Hard X-ray Emission from Partially Occulted Solar Flares

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Nugget
Number: 291
1st Author: Frederic Effenberger
2nd Author: and Fatima Rubio da Costa
Published: 30 January 2017
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Contents

Introduction

Hard X-ray emission of solar flares can enable insights into the non-thermal energetic particle properties created during these eruptive events. Depending on the coronal densities and plasma properties, a part of the non-thermal electron population can be trapped at the loop-top. Theory suggest that the coronal region at the loop-top is the main acceleration site for electrons. At high energies, however, the bright footpoint emission from the flare loops can prevent a detailed analysis of the usually weaker loop-top source due to the limited dynamic range of instruments like RHESSI. Thus, flares close to the solar limb, where the footpoints are occulted, are interesting events to study because they can reveal the emission in this region in isolation. Here, we report on recent findings of a statistical study of such events, comprising of about 120 flares during solar cycles 23 and 24 (Ref. [1]).

It is interesting to also study the so-called Neupert effect (Ref. [2]) in this context of coronal sources. This is an empirically observed correlation in solar flares, which relates the changes (i.e. the time derivative) in the soft X-ray (SXR) flux to the temporal hard X-ray (HXR) variations. It is usually assumed that the HXRs originate in strong footpoint emissions from accelerated electron beams hitting the transition region and chromosphere. This in turn can lead to heating processes, increasing the overall SXR and extreme ultraviolet (EUV) emission, as observed by the GOES satellites. Here, we interestingly found this relation to hold also for a large fraction of flares when only observed as coronal sources above the limb.


Figure 1: The solar disk positions of the partially occulted flares selected (C-Class: dark green; M-Class: dark blue; X-Class: light green) in context of all C-Class and above flares from the RHESSI flare catalog till end of 2015 (yellow and red colors). The size of the circles is scaled with the observed GOES level and the solar limb is drawn at 940 to guide the eye. We omitted outliers with latitudes more or less than +-600", respectively.

Occulted Flare Selection and Results

An earlier analysis studied 55 partially occulted flares from solar cycle 23 were already analyzed in Ref. [3]. We extended this list with selection criteria based on flares from the RHESSI list with significant counts at energies of 25 keV and occulted footpoints, having their centroid position above the solar limb. We studied 61 flares from solar cycle 24 in addition to the 55 from cycle 23. Figure 1 shows their distribution on the solar disk.

Using GOES, SDO/AIA, and RHESSI we performed a spectral analysis, a light curve correlation between different wavelength ranged, and X-ray imaging to study the spatial relation between soft and hard X-rays.

Spectral Analysis

Two kinds of spectral analysis were performed: a fit of the observed photon spectrum by a thermal spectrum plus broken power-law model, and a fit to a thermal spectrum plus a kappa spectral model for the flux of accelerated electrons.

Figure 2 shows the resulting spectral index κ versus the photon index γ. The mean values are <γ> 5.7, similar to the previously reported value of 5.4, and <κ> = 5.4. These are softer than what is found for the high-energy index of disk flares, which contain the footpoint emission with harder spectrum.

Figure 2: Correlation between the broken power-law photon spectral index γ and the electron κ index values of the thermal plus thin-target kappa fit for the data of both solar cycles (cycle 23: blue stars, cycle 24: red circles). The black dashed line shows the result of a linear fit to the complete data set (κ = 1.15γ - 0.83). The green dotted line indicates the theoretical thin-target relation.

The relation between the electron flux spectral index δ and the electron kappa distribution index $\kappa$ is δ = κ. In the thin-target case, we expect δ = κ - 1 (the green dotted line in Figure 2). A linear-least-square fit to the fitting parameters gives δ = 0.83κ -1.15 (black dashed line).


Spatial separation of thermal and non-thermal emission

Images in a low 6-14 keV and high-energy (>20 keV) range allow us to estimate the radial separation between the thermal and non-thermal emission, by measuring the distance dmax between the maximum of both sources (see Figure 2).

Figure 3: SDO/AIA 131 &Aring: emission and RHESSI X-ray at 614 keV (red) and 2230 keV (blue) contours for the M1.4 class flare SOL2014-10-22, and the C8.2-class flare SOL2014-10-31. October 22 and an C8.2 class flare from 2014 October 31. The rightmost panel shows the frequency distribution of the radial separation between the low and high energy X-ray sources (positive values mean that the non-thermal source is located farther away from the limb than the thermal component.

Although we did not find a clear tendency toward positive or negative separations between both sources,<dmax> = 0.3 Mm, which may imply that higher-energy emission is radially farther out in the corona.

Light-curves and the Neupert effect

We analyzed the time evolution of the hard X-ray flux measured by RHESSI and compared it with the temporal derivative of the soft X-ray flux measured by GOES at (0.5-4 Å). We calculated the linear correlation between soft and hard X-rays.

Figure 4: Left: Light curves of {\it RHESSI} count rates of the flare SOL2014-09-11 (M2.1) at four energy ranges (red, blue, purple and green). The GOES high energy (0.5-4 Å) and low energy (1-8 Å) fluxes are plotted as solid and dashed grey lines, while their derivatives are given by the respective black lines. The counts in the two high energy RHESSI channels are multiplied by 20 and 15, respectively, to make them comparable in magnitude. Right: Correlation coefficients for the complete ensemble of partially occulted flares as calculated from the light curve cross-correlation analysis of the GOES soft X-ray time derivative (low channel: red; high channel: blue) and the

In Figure 4 we find that the 25-50 keV RHESSI energy channel correlates well with the GOES time derivative during the rise phase, with a small temporal lag. The statistical results for the correlation coefficient are significant for a large fraction of flares in the sample.

Conclusions

The three parts of the study of occulted flares allow us to conclude

• Spectra of occulted flares tend to be softer than general disk flares with the relation between the photon and electron indexes in rough agreement with that expected in a thin-target model;

• There is no clear trend for large positive or negative radial separations between low and high energy hard X-ray components. There are, however, notable exceptions with larger separations and a richer coronal source structure;

• There is a significant correlation between the time derivative of the soft X-ray and the observed hard X-rays light curves for a large fraction of our sample, consistent with earlier studies for on-disk flares (Ref. [5]).

This latter conclusions indicates the presence of the simple Neupert effect for purely coronal sources and supports the scenario that the main source of non-thermal particles is produced near the looptop. The lags found in some flares indicate that additional processes like thermal conduction can play important roles.

References

[1] "Hard X-Ray Emission from Partially Occulted Solar Flares: RHESSI Observations in Two Solar Cycles"

[2] "Comparison of Solar X-Ray Line Emission with Microwave Emission during Flares"

[3] "Hard X-ray emission from the solar corona"

[4] "Kappa distribution and hard X-ray emission of solar flares"

[5] "Investigation of the Neupert effect in solar flares"

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