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Observations and Models of the Dynamical Evolution of Solar Flares  

Paolo Grigis   Submitted: 2006-11-30 03:18

Solar flares and associated Coronal Mass Ejections (CMEs) are the biggest explosions in the solar system, converting huge amounts of magnetic energy into kinetic energy of accelerated particles and heat. The key questions at the core of flare physics research are: how is the energy stored in the solar corona before the flare? What triggers the sudden release of that energy? How are the particles accelerated and heated during the flare? Notwithstanding the strong theoretical and observational progress of the last few decades, this questions still remain open. Hard X-ray observations of the Sun, such as provided by the Reuven Ramaty High-Energy Solar Spectroscopic Imager (RHESSI), are the best tools to probe the population of flare-accelerated particles, because X-rays are the direct signature of energetic electrons. In this thesis, novel RHESSI hard X-ray observations of solar flares are compared with quantitative predictions from modern theoretical models of stochastic acceleration of electrons. The focus lies on the spectral evolution, which has been discovered in the early days of hard X-ray observations, but, with a few exceptions, neglected by theorists. The work presented here starts with RHESSI observations of the spectral evolution of the non-thermal component in the hard X-ray spectrum of solar flares. A representative sample of 24 M class impulsive flares is analyzed. They show rapid changes in the spectral hardness during distinct emission spikes. The maximum hardness is reached at peak time, thus the spectral behavior can be classified as soft-hard-soft. A quantitative relation between the normalization of the power-law component and its spectral index is found, holding for single emission spikes, as well as for the whole dataset comprising all events. The analysis is then expanded, transforming the data from photon space to electron space and comparing the results with predictions from simple available electron acceleration models featuring soft-hard-soft behavior. This simple approach yields plausible best-fit model parameters for about 77% of the 141 events consisting of rise and decay phases of individual hard X-ray spikes. This success suggests that stochastic acceleration is a viable mechanism to explain the observed spectral evolution. Therefore, a recent stochastic acceleration model, the transit-time damping acceleration scenario, was chosen for further investigation. A mechanism that accounts for particle trapping in the accelerator was added in order to account for changes in the spectral hardness. The model predictions for the spectral evolution were compared with spectral observations of looptop hard X-ray sources, delivering a snapshot of the particles still residing in the accelerator. A novel parameter was used for the comparison, the pivot point (that is, a common crossing point of the accelerated particle spectra at different times). The model computations show the presence of a pivot point at an energy of 10 keV. This value can be brought in agreement with the observed value of 20 keV by enhanced trapping through an electric potential. Lastly, some puzzling observations of the motion of hard X-ray sources during an impulsive M class flare are reported. The double sources, interpreted as footpoints of magnetic loops, show continuous motion along an arcade of magnetic loops, contradicting the predictions of the translation invariant 2.5D reconnection models, where motion perpendicular to the arcade is expected. Therefore, the development of more realistic 3D models is needed to account for such behavior.

Authors: Paolo C. Grigis
Projects: None

Publication Status: Ph.D. Thesis
Last Modified: 2006-11-30 06:41
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Electron Acceleration in Solar Flares: Theory of Spectral Evolution  

Paolo Grigis   Submitted: 2006-08-21 03:14

Context: Stochastic acceleration is thought to be a key mechanism in the energization of solar flare electrons. Aims: We study whether stochastic acceleration can reproduce the observed soft-hard-soft evolution of the spectral features of the hard X-ray emitted by suprathermal electron. We pay special attention to the effects of particle trapping and escape. Methods: The Fokker-Planck equation for the electron distribution is integrated numerically using the coefficients derived by Miller et al. for transit-time damping acceleration. The electron spectra are then converted to photon spectra for comparison with RHESSI observation of looptop sources. Results: The presence of particle escape softens the model spectra computed in the stochastic acceleration framework. The ratio between the efficiency of trapping and acceleration controls the spectral evolution which follows a soft-hard-soft pattern. Furthermore, a pivot point (that is, a common crossing point of the accelerated particle spectra at different times) is found at around 10 keV. It can be brought into agreement with the observed value of 20 keV by enhanced trapping through an electric potential. Conclusions: The model proposed here accounts for the key features observed in the spectral evolution of hard X-ray emission from looptop sources.

Authors: Paolo C. Grigis and Arnold O. Benz
Projects: RHESSI

Publication Status: accepted by A&A
Last Modified: 2006-08-21 10:51
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Electron Acceleration in Solar Flares: Theory of Spectral Evolution  

Paolo Grigis   Submitted: 2006-08-21 03:13

Context: Stochastic acceleration is thought to be a key mechanism in the energization of solar flare electrons. Aims: We study whether stochastic acceleration can reproduce the observed soft-hard-soft evolution of the spectral features of the hard X-ray emitted by suprathermal electron. We pay special attention to the effects of particle trapping and escape. Methods: The Fokker-Planck equation for the electron distribution is integrated numerically using the coefficients derived by Miller et al. for transit-time damping acceleration. The electron spectra are then converted to photon spectra for comparison with RHESSI observation of looptop sources. Results: The presence of particle escape softens the model spectra computed in the stochastic acceleration framework. The ratio between the efficiency of trapping and acceleration controls the spectral evolution which follows a soft-hard-soft pattern. Furthermore, a pivot point (that is, a common crossing point of the accelerated particle spectra at different times) is found at around 10 keV. It can be brought into agreement with the observed value of 20 keV by enhanced trapping through an electric potential. Conclusions: The model proposed here accounts for the key features observed in the spectral evolution of hard X-ray emission from looptop sources.

Authors: Paolo C. Grigis and Arnold O. Benz
Projects: RHESSI

Publication Status: accepted by A&A
Last Modified: 2006-08-21 03:13
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Evolution of reconnection along an arcade of magnetic loops  

Paolo Grigis   Submitted: 2005-04-20 06:37

RHESSI observations of a solar flare showing continuous motions of double hard X-ray sources interpreted as footpoints of magnetic loops are presented. The temporal evolution shows many distinct emission peaks of duration of some tens of seconds ('elementary flare bursts'). Elementary flare bursts have been interpreted as instabilities or oscillations of the reconnection process leading to an unsteady release of magnetic energy. These interpretations based on two-dimensional concepts cannot explain these observations, showing that the flare elements are displaced in a third dimension along the arcade. Therefore, the observed flare elements are not a modulation of the reconnection process, but originate as this process progresses along an arcade of magnetic loops. Contrary to previous reports, we find no correlation between footpoint motion and hard X-ray flux. This flare apparently contradicts the predictions of the standard translation invariant 2.5D reconnection models.

Authors: Grigis, Paolo C. and Benz, Arnold O.
Projects: RHESSI

Publication Status: ApJ Letters (in press)
Last Modified: 2005-04-20 06:38
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The spectral evolution of impulsive solar X-ray flares. II.Comparison of observations with models  

Paolo Grigis   Submitted: 2005-01-20 08:10

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 1036 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.

Authors: Grigis, P. C. and Benz, A. O.
Projects: RHESSI

Publication Status: accepted by A&A
Last Modified: 2005-01-20 08:10
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The spectral evolution of impulsive solar X-ray flares  

Paolo Grigis   Submitted: 2004-08-23 03:47

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.

Authors: Paolo C. Grigis and Arnold O. Benz
Projects: RHESSI

Publication Status: A&A, in press
Last Modified: 2004-08-23 03:47
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Abstracts by Author
Observations and Models of the Dynamical Evolution of Solar Flares
Electron Acceleration in Solar Flares: Theory of Spectral Evolution
Electron Acceleration in Solar Flares: Theory of Spectral Evolution
Evolution of reconnection along an arcade of magnetic loops
The spectral evolution of impulsive solar X-ray flares. II.Comparison of observations with models
The spectral evolution of impulsive solar X-ray flares

Related Pages
MSU Solar Physics.
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Max Millennium Flare Catalog

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