Fast spectral fitting of hard X-ray bremsstrahlung from truncated power-law electron spectra

<p><b>Context:</b> Hard X-ray bremsstrahlung continuum spectra, such as from solar flares, are commonly described in terms of power-law fits, either to the photon spectra themselves or to the electron spectra responsible for them. In applications various approximate relations between electron and photon spectral indices are often used for energies both above and below electron low-energy cutoffs.</p> <p><b>Aims:</b> We examine the form of the exact relationships in various situations, and for various cross-sections, showing that empirical relations sometimes used can be highly misleading especially at energies below the low-energy cutoff, and consider how to improve fitting procedures.</p> <p><b>Methods:</b> We obtain expressions for photon spectra from single, double and truncated power-law electron spectra for a variety of cross-sections and for the thin and thick target models and simple analytic expressions for the non-relativistic Bethe-Heitler case.</p> <p><b>Results:</b> We show that below the low-energy cutoff Kramers and other constant spectral index forms commonly used are very poor approximations to accurate results, but that our analytical forms are a good match; and that above a low-energy cutoff, the Kramers and non-relativistic Bethe-Heitler results match reasonably well with results for up to energies around 100 keV.</p> <p><b>Conclusions:</b> Analytical forms of the non-relativistic Bethe-Heitler photon spectra from general power-law electron spectra are good match to exact results for both thin and thick targets and they enable much faster spectral fitting than evaluation of the full spectral integrations.</p&gt

Hydrogen Balmer line formation in solar flares affected by return currents

Aims. We investigate the effect of the electric return currents in solar flares on the profiles of hydrogen Balmer lines. We consider the monoenergetic approximation for the primary beam and runaway model of the neutralizing return current. Methods. Propagation of the 10 keV electron beam from a coronal reconnection site is considered for the semiempirical chromosphere model F1. We estimate the local number density of return current using two approximations for beam energy fluxes between $4\times 10^{11}$ and $1\times 10^{12} {\rm erg cm^{-2} s^{-1}}$. Inelastic collisions of beam and return-current electrons with hydrogen are included according to their energy distributions, and the hydrogen Balmer line intensities are computed using an NLTE radiative transfer approach. Results. In comparison to traditional NLTE models of solar flares that neglect the return-current effects, we found a significant increase emission in the Balmer line cores due to nonthermal excitation by return current. Contrary to the model without return current, the line shapes are sensitive to a beam flux. It is the result of variation in the return-current energy that is close to the hydrogen excitation thresholds and the density of return-current electrons.Comment: 4 pages, 3 figures, 1 table, accepted for publication in Astronomy and Astrophysics Letter

Low-energy cutoffs in electron spectra of solar flares: statistical survey

The Ramaty High Energy Solar Spectroscopic Imager (RHESSI) X-ray data base (February 2002 -- May 2006) has been searched to find solar flares with weak thermal components and flat photon spectra. Using a regularised inversion technique, we determine the mean electron flux distribution from count spectra of a selection of events with flat photon spectra in the 15--20 keV energy range. Such spectral behaviour is expected for photon spectra either affected by photospheric albedo or produced by electron spectra with an absence of electrons in a given energy range, e.g. a low-energy cutoff in the mean electron spectra of non-themal particles. We have found 18 cases which exhibit a statistically significant local minimum (a dip) in the range of 10--20 keV. The positions and spectral indices of events with low-energy cutoff indicate that such features are likely to be the result of photospheric albedo. It is shown that if the isotropic albedo correction was applied, all low-energy cutoffs in the mean electron spectrum were removed and hence the low energy cutoffs in the mean electron spectrum of solar flares above $\sim$12 keV cannot be viewed as real features in the electron spectrum. If low-energy cutoffs exist in the mean electron spectra, the energy of low energy cutoffs should be less than $\sim$12 keV.Comment: 9 pages, 5 figures, submitted to Solar Physic

Approximations for radiative cooling and heating in the solar chromosphere

Context. The radiative energy balance in the solar chromosphere is dominated by strong spectral lines that are formed out of LTE. It is computationally prohibitive to solve the full equations of radiative transfer and statistical equilibrium in 3D time dependent MHD simulations. Aims. To find simple recipes to compute the radiative energy balance in the dominant lines under solar chromospheric conditions. Methods. We use detailed calculations in time-dependent and 2D MHD snapshots to derive empirical formulae for the radiative cooling and heating. Results. The radiative cooling in neutral hydrogen lines and the Lyman continuum, the H and K and intrared triplet lines of singly ionized calcium and the h and k lines of singly ionized magnesium can be written as a product of an optically thin emission (dependent on temperature), an escape probability (dependent on column mass) and an ionization fraction (dependent on temperature). In the cool pockets of the chromosphere the same transitions contribute to the heating of the gas and similar formulae can be derived for these processes. We finally derive a simple recipe for the radiative heating of the chromosphere from incoming coronal radiation. We compare our recipes with the detailed results and comment on the accuracy and applicability of the recipes.Comment: accepted for publication in Astronomy & Astrophysic

The influence of albedo on the size of hard X-ray flare sources

Context: Hard X-rays from solar flares are an important diagnostic of particle acceleration and transport in the solar atmosphere. Any observed X-ray flux from on-disc sources is composed of direct emission plus Compton backscattered photons (albedo). This affects both the observed spectra and images as well as the physical quantities derived from them such as the spatial and spectral distributions of accelerated electrons or characteristics of the solar atmosphere. Aims: We propose a new indirect method to measure albedo and to infer the directivity of X-rays in imaging using RHESSI data. Methods: Visibility forward fitting is used to determine the size of a disc event observed by RHESSI as a function of energy. This is compared to the sizes of simulated sources from a Monte Carlo simulation code of photon transport in the chromosphere for different degrees of downward directivity and true source sizes to find limits on the true source size and the directivity. Results: The observed full width half maximum of the source varies in size between 7.4 arcsec and 9.1 arcsec with the maximum between 30 and 40 keV. Such behaviour is expected in the presence of albedo and is found in the simulations. A source size smaller than 6 arcsec is improbable for modest directivities and the true source size is likely to be around 7 arcsec for small directivities. Conclusions: While it is difficult to image the albedo patch directly, the effect of backscattered photons on the observed source size can be estimated. The increase in source size caused by albedo has to be accounted for when computing physical quantities that include the size as a parameter such as flare energetics. At the same time, the study of the albedo signature provides vital information about the directivity of X-rays and related electrons.Comment: 8 pages, 6 figures, A&A (accepted

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

Kappa distribution and hard X-ray emission of solar flares

We investigate whether the so-called kappa distribution, often used to fit electron distributions detected in-situ in the solar wind, can describe electrons producing the hard X-ray emission in solar flares. Using Ramaty High Energy Solar Spectroscopic imager (RHESSI) flare data we fit spatially- and feature-integrated spectra, assuming kappa distribution for the mean electron flux spectrum. We show that a single kappa distribution generally cannot describe spatially integrated X-ray emission composed of both footpoint and coronal sources. In contrast, the kappa distribution is consistent with mean electron spectra producing hard X-ray emission in some coronal sources.Comment: 4 pages, 4 figures, changed content, accepted to A&

Current status of NLTE analysis of stellar atmospheres

Various available codes for NLTE modeling and analysis of hot star spectra are reviewed. Generalizations of standard equations of kinetic equilibrium and their consequences are discussed.Comment: in Determination of Atmospheric Parameters of B-, A-, F- and G-Type Stars, E. Niemczura et al. eds., Springer, in pres

Metals – impact and implications

Impact of metal in vitro administration on rat tissue oxygen consumption is referred in the first part. Toxicological implications of in vivo metal administration to rats and the study of potential penetration of metal into the rat brain, which may eventually result in oxygen radical production are presented in second part