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Determination of Stochastic Acceleration Model Characteristics in Solar Flares  

Qingrong Chen   Submitted: 2013-07-09 15:23

Following our recent paper (Petrosian & Chen 2010), we have developed an inversion method to determine the basic characteristics for the model of stochastic acceleration of particles by plasma waves or turbulence directly and non-parametrically from observations in the framework of the leaky box version of the Fokker-Planck kinetic equation. These characteristics are determined by wave-particle interactions as described by the momentum and pitch angle diffusion coefficients. Our method relates these coefficients directly to observations. In particular, we show that by inverting the Fokker-Planck equation to its integral form, one can derive the energy diffusion coefficient and direct acceleration rate by turbulence in terms of the accelerated and escaping particle spectra. We apply the analytic formulas to the suprathermal electrons in solar flares, which produce hard X-ray emission at the coronal loop top (LT) region and two thick target footpoint regions of the flare loop. We utilize the regularized electron flux spectral images recently developed for the Reuven Ramaty High Energy Solar Spectroscopic Imager ({it RHESSI}). From the spatially resolved electron flux spectra, we determine the electron escape time, which is related to the pitch angle scattering rate, and the energy diffusion coefficient at the LT acceleration region. Results obtained from two relatively intense {it RHESSI} events indicate that the escape time increases with energy and the energy diffusion (or direct acceleration) time and scattering time have dramatically different energy dependences. Such behaviors may be difficult to explain by existing wave-particle interaction models, and may indicate that a different acceleration mechanism is at work or imply a breakdown of the basic interpretation of the escape of electrons being a random walk process. The discrepant energy dependences can be alleviated somewhat by a turbulence spectrum that is much steeper than the Kolmogorov-type spectrum. On the other hand, a more likely explanation could be that the escape of electrons out of the LT acceleration region is governed by converging field lines in a magnetic mirror geometry, in which the escape time is proportional to scattering time. The results demonstrate the critical importance of combined modeling of electron acceleration by plasma wave turbulence and the large scale magnetic field variations in a reconnection environment.

Authors: Qingrong Chen and Vahe' Petrosian
Projects: RHESSI

Publication Status: submitted to ApJ
Last Modified: 2013-07-10 13:40
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Impulsive Phase Coronal Hard X-ray Sources in an X3.9 Class Solar Flare  

Qingrong Chen   Submitted: 2012-01-10 12:56

[Abridged]We present analysis of a pair of unusually energetic coronal hardX-ray (HXR) sources detected by RHESSI during the impulsive phase of an X3.9class solar flare on 2003 November 3, which simultaneously shows two intensefootpoint (FP) sources. A distinct loop top (LT) coronal source is detected upto ~150 keV and a second (upper) coronal source up to ~80 keV. These photonenergies are much higher than commonly observed in coronal sources and posegrave modeling challenges. The LT source in general appears higher in altitudewith increasing energy and exhibits a more limited motion compared to theexpansion of the thermal loop. The high energy LT source shows an impulsivetime profile and its nonthermal power law spectrum exhibits soft-hard-softevolution during the impulsive phase, similar to the FP sources. The uppercoronal source exhibits an opposite spatial gradient and a similar spectralslope compared to the LT source. These properties are consistent with the modelof stochastic acceleration of electrons by plasma waves or turbulence. However,the LT and FP spectral index difference (varying from ~0-1) is much smallerthan commonly measured and than that expected from a simple stochasticacceleration model. Additional confinement or trapping mechanisms of highenergy electrons in the corona are required. Comprehensive modeling includingboth kinetic effects and the macroscopic flare structure may shed light on thisbehavior. These results highlight the importance of imaging spectroscopicobservations of the LT and FP sources up to high energies in understandingelectron acceleration in solar flares. Finally, we show that the electronsproducing the upper coronal HXR source may very likely be responsible for thetype III radio bursts at the decimetric/metric wavelength observed during theimpulsive phase of this flare.

Authors: Qingrong Chen, Vahé Petrosian
Projects: RHESSI

Publication Status: accepted for publication in ApJ
Last Modified: 2012-01-10 15:42
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Derivation of Stochastic Acceleration Model Characteristics for Solar Flares From RHESSI Hard X-Ray Observations  

Qingrong Chen   Submitted: 2010-02-12 20:20

The model of stochastic acceleration of particles by turbulence has been successful in explaining many observed features of solar flares. Here we demonstrate a new method to obtain the accelerated electron spectrum and important acceleration model parameters from the high resolution hard X-ray observations provided by the Reuven Ramaty High Energy Solar Spectroscopic Imager (RHESSI). In our model, electrons accelerated at or very near the loop top produce thin target bremsstrahlung emission there and then escape downward producing thick target emission at the loop footpoints. Based on the electron flux spectral images obtained by the regularized inversion of the RHESSI count visibilities, we derive several important parameters for the acceleration model. We apply this procedure to the 2003 November 03 solar flare, which shows a loop top source up to 100-150 keV in hard X-ray with a relatively flat spectrum in addition to two footpoint sources. The results imply presence of strong scattering and a high density of turbulence energy with a steep spectrum in the acceleration region.

Authors: Vahé Petrosian, Qingrong Chen
Projects: RHESSI

Publication Status: Revised manuscript submitted to ApJL
Last Modified: 2010-02-13 10:12
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Footpoint Motion of the Continuum Emission in the 2002 September 30 White-Light Flare  

Qingrong Chen   Submitted: 2005-12-21 05:50

We present observations of the 2002 September 30 white-light flare, in which the optical continuum emission near the Hα line is enhanced by ~10%. The continuum emission exhibits a close temporal and spatial coincidence with the hard X-ray (HXR) footpoint observed by RHESSI. We find a systematic motion of the flare footpoint seen in the continuum emission; the motion history follows roughly that of the HXR source. This gives strong evidence the this white-light flare is powered by heating of nonthermal electrons. We note that the HXR spectrum in 10-50 keV is quite soft with gamma being ~7 and there is no HXR emission above 50 keV. The magnetic configuration of the flaring region implies magnetic reconnection taking place at a relatively low altitude during the flare. Despite a very soft spectrum of the electron beam, its energy content is still sufficient to produce the heating in the lower atmosphere where the continuum emission originates. This white-light flare highlights the importance of radiative backwarming to transport the energy below when direct heating by beam electrons is obviously impossible.

Authors: Q. R. Chen, M. D. Ding
Projects: RHESSI

Publication Status: accepted for publication in ApJ
Last Modified: 2005-12-21 05:50
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On the Relationship between the Continuum Enhancement and Hard X-ray Emission in a White-Light Flare  

Qingrong Chen   Submitted: 2004-12-08 22:20

We investigate the relationship between the continuum enhancement and the hard X-ray (HXR) emission of a white-light flare on 2002 September 29. By reconstructing the RHESSI HXR images in the impulsive phase, we find two bright conjugate footpoints (FPs) on the two sides of the magnetic neutral line. Using the thick-target model and assuming a low-energy cutoff of 20 keV, the energy fluxes of non-thermal electron beams bombarding FPs A and B are estimated to be 1.0 1010 and 0.8 1010 ergs/cm^2/s, respectively. However, the continuum enhancement at the two FPs is not simply proportional to the electron beam flux. The continuum emission at FP B is relatively strong with a maximum enhancement of about 8% and correlates temporally well with the HXR profile; however, that at FP A is less significant with an enhancement of only about 4-5%, regardless of the relatively strong beam flux. By carefully inspecting the Hα line profiles, we ascribe such a contrast to different atmospheric conditions at the two FPs. The Hα line profile at FP B exhibits a relatively weak amplitude with a pronounced central reversal, while the profile at FP A is fairly strong without a visible central reversal. This indicates that in the early impulsive phase of the flare, the local atmosphere at FP A has been appreciably heated and the coronal pressure is high enough to prevent most high-energy electrons from penetrating into the deeper atmosphere; while at FP B, the atmosphere has not been fully heated, the electron beam can effectively heat the chromosphere and produce the observed continuum enhancement via the radiative backwarming effect.

Authors: Q. R. Chen and M. D. Ding
Projects: RHESSI

Publication Status: accepted for publication in ApJ
Last Modified: 2004-12-08 22:20
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Abstracts by Author
Determination of Stochastic Acceleration Model Characteristics in Solar Flares
Impulsive Phase Coronal Hard X-ray Sources in an X3.9 Class Solar Flare
Derivation of Stochastic Acceleration Model Characteristics for Solar Flares From RHESSI Hard X-Ray Observations
Footpoint Motion of the Continuum Emission in the 2002 September 30 White-Light Flare
On the Relationship between the Continuum Enhancement and Hard X-ray Emission in a White-Light Flare

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