have a similar failure rate. The peaks inconsistent with the simple acceleration models have smaller variations in the spectral index. The cases compatible with a simple stochastic model require typically a few times 10^36 electrons accelerated per second at a threshold energy of 18 keV in the rise phases and 24 keV in the decay phases of the flare peaks.Comment: 9 pages, 4 figures, accepted for publication by A&

Relations between concurrent hard X-ray sources in solar flares

Context: Solar flares release a large fraction of their energy into non-thermal electrons, but it is not clear where and how. Bremsstrahlung X-rays are observed from the corona and chromosphere. Aims: We aim to characterize the acceleration process by the coronal source and its leakage toward the footpoints in the chromosphere. The relations between the sources reflect the geometry and constrict the configuration of the flare. Methods: We studied solar flares of GOES class larger than M1 with three or more hard X-ray sources observed simultaneously in the course of the flare. The events were observed with the X-ray satellite RHESSI from February 2002 until July 2005. We used imaging spectroscopy methods to determine the spectral evolution of each source in each event. The images of all of the five events show two sources visible only at high energies (footpoints) and one source only visible at low energies (coronal or looptop source, in two cases situated over the limb). Results: We find soft-hard-soft behavior in both, coronal source and footpoints. The coronal source is nearly always softer than the footpoints. The footpoint spectra differ significantly only in one event out of five. Conclusions: The observations are consistent with acceleration in the coronal source and an intricate connection between the corona and chromosphere.Comment: accepted for publication in A&A, 11 pages, 9 figure

Size dependence of solar X-ray flare properties

Non-thermal and thermal parameters of 85 solar flares of GOES class B1 to M6 (background subtracted classes A1 to M6) have been compared to each other. The hard X-ray flux has been measured by RHESSI and a spectral fitting provided flux and spectral index of the non-thermal emission, as well as temperature and emission measure of the thermal emission. The soft X-ray flux was taken from GOES measurements. We find a linear correlation in a double logarithmic plot between the non-thermal flux and the spectral index. The higher the acceleration rate of a flare, the harder the non-thermal electron distribution. The relation is similar to the one found by a comparison of the same parameters from several sub-peaks of a single flare. Thus small flares behave like small subpeaks of large flares. Thermal flare properties such as temperature, emission measure and the soft X-ray flux also correlate with peak non-thermal flux. A large non-thermal peak flux entails an enhancement in both thermal parameters. The relation between spectral index and the non-thermal flux is an intrinsic feature of the particle acceleration process, depending on flare size. This property affects the reported frequency distribution of flare energies.Comment: Astronomy and Astrophysics, in pres

Do solar decimetric spikes originate in coronal X-ray sources?

In the standard solar flare scenario, a large number of particles are accelerated in the corona. Nonthermal electrons emit both X-rays and radio waves. Thus, correlated signatures of the acceleration process are predicted at both wavelengths, coinciding either close to the footpoints of a magnetic loop or near the coronal X-ray source. We attempt to study the spatial connection between coronal X-ray emission and decimetric radio spikes to determine the site and geometry of the acceleration process. The positions of radio-spike sources and coronal X-ray sources are determined and analyzed in a well-observed limb event. Radio spikes are identified in observations from the Phoenix-2 spectrometer. Data from the Nan\c{c}ay radioheliograph are used to determine the position of the radio spikes. RHESSI images in soft and hard X-ray wavelengths are used to determine the X-ray flare geometry. Those observations are complemented by images from GOES/SXI. We find that decimetric spikes do not originate from coronal X-ray flare sources contrary to previous expectations. However, the observations suggest a causal link between the coronal X-ray source, related to the major energy release site, and simultaneous activity in the higher corona.Comment: 4 pages, 3 figures, A&AL accepte

The wave front set of oscillatory integrals with inhomogeneous phase function

A generalized notion of oscillatory integrals that allows for inhomogeneous phase functions of arbitrary positive order is introduced. The wave front set of the resulting distributions is characterized in a way that generalizes the well-known result for phase functions that are homogeneous of order one.Comment: 12 pages, published versio