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&

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

Perturbations of eigenvalues embedded at threshold: one, two and three dimensional solvable models

We examine perturbations of eigenvalues and resonances for a class of multi-channel quantum mechanical model-Hamiltonians describing a particle interacting with a localized spin in dimension $d=1,2,3$. We consider unperturbed Hamiltonians showing eigenvalues and resonances at the threshold of the continuous spectrum and we analyze the effect of various type of perturbations on the spectral singularities. We provide algorithms to obtain convergent series expansions for the coordinates of the singularities.Comment: 20 page

A broadband FFT spectrometer for radio and millimeter astronomy

The core architecture, tests in the lab and first results of a Fast Fourier Transform (FFT) spectrometer are described. It is based on a commercially available fast digital sampler (AC240) with an on-board Field Programmable Gate Array (FPGA). The spectrometer works continuously and has a remarkable total bandwidth of 1 GHz, resolved into 16384 channels. The data is sampled with 8 bits, yielding a dynamic range of 48 dB. An Allan time of more than 2000 s and an SFDR of 37 dB were measured. First light observations with the KOSMA telescope show a perfect spectrum without internal or external spurious signals.Comment: Astronomy and Astrophysics, in pres

Hard X-ray footpoint sizes and positions as diagnostics of flare accelerated energetic electrons in the low solar atmosphere

The hard X-ray (HXR) emission in solar flares comes almost exclusively from a very small part of the flaring region, the footpoints of magnetic loops. Using RHESSI observations of solar flare footpoints, we determine the radial positions and sizes of footpoints as a function of energy in six near-limb events to investigate the transport of flare accelerated electrons and the properties of the chromosphere. HXR visibility forward fitting allows to find the positions/heights and the sizes of HXR footpoints along and perpendicular to the magnetic field of the flaring loop at different energies in the HXR range. We show that in half of the analyzed events, a clear trend of decreasing height of the sources with energy is found. Assuming collisional thick-target transport, HXR sources are located between 600 and 1200 km above the photosphere for photon energies between 120 and 25 keV respectively. In the other events, the position as a function of energy is constant within the uncertainties. The vertical sizes (along the path of electron propagation) range from 1.3 to 8 arcseconds which is up to a factor 4 larger than predicted by the thick-target model even in events where the positions/heights of HXR sources are consistent with the collisional thick-target model. Magnetic mirroring, collisional pitch angle scattering and X-ray albedo are discussed as potential explanations of the findings.Comment: 10 pages, 8 figures, accepted for publication in Ap

The spectral evolution of impulsive solar X-ray flares

The time evolution of the spectral index and the non-thermal flux in 24 impulsive solar hard X-ray flares of GOES class M was studied in RHESSI observations. The high spectral resolution allows for a clean separation of thermal and non-thermal components in the 10-30 keV range, where most of the non-thermal photons are emitted. Spectral index and flux can thus be determined with much better accuracy than before. The spectral soft-hard-soft behavior in rise-peak-decay phases is discovered not only in the general flare development, but even more pronounced in subpeaks. An empirically found power-law dependence between the spectral index and the normalization of the non-thermal flux holds during the rise and decay phases of the emission peaks. It is still present in the combined set of all flares. We find an asymmetry in this dependence between rise and decay phases of the non-thermal emission. There is no delay between flux peak and spectral index minimum. The soft-hard-soft behavior appears to be an intrinsic signature of the elementary electron acceleration process.Comment: 10 pages, 7 figures. Accepted for publication by A&

X-Ray Polarization of Solar Flares Measured with Rhessi

The degree of linear polarization in solar flares has not yet been precisely determined despite multiple attempts to measure it with different missions. The high energy range, in particular, has very rarely been explored, due to its greater instrumental difficulties. We approached the subject using the Reuven Ramaty High Energy Spectroscopic Imager (RHESSI) satellite to study six X-class and 1 M-class flares in the energy range between 100 and 350 keV. Using RHESSI as a polarimeter requires the application of strict cuts to the event list in order to extract those photons that are Compton scattered between two detectors. Our measurements show polarization values between 2 and 54%, with errors ranging from 10 to 26% in 1σ level. In view of the large uncertainties in both the magnitude and direction of the polarization vector, the results can only reject source models with extreme propertie

A Physicist's Proof of the Lagrange-Good Multivariable Inversion Formula

We provide yet another proof of the classical Lagrange-Good multivariable inversion formula using techniques of quantum field theory.Comment: 9 pages, 3 diagram