Diagnostics of non-thermal distributions in solar flare spectra observed by RESIK and RHESSI

We focus on the non-thermal components of the electron distribution in the keV range and analyse high-energy resolution X-ray spectra detected by RESIK and RHESSI for three solar flares.In the 2-4 keV range we assume that the electron distribution can be modelled by an n-distribution. Using a method of line-intensity ratios, we analyse allowed and satellite lines of Si observed by RESIK and estimate the parameters of this n-distribution. At higher energies we explore RHESSI bremsstrahlung spectra. Adopting a forward-fitting approach and thick-target approximation, we determine the characteristics of injected electron beams. RHESSI non-thermal component associated with the electron beam is correlated well with presence of the non-thermal n-distribution obtained from the RESIK spectra. In addition, such an n-distribution occurs during radio bursts observed in the 0.61-15.4 GHz range. Furthermore, we show that the n-distribution could also explain RHESSI emission below ~5 keV. Therefore, two independent diagnostics methods indicate the flare plasma being affected by the electron beam can have a non-thermal component in the ~2-5 keV range, which is described by the n-distribution well. Finally, spectral line analysis reveals that the n-distribution does not occupy the same location as the thermal component detected by RHESSI at ~10 keV.Comment: 18 pages, 14 figures, 10 table

Collisional and Radiative Processes in Optically Thin Plasmas

Most of our knowledge of the physical processes in distant plasmas is obtained through measurement of the radiation they produce. Here we provide an overview of the main collisional and radiative processes and examples of diagnostics relevant to the microphysical processes in the plasma. Many analyses assume a time-steady plasma with ion populations in equilibrium with the local temperature and Maxwellian distributions of particle velocities, but these assumptions are easily violated in many cases. We consider these departures from equilibrium and possible diagnostics in detail

Diagnostics of the

Aims. The solar transition region satisfies the conditions for appearance of the non-thermal κ-distribution. We aim to prove the occurrence of the non-thermal κ-distribution in the solar transition region and diagnose its parameters. Methods. The intensity ratios of Si ii

The bound-bound and free-free radiative losses for the nonthermal distributions in solar and stellar coronae

Context. The radiative-loss function is an important ingredient in the physics of the solar corona, transition region, and flares. Aims. We investigate the radiative losses due to the bound-bound transitions and bremsstrahlung for nonthermal κ- and n-distributions. Methods. The bound-bound radiative losses are computed by integrating synthetic spectra. An analytical expression is derived for nonthermal bremsstrahlung. The bremsstrahlung is computed numerically using accurate values of the free-free Gaunt factor. Results. We find that the changes in radiative-loss functions due to nonthermal distributions are several times greater than the errors due to the missing contribution of the free-bound continuum or errors in atomic data. For κ-distributions, the radiative-loss functions are in general weaker than for Maxwellian distribution, with a few exceptions caused by the behavior of Fe. The peaks of the radiative-loss functions are in general flatter. The situation is opposite for n-distributions, for which the radiative-loss functions have higher and narrower peaks. Local minima and maxima of the radiative-loss functions may also be shifted. The contribution from bremsstrahlung only changes by a few percent except in the extreme nonthermal case of κ = 2. Stability analysis reveals that the X-ray loops are stable against the radiatively-driven thermal instability

EUV filter responses to plasma emission for the nonthermal

The responses to plasma emission of the TRACE EUV filters are computed by integrating their spectral responses over the synthetic spectra obtained from the CHIANTI database. The filter responses to emission are functions of temperature, electron density, and the assumed electron distribution function. It is shown here that, for the nonthermal κ-distributions, the resulting responses to emission are more broadly dependent on T, and their maxima are flatter than for the Maxwellian electron distribution. The positions of the maxima can also be shifted. Filter reponses to T are density-dependent as well. The influence of the nonthermal κ-distributions on the diagnostics of T from the observations in all three EUV filters is discussed

Is it possible to model observed active region coronal emission simultaneously in EUV and X-ray filters?

Aims. We investigate the possibility of modeling the active region coronal emission in the EUV and X-ray filters using one, universal, steady heating function, tied to the properties of the magnetic field. Methods. We employ a simple, static model to compute the temperature and density distributions in the active region corona. The model allows us to explore a wide range of parameters of the heating function. The predicted EUV and X-ray emission in the filters of EIT/SOHO and XRT/Hinode are calculated and compared with observations. Using the combined improved filter-ratio (CIFR) method, a temperature diagnostic is employed to compare the modeled temperature structure of the active region with the temperature structure derived from the observations. Results. The global properties of the observations are most closely matched for heating functions scaling as \hbox{$B_0^{0.7-0.8}/L_0^{0.5}$} that depend on the spatially variable heating scale-length. The modeled X-ray emission originates from locations where large heating scale-lengths are found. However, the majority of the loops observed in the 171 and 195 filters can be modeled only by loops with very short heating scale-lengths. These loops are known to be thermally unstable. We are unable to find a model that both matches the observations in all EUV and X-ray filters, and contains only stable loops. As a result, although our model with a steady heating function can explain some of the emission properties of the 171 and 195 loops, it cannot explain their observed lifetimes. Thus, the model does not lead to a self-consistent solution. The performance of the CIFR method is evaluated and we find that the diagnosed temperature can be approximated with a geometric mean of the emission-measure weighted and maximum temperature along the line of sight. Conclusions. We conclude that if one universal heating function exists, it should be at least partially time-dependent

Analytical model of static coronal loops

By solving the energy-equilibrium equation in the stationary case, we derive analytical formulae in the form of scaling laws for non-uniformly heated and gravitationally stratified coronal loops. The heating is assumed to be localized in the chromosphere and to exponentially decrease with increasing distance along the loop strand. This exponential behavior of the heating and pressure profiles implies that we need to use the mean-value theorem, and in turn fit the mean-value parameters of the scaling laws to the results of the numerical simulations. The radiative-loss function is approximated by a power-law function of the temperature, and its effect on the resulting scaling laws for coronal loops is studied. We find that this effect is more important than the effect of varying loop geometry. We also find that the difference in lengths of the different loop strands in a loop with expanding cross-section does not produce differences in the EUV emission of these strands significant enough to explain the observed narrowness of the coronal loops

Nonthermal and thermal diagnostics of a solar flare observed with RESIK and RHESSI

Aims. We aim to prove and diagnose the occurrence of nonthermal electron distributions in solar flare plasma using X-ray spectral observations. Methods. An M4.9 flare on 2003 January 7/8 was observed with the RESIK instrument in the 3-6 Å wavelength range (2-4 keV) and with RHESSI at energies above 6 keV. The temporal behavior of RESIK flare spectra has been analyzed for two different types of velocity distributions – a thermal (Maxwellian) distribution and a nonthermal plasma distribution of free electrons. The \ion{Si}{xiv}, \ion{Si}{xiii}, and \ion{Si}{xii}d satellite lines observed with RESIK in the 5-6 Å range were used to determine the degree of deviation from Maxwellian, and the equivalent non-Maxwellian pseudo-temperature, τ. The diagnostics presented are sensitive to the shape of the distribution in the energy range where the maximum of the electron distribution occurs (where the bulk of electrons reside) and does not include the influence of the shape of the high-energy tail of the distribution. Under the assumption of a Maxwellian distribution of electron velocities, the plasma temperature was determined from an emission measure (EM) loci analysis and a differential emission measure (DEM) analysis of RESIK spectra. The high-energy end of the flare radiative emission was investigated through RHESSI spectral analysis. Results. The nonthermal analysis of RESIK spectra has shown that the largest deviations of the plasma electron distribution from Maxwellian appeared during the impulsive phase of the flare. The decay phase spectra had an almost isothermal character. The pseudo-temperature, τ, reached its maximum around the peak time of the soft and hard X-ray fluxes. The temporal behavior of the temperatures derived from the thermal analysis was similar to the behavior of the nonthermal pseudo-temperature. The values of the pseudo-temperature were consistent with the temperatures obtained in both thermal analyses, but lower than the temperatures derived from the slope of the RHESSI continua. In comparison with the synthetic isothermal or multithermal spectra, the nonthermal synthetic spectra fitted the observed \ion{Si}{xii}d satellite lines much more closely (the error is less than 10%). The fluxes in the Si XIId satellite lines in isothermal or multithermal spectra have been underestimated by a factor of three or more in comparison to the observed fluxes. The value of this factor varies with time and it is different for the different satellite lines. Conclusions. Evidence was found for considerable deviations of the distribution of free electrons from Maxwellian in the plasma during a solar flare. These occurred mainly during the flare impulsive phase and can be diagnosed using existing X-ray spectral observations