Electron Scattering in the Flaring Corona

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Nugget
Number: 309
1st Author: Sophie Musset
2nd Author:
Published: 24 October 2017
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Contents

Introduction

The physics of Solar flares depends upon the acceleration of particles to energies far above that of the ambient medium; even in the corona the thermal particle energy may be of order 0.1 keV (or less), whereas the bremsstrahlung hard X-ray spectrum of energetic electrons in a flare may extend to well above 100 keV. The X-ray and radio emissions from these electrons do not come directly from the site of their acceleration. From this site they must propagate, guided by the magnetic field, and emit gyro-synchrotron emission in radio and bremsstrahlung emission in X-rays during this propagation. Transport effects can change the properties of electron populations between acceleration site and emission sites.

Electron transport in a flaring loop

Imaging spectroscopy with RHESSI allows us to study the transport effects on energetic electron distributions in coronal flaring magnetic loops, if the X-ray emission from the coronal part of the loop is bright enough to be observed by RHESSI in the presence of the chromospheric footpoint emission. Such looptop emission could be present if the source can be collisionally thick, for example can remain trapped for a sufficiently long time to slow down via collisional interactions with the ambient plasma.

The flare SOL2004-05-21 was such a "coronal thick-target" flare, with two footpoints and a coronal looptop X-ray source all visible in the RHESSI hard X-ray images (see Figure 1). Imaging spectroscopy on the three sources reveals that non-thermal emission is present in all the sources; however, the properties of the non-thermal spectrum of energetic electrons differ from those in the footpoint sources: the spectrum is harder in the footpoints, and the electron rate is greater in the looptop source. This last observation suggests that energetic electrons are indeed trapped in the coronal part of the loop.

Figure 1: Imaging Spectroscopy of SOL2004-05-21 in hard X-rays. The image shows the 25-50 keV emission integrated for one minute at flare peak, 23:50:00 UT. The contours of the 10-25 keV emission (red) and 50-100 keV emission (blue) show the location of the looptop and footpoint sources respectively. The boxes highlight the three regions where spectroscopy was done, as shown in the photon flux spectra at right. For each spectrum we show the data in black and a model fit in green. Here the model consists of a thermal component (red line), a non-thermal component (thin target in the looptop source and thick target in the footpoints, blue lines), including an estimated albedo contribution (yellow line). Figure legends give model parameters, including the estimated electron fluxes above 25 keV.

The conclusions here agree with observation and modeling of the gyrosynchrotron emission of the same flare, which showed that energetic electrons are trapped near the looptop at the time of the peak of the flare [Ref. 1]. However, the ratio between the density of energetic electrons in the looptop to the density in the footpoints is higher for radio-emitting electrons than for X-ray-emitting electrons, by a factor of about 3 (see Figure 2). Does this mean that the trapping mechanism is more efficient for the few-hundred-keV electrons emitting radio than for the few tens-of-keV electrons emitting hard X-rays?

Figure 2: Distribution of the density of energetic electrons above 25 keV, deduced from X-ray observations (left) and above 60 keV, deduced from radio observations (right). The numbers in blue are the ratio of the looptop density to the footpoint densities, for the two footpoints seen in the X-ray image.

The physics of the loop-top trapping

The standard model of flare electron transport only collisions are considered, in addition to the bouncing motion due to the mirror force itself. Energetic electrons propagating along the loop are subjected only to a small amount of collisions in the corona and therefore, reach the footpoints on a timescale smaller than our observation time. In that scenario, the electron rates in the looptop source and in the footpoints should be the same. Such a model does not explain our observations of the May 21, 2004 flare: thus the need for an additional trapping mechanism. Figure 3 illustrates the general picture.

Figure 3: Schematics of the flaring loop. Distance scales for the flare of May 21, 2004 are indicated, to be compared to the values of the scattering mean free path

In this scenario, should the trapping efficiency depend on the electron energy? This would not be the case without additional physics. The trapping of energetic electrons in flaring loops can also be affected by diffusive transport of electrons through any turbulent fluctuations of the coronal magnetic field. In this case, a key parameter of the electron transport is the scattering mean free path of energetic electrons, and this can depend upon the electron energy. We fitted both the spatial and spectral distributions of X-ray producing-electrons with a simple model of the diffusive transport of energetic electrons in a collisional plasma [Ref. 2]. The model of the flaring loop in that context is shown in the sketch. We find that this model can explain both X-ray and radio observations of the May 21, 2004 flare, but only if the scattering mean free path is energy-dependent, and decreases with increasing electron energy.

Conclusions

Our modeling of SOL2004-05-21 suggests that diffusive propagation plays a role in the particle trapping, which both the image morphology and the quantitative estimates of rates requires. Our analysis furthermore suggests that the scattering decreases with electron energy, a conclusion generally reached for electron propagation in the heliosphere at higher energies. The full details, including the comparison with the interplanetary observations, is in Ref. [3].

References

[1] "Spatially Resolved Energetic Electron Properties for the 21 May 2004 Flare from Radio Observations and 3D Simulations"

[2] "Turbulent Pitch-angle Scattering and Diffusive Transport of Hard X-Ray-producing Electrons in Flaring Coronal Loops"

[3] "Diffusive Transport of Energetic Electrons in the Solar Corona: X-ray and Radio Diagnostics" (in press at ApJ, 2017).

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