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Stereoscopic electron spectroscopy of solar hard X-ray flares with a single spacecraft  

Eduard Kontar   Submitted: 2006-11-06 05:36

Hard X-ray (HXR) spectroscopy is the most direct method of diagnosing energetic electrons in solar flares. Here we present a technique which allows us to use a single HXR spectrum to determine an effectively stereoscopic electron energy distribution. Considering the Sun's surface to act as a 'Compton mirror' allows us to look at emitting electrons also from behind the source, providing vital information on downward-propagating particles. Using this technique we determine simultaneously the electron spectra of downward and upward directed electrons for two solar flares observed by the Ramaty High Energy Solar Spectroscopic Imager (RHESSI). The results reveal surprisingly near-isotropic electron distributions, which contrast strongly with the expectations from the standard model which invokes strong downward beaming, including collisional thick-target model.

Authors: Eduard P. Kontar and John C. Brown
Projects: RHESSI

Publication Status: Accepted to ApJ Letters
Last Modified: 2006-11-09 02:58
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Compton backscattered and primary X-rays from solar flares: angle dependent Green's function correction for photospheric albedo  

Eduard Kontar   Submitted: 2005-10-06 04:48

The observed hard X-ray (HXR) flux spectrum I(epsilon) from solar flares is a combination of primary bremsstrahlung photons I_P(epsilon) with a spectrally modified component from photospheric Compton backscatter of downward primary emission. The latter can be significant, distorting or hiding the true features of the primary spectrum which are key diagnostics for acceleration and propagation of high energy electrons and of their energy budget. For the first time in solar physics, we use a Green's function approach to the backscatter spectral deconvolution problem, constructing a Green's matrix including photoelectric absorption. This approach allows spectrum-independent extraction of the primary spectrum for several HXR flares observed by the {it Ramaty High Energy Solar Spectroscopic Imager} (RHESSI). We show that the observed and primary spectra differ very substantially for flares with hard spectra close to the disk centre. We show in particular that the energy dependent photon spectral index gamma (epsilon)=-d log I/d log epsilon is very different for I_P(epsilon) and for I(epsilon) and that inferred mean source electron spectra {overline F}(E) differ greatly. Even for a forward fitting of a parametric {overline F}(E) to the data, a clear low-energy cutoff required to fit I(epsilon) essentially disappears when the fit is to I_P(epsilon) - i.e. when albedo correction is included. The self-consistent correction for backscattered photons is thus shown to be crucial in determining the energy spectra of flare accelerated electrons, and hence their total number and energy.

Authors: Eduard P. Kontar, Alec L. MacKinnon, Richard A. Schwartz, and John C. Brown
Projects: RHESSI

Publication Status: Accepted to Astronomy and Astrophysics
Last Modified: 2005-10-06 04:48
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Solar Flare Hard X-ray Spectra Possibly Inconsistent with the Collisional Thick Target Model  

Eduard Kontar   Submitted: 2005-08-19 10:34

Recent progress in solar Hard X-ray (HXR) observations with RHESSI data and methods for spectral inversion allow us to study model-independent mean electron flux spectra in solar flares. We report several hard X-ray events observed by RHESSI in which the photon spectra I(epsilon) are such that the inferred source mean electron spectra are not consistent with the standard model of collisional transport in solar flares. The observed photon spectra are so flat locally that the recovered mean electron flux spectra show a dip around 17-31 keV. While we note that alternative explanations, unrelated to electron transport, have not been ruled out, we focus on the physical implications of this tentative result for the collisional thick-target model.

Authors: Eduard P. Kontar and John C. Brown
Projects: RHESSI

Publication Status: Advances in Space Research (submitted)
Last Modified: 2005-08-19 10:34
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Regularized Energy-Dependent Solar Flare Hard X-Ray Spectral Index  

Eduard Kontar   Submitted: 2005-01-20 13:23

The deduction from solar flare X-ray photon spectroscopic data of the energy dependent model-independent spectral index is considered as an inverse problem. Using the well developed regularization approach we analyze the energy dependency of spectral index for a high resolution energy spectrum provided by Ramaty High Energy Solar Spectroscopic Imager (RHESSI). The regularization technique produces much smoother derivatives while avoiding additional errors typical of finite differences. It is shown that observations imply a spectral index varying significantly with energy, in a way that also varies with time as the flare progresses. The implications of these findings are discussed in the solar flare context.

Authors: E.P. Kontar and A.L. MacKinnon
Projects: RHESSI

Publication Status: Solar Physics, (in press)
Last Modified: 2005-01-20 13:23
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Determination Of Electron Flux Spectra In A Solar Flare With An Augmented Regularization Method: Application To RHESSI Data  

Eduard Kontar   Submitted: 2004-09-08 12:09

Kontar et al. (2004) (Paper I) have shown how to recover mean source electron spectra in solar flares through a physical constraint regularization analysis of the bremsstrahlung photon spectra that they produce. They emphasize the use of non-square inversion techniques, and preconditioning combined with physical properties of the spectra to achieve the most meaningful solution to the problem. Higher-order regularization techniques may be used to generate {overline F}(E) forms with certain desirable properties (e.g., higher order derivatives). They further note that such analyses may be used to infer properties of the electron energy spectra at energies well above the maximum photon energy observed. In this paper we apply these techniques to data from a solar flare observed by RHESSI on 26 February, 2002. Results using different orders of regularization are presented and compared for various time intervals. Clear evidence is presented for a change in the value of the high-energy cutoff in the mean source electron spectrum with time. We also show how the construction of the injected (accelerated) electron spectrum F_0(E_0) (assuming that Coulomb collisions in a cold target dominate the electron energetics) is facilitated by the use of higher-order regularization methods.

Authors: E.P. Kontar, A.G. Emslie, M. Piana, A.M. Massone, and J.C. Brown
Projects: RHESSI

Publication Status: Solar Physics, (submitted)
Last Modified: 2005-12-07 05:25
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Generalized Regularization Techniques With Constraints For The Analysis Of Solar Bremsstrahlung X-Ray Spectra  

Eduard Kontar   Submitted: 2004-09-08 12:02

Hard X-ray spectra in solar flares provide knowledge of the electron spectrum that results from acceleration and propagation in the solar atmosphere. However, the inference of the electron spectra from solar X-ray spectra is an ill-posed inverse problem. Here we develop and apply an enhanced regularization algorithm for this process making use of physical constraints on the form of the electron spectrum. The algorithm incorporates various features not heretofore employed in the solar flare context: Generalized Singular Value Decomposition (GSVD) to deal with different orders of constraints; rectangular form of the cross-section matrix to extend the solution energy range; regularization with various forms of the smoothing operator; and ''preconditioning'' of the problem. We show by simulations that this technique yields electron spectra with considerably more information and higher quality than previous algorithms.

Authors: E.P. Kontar, M. Piana, A.M. Massone, A.G. Emslie, and J.C. Brown
Projects: RHESSI

Publication Status: Solar Physics (submitted)
Last Modified: 2004-09-08 12:02
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Nonuniform Target Ionisation and Fitting Thick Target Electron Injection Spectra to RHESSI Data  

Eduard Kontar   Submitted: 2003-03-26 15:02

Past analysis of flare Hard X-Ray (HXR) spectra have largely ignored the effect of nonuniform ionisation along the electron paths in the thick target model, though it is very significant for well-resolved spectra. The inverse problem (photon spectrum to electron injection spectrum {cal F}_0(E_0)) is disturbingly non-unique. However, we show that it is relatively simple to allow for the effect in forward fitting of parametric models of {cal F}_0(E_0) and provide an expression to evaluate it for the usual single power law form of {cal F}_0(E_0). The expression involves the column depth N_* of the transition region in the flare loop as one of the parameters so data fitting can enable derivation of N_* (and its evaporative evolution) as part of the fitting procedure. The fit to RHESSI data on four flares for a single power law {cal F}_0(E_0) is much improved when ionisation structure is included compared to when the usual fully ionised approximation is used. This removes the need, in these events at least, to invoke broken power-laws, or other forms, of the acceleration spectrum {cal F}_0(E_0) to explain the observed photon spectrum.

Authors: E.P. Kontar, J.C. Brown, and G. K. McArthur
Projects: RHESSI

Publication Status: Solar Physics, (in press)
Last Modified: 2005-12-07 05:18
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Nonuniform Target Ionisation and Fitting Thick Target Electron Injection Spectra to RHESSI Data  

Eduard Kontar   Submitted: 2003-03-26 15:02

Past analysis of flare Hard X-Ray (HXR) spectra have largely ignored the effect of nonuniform ionisation along the electron paths in the thick target model, though it is very significant for well-resolved spectra. The inverse problem (photon spectrum to electron injection spectrum {cal F}_0(E_0)) is disturbingly non-unique. However, we show that it is relatively simple to allow for the effect in forward fitting of parametric models of {cal F}_0(E_0) and provide an expression to evaluate it for the usual single power law form of {cal F}_0(E_0). The expression involves the column depth N_* of the transition region in the flare loop as one of the parameters so data fitting can enable derivation of N_* (and its evaporative evolution) as part of the fitting procedure. The fit to RHESSI data on four flares for a single power law {cal F}_0(E_0) is much improved when ionisation structure is included compared to when the usual fully ionised approximation is used. This removes the need, in these events at least, to invoke broken power-laws, or other forms, of the acceleration spectrum {cal F}_0(E_0) to explain the observed photon spectrum.

Authors: E.P. Kontar, J.C. Brown, and G. K. McArthur
Projects: RHESSI

Publication Status: Solar Physics, (in press)
Last Modified: 2005-12-07 05:18
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Nonuniform Target Ionisation and Fitting Thick Target Electron Injection Spectra to RHESSI Data  

Eduard Kontar   Submitted: 2003-03-26 15:02

Past analysis of flare Hard X-Ray (HXR) spectra have largely ignored the effect of nonuniform ionisation along the electron paths in the thick target model, though it is very significant for well-resolved spectra. The inverse problem (photon spectrum to electron injection spectrum {cal F}_0(E_0)) is disturbingly non-unique. However, we show that it is relatively simple to allow for the effect in forward fitting of parametric models of {cal F}_0(E_0) and provide an expression to evaluate it for the usual single power law form of {cal F}_0(E_0). The expression involves the column depth N_* of the transition region in the flare loop as one of the parameters so data fitting can enable derivation of N_* (and its evaporative evolution) as part of the fitting procedure. The fit to RHESSI data on four flares for a single power law {cal F}_0(E_0) is much improved when ionisation structure is included compared to when the usual fully ionised approximation is used. This removes the need, in these events at least, to invoke broken power-laws, or other forms, of the acceleration spectrum {cal F}_0(E_0) to explain the observed photon spectrum.

Authors: E.P. Kontar, J.C. Brown, and G. K. McArthur
Projects: RHESSI

Publication Status: Solar Physics, (in press)
Last Modified: 2005-12-07 05:20
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An Explanation for Non-Power-law Behavior in the Hard X-ray Spectrum of the July 23, 2002 Solar  

Eduard Kontar   Submitted: 2003-03-26 14:51

High-resolution RHESSI data reveal that solar flare hard X-ray spectra show systematic deviations from power-law behavior. Even for injection of a power-law electron spectrum, such deviations are expected because of a number of effects, including nonuniform target ionization and solar albedo backscattering of the primary hard X-ray flux. In this paper we examine 1 keV resolution hard X-ray spectra for the intense July 23, 2002 event, corrected for the effects of decimation, pulse pile-up and background. We find that the observed spectra indeed deviate from a power-law behavior in a manner consistent with the effects of nonuniform target ionization. Further, this interpretation of the observed deviations requires that the amount of coronal material increases during the initial phase of the flare. The implications of this discovery for models of atmospheric response to flare heating are discussed.

Authors: E.P. Kontar, J.C. Brown, A.G. Emslie, R.A. Schwartz, D.M. Smith, and R.C. Alexander
Projects:

Publication Status: ApJ Letters (in press)
Last Modified: 2003-03-26 14:51
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Abstracts by Author
Determination of the total accelerated electron rate and power using solar flare hard X-ray spectra
Spatially inhomogeneous acceleration of electrons in solar flares
Heating and cooling of coronal loops with turbulent suppression of parallel heat conduction
Imaging Spectroscopy of Solar Radio Burst Fine Structures
Turbulent kinetic energy in the energy balance of a solar flare
The role of diffusion in the transport of energetic electrons during solar flares
Suppression of parallel transport in turbulent magnetized plasmas and its impact on non-thermal and thermal aspects of solar flares
Collisional relaxation of electrons in a warm plasma and accelerated nonthermal electron spectra in solar flares
The Formation of Kappa-Distribution Accelerated Electron Populations in Solar Flares
Turbulent pitch-angle scattering and diffusive transport of hard-X-ray producing electrons in flaring coronal loops
Electron acceleration during three-dimensional relaxation of an electron beam-return current plasma system in a magnetic field
A Classification Scheme For Turbulent Acceleration Processes In Solar Flares
Turbulent cross-field transport of non-thermal electrons in coronal loops: theory and observations
Wave-particle interactions in non-uniform plasma and the interpretation of Hard X-ray spectra in solar flares
Acceleration, magnetic fluctuations and cross-field transport of energetic electrons in a solar flare loop
The sub-arcsecond hard X-ray structure of loop footpoints in a solar flare
Local re-acceleration and a modified thick target model of solar flare electrons
Onsets and spectra of impulsive solar energetic electron events observed near the Earth
Chromospheric magnetic field and density structure measurements using hard X-rays in a flaring coronal loop
Low-Energy Cutoffs in Electron Spectra of Solar Flares: Statistical Survey
Stereoscopic electron spectroscopy of solar hard X-ray flares with a single spacecraft
Compton backscattered and primary X-rays from solar flares: angle dependent Green's function correction for photospheric albedo
Solar Flare Hard X-ray Spectra Possibly Inconsistent with the Collisional Thick Target Model
Regularized Energy-Dependent Solar Flare Hard X-Ray Spectral Index
Determination Of Electron Flux Spectra In A Solar Flare With An Augmented Regularization Method: Application To RHESSI Data
Generalized Regularization Techniques With Constraints For The Analysis Of Solar Bremsstrahlung X-Ray Spectra
Nonuniform Target Ionisation and Fitting Thick Target Electron Injection Spectra to RHESSI Data
Nonuniform Target Ionisation and Fitting Thick Target Electron Injection Spectra to RHESSI Data
Nonuniform Target Ionisation and Fitting Thick Target Electron Injection Spectra to RHESSI Data
An Explanation for Non-Power-law Behavior in the Hard X-ray Spectrum of the July 23, 2002 Solar

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