Hard X-ray Emission from Partially Occulted Solar Flares

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|number = 291
|number = 291
|first_author = Frederic Effenberger
|first_author = Frederic Effenberger
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|second_author = and Fatima Rubio da Costa
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|second_author = Fatima Rubio da Costa
|publish_date = 30 January 2017
|publish_date = 30 January 2017
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|next_nugget = Eclipses
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|next_nugget={{#ask: [[Category:Nugget]] [[RHESSI Nugget Index::292]]}}
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|previous_nugget = [http://sprg.ssl.berkeley.edu/~tohban/wiki/index.php/GOES_Hard_X-rays%3F GOES Hard X-rays?]
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|previous_nugget={{#ask: [[Category:Nugget]] [[RHESSI Nugget Index::290]]}}
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=== Introduction ===
+
== Introduction ==
Hard X-ray emission of solar flares can enable insights  
Hard X-ray emission of solar flares can enable insights  
into the non-thermal energetic particle properties created during these eruptive events.  
into the non-thermal energetic particle properties created during these eruptive events.  
Depending on the coronal densities and plasma properties, a  
Depending on the coronal densities and plasma properties, a  
-
part of the non-thermal electron population can be trapped at the loop-top.  
+
part of the non-thermal electron population can be trapped in coronal magnetic fields.
-
Theory suggest that the coronal region at the loop-top is the  
+
Theory suggests that the coronal region at the top of magnetic loops may be the  
main acceleration site for electrons.  
main acceleration site for electrons.  
-
At high energies, however, the bright footpoint emission from the flare  
+
At high energies, however, the bright footpoint emission from these flare  
-
loops can prevent a detailed analysis of the usually weaker loop-top  
+
loops can obscure weaker loop-top sources due to the limited dynamic range of instruments like RHESSI.  
-
source due to the limited dynamic range of instruments like RHESSI.  
+
Thus, flares close to the solar limb, where the footpoints are occulted,   
Thus, flares close to the solar limb, where the footpoints are occulted,   
are interesting events to study because they can reveal the  
are interesting events to study because they can reveal the  
-
emission in this region in isolation. Here, we report on recent findings  
+
emission in this region in isolation.  
-
of a statistical study of such events, comprising of about 120  
+
This method has revealed [http://sprg.ssl.berkeley.edu/~tohban/wiki/index.php/A_new_development_in_the_Frost-Dennis_paradigm many things].
 +
Here, we report on recent findings  
 +
of a statistical study of occulted events, comprising of about 120  
flares during solar cycles 23 and 24 (Ref. [1]).
flares during solar cycles 23 and 24 (Ref. [1]).
-
It is interesting to also study the so-called Neupert effect (Ref. [2])
+
It is interesting to also study the so-called Neupert effect (Ref. [2]) in this context of coronal sources.  
-
in this context of coronal sources. This is an empirically observed
+
The [http://sprg.ssl.berkeley.edu/~tohban/wiki/index.php/EVE/ESP_and_the_Neupert_Effect Neupert effect] is an empirical
correlation in solar flares, which relates the changes (i.e. the
correlation in solar flares, which relates the changes (i.e. the
time derivative) in the soft X-ray (SXR) flux to the temporal hard
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
+
X-ray (HXR) variations.  
-
in strong footpoint emissions from accelerated electron beams hitting
+
These HXRs tend strongly to originate in the footpoint regions, leading to the "thick target" interpretation
-
the transition region and chromosphere. This in turn can lead to
+
of  coronally accelerated electron beams hitting
 +
the transition region and chromosphere.  
 +
This in turn can lead to
heating processes, increasing the overall SXR and extreme ultraviolet
heating processes, increasing the overall SXR and extreme ultraviolet
-
(EUV) emission, as observed by the GOES satellites. Here, we
+
(EUV) emission, as observed by the  
-
interestingly found this relation to hold also for a large fraction
+
[http://sprg.ssl.berkeley.edu/~tohban/wiki/index.php/GOES_Hard_X-rays%3F GOES] photometers.  
-
of flares when only observed as coronal sources above the limb.
+
-
 
+
[[File:291f1.png|500px|thumb|center|  
-
[[File:291f1.png|600px|thumb|center|  
+
Figure 1: The solar disk positions of the partially occulted flares
Figure 1: The solar disk positions of the partially occulted flares
selected (C-Class: dark green; M-Class: dark blue; X-Class: light
selected (C-Class: dark green; M-Class: dark blue; X-Class: light
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flare catalog till end of 2015 (yellow and red colors). The size
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
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
+
limb is drawn at 940" to guide the eye. We omitted outliers with
latitudes more or less than +-600", respectively.
latitudes more or less than +-600", respectively.
]]
]]
-
=== Occulted Flare Selection and Results ===
+
== Occulted Flare Selection and Results ==
-
An earlier analysis studied 55 partially occulted flares from solar cycle  
+
An earlier analysis studied 55 partially occulted flares from solar cycle 23 (Ref. [3]).  
-
23 were already analyzed in Ref. [3].  
+
We have now extended this list to Cycle 24 with selection criteria based on flares from the  
-
We extended this list with selection criteria based on flares from the  
+
RHESSI [http://sprg.ssl.berkeley.edu/~tohban/wiki/index.php/Hsi_flare_list_fill:_How_the_RHESSI_Flare_List_is_Generated flare catalog],
-
RHESSI list
+
requiring significant counts at energies of 25 keV and occulted footpoints as indicated by having the centroid position above the solar limb.  
-
with significant counts at energies of 25 keV and occulted footpoints,
+
We studied 61 flares from solar cycle 24 in addition to the 55 from cycle 23.
-
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.
Figure 1 shows their distribution on the solar disk.
-
Using GOES, SDO/AIA, and RHESSI we performed a spectral analysis,
+
Using  
-
a light curve correlation between different wavelength ranged, and
+
[http://www.swpc.noaa.gov/products/goes-x-ray-flux GOES],  
 +
[http://aia.lmsal.com SDO/AIA], and RHESSI we performed a spectral analysis,
 +
a light curve correlation between different wavelength ranges, and
X-ray imaging to study the spatial relation between soft and hard
X-ray imaging to study the spatial relation between soft and hard
X-rays.
X-rays.
-
=== Spectral Analysis ===
+
== Spectral Analysis ==
-
Two kinds of spectral analysis were performed:  
+
We performed two kinds of [http://sprg.ssl.berkeley.edu/~tohban/wiki/index.php/OSPEX_Users_Guide spectral analysis]:   
-
  The first is a fit of the observed photon spectrum by a thermal plus broken power-law model.
+
a ''thermal'' spectrum (see [http://www.chiantidatabase.org CHIANTI]) plus the usual ''ad hoc'' broken power-law model to describe
-
The second method fits the observed photon spectrum to a thermal plus a kappa spectral model for the flux of accelerated electrons.
+
the accelerated electrons, and a thermal spectrum plus a  
 +
[http://www.lesia.obspm.fr/perso/michel-moncuquet/theseweb/tempioweb/node12.html kappa-distribution] spectral model for the accelerated electrons.
Figure 2 shows the resulting spectral index κ versus the
Figure 2 shows the resulting spectral index κ versus the
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spectrum.
spectrum.
-
[[File:291f2.png|600px|thumb|center|  
+
[[File:291f2.png|500px|thumb|center|  
Figure 2: Correlation between the broken power-law photon spectral
Figure 2: Correlation between the broken power-law photon spectral
index γ and the electron κ index values of the thermal
index γ and the electron κ index values of the thermal
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The relation between the electron flux spectral index δ and
The relation between the electron flux spectral index δ and
-
the electron kappa distribution index $\kappa$ is δ = κ.
+
the electron kappa distribution index is δ = κ.
-
In the thin-target case, we expect δ = κ - 1
+
In the thin-target case, we expect δ = 1.15κ - 0.83
(the green dotted line in Figure 2).  
(the green dotted line in Figure 2).  
A linear-least-square fit to the
A linear-least-square fit to the
fitting parameters gives δ = 0.83κ -1.15 (black dashed line).
fitting parameters gives δ = 0.83κ -1.15 (black dashed line).
-
== Spatial separation of thermal and non-thermal emission ==
+
 
 +
=== Spatial separation of thermal and non-thermal emission ===
Images in a low 6-14 keV and high-energy (>20 keV) range
Images in a low 6-14 keV and high-energy (>20 keV) range
allow us to estimate the radial separation between the thermal and
allow us to estimate the radial separation between the thermal and
non-thermal emission, by measuring the distance d<sub>max</sub>
non-thermal emission, by measuring the distance d<sub>max</sub>
-
between the maximum of both sources (see Figure 2).
+
between the maximum of both sources (see Figure 3).
-
 
+
[[File:291f3.png|700px|thumb|center|  
-
[[File:291f3.png|600px|thumb|center|  
+
Figure 3:  SDO/AIA 131 &Aring; emission and RHESSI X-ray at 6-14 keV
-
Figure 3:  SDO/AIA 131 &Aring: emission and RHESSI X-ray at 614 keV
+
(red) and 22-30 keV (blue) contours for the M1.4 class flare  
-
(red) and 2230 keV (blue) contours for the M1.4 class flare  
+
SOL2014-10-22, and the C8.2-class flare SOL2014-10-31.
SOL2014-10-22, and the C8.2-class flare SOL2014-10-31.
October 22 and an C8.2 class flare from 2014 October 31.  
October 22 and an C8.2 class flare from 2014 October 31.  
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corona.
corona.
-
== Light-curves and the Neupert effect ==
+
=== Light-curves and the Neupert effect ===
We analyzed the time evolution of the hard X-ray flux measured by
We analyzed the time evolution of the hard X-ray flux measured by
RHESSI and compared it with the temporal derivative of the
RHESSI and compared it with the temporal derivative of the
-
soft X-ray flux measured by GOES at (0.5-4 &Aring;). We calculated the
+
soft X-ray flux measured by GOES at 0.5-4 &Aring;. We calculated the
linear correlation between soft and hard X-rays.
linear correlation between soft and hard X-rays.
[[File:291f4.png|600px|thumb|center|  
[[File:291f4.png|600px|thumb|center|  
-
Figure 4: Left: Light curves of {\it RHESSI} count rates of the flare
+
Figure 4: Left: Light curves of RHESSI count rates of the flare
SOL2014-09-11 (M2.1)
SOL2014-09-11 (M2.1)
at four energy ranges (red, blue,
at four energy ranges (red, blue,
-
purple and green). The {\it GOES} high energy (0.5-4 &Aring;) and low
+
purple and green). The GOES high energy (0.5-4 &Aring;) and low
energy (1-8 &Aring;) fluxes are plotted as solid and dashed grey
energy (1-8 &Aring;) fluxes are plotted as solid and dashed grey
lines, while their derivatives are given by the respective black
lines, while their derivatives are given by the respective black
-
lines. The counts in the two high energy {\it RHESSI} channels are
+
lines. The counts in the two high energy RHESSI channels are
multiplied by 20 and 15, respectively, to make them comparable in
multiplied by 20 and 15, respectively, to make them comparable in
magnitude. Right: Correlation coefficients for the complete ensemble
magnitude. Right: Correlation coefficients for the complete ensemble
of partially occulted flares as calculated from the light curve
of partially occulted flares as calculated from the light curve
-
cross-correlation analysis of the \emph{GOES} soft X-ray time
+
cross-correlation analysis of the GOES soft X-ray time
derivative (low channel: red; high channel: blue) and the  
derivative (low channel: red; high channel: blue) and the  
]]
]]
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flares in the sample.
flares in the sample.
-
=== Conclusion ===
+
== Conclusions ==
 +
 
The three parts of the study of occulted flares allow us to conclude
The three parts of the study of occulted flares allow us to conclude
-
that
+
 
-
  (1) 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;
+
&bull; 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;
-
  (2) 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;  
+
 
-
  (3)~we found 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]).  
+
&bull; 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;  
 +
 
 +
&bull; 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
This latter conclusions indicates  the
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can play important roles.
can play important roles.
-
=== References ===
+
== References ==
[1] [http://adsabs.harvard.edu/abs/2016arXiv161202856E "Hard X-Ray Emission from Partially Occulted Solar Flares: RHESSI Observations in Two Solar Cycles"]
[1] [http://adsabs.harvard.edu/abs/2016arXiv161202856E "Hard X-Ray Emission from Partially Occulted Solar Flares: RHESSI Observations in Two Solar Cycles"]

Latest revision as of 19:01, 22 August 2018


Nugget
Number: 291
1st Author: Frederic Effenberger
2nd Author: 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 in coronal magnetic fields. Theory suggests that the coronal region at the top of magnetic loops may be the main acceleration site for electrons. At high energies, however, the bright footpoint emission from these flare loops can obscure weaker loop-top sources 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. This method has revealed many things. Here, we report on recent findings of a statistical study of occulted 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. The Neupert effect is an empirical 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. These HXRs tend strongly to originate in the footpoint regions, leading to the "thick target" interpretation of coronally 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 photometers.

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 (Ref. [3]). We have now extended this list to Cycle 24 with selection criteria based on flares from the RHESSI flare catalog, requiring significant counts at energies of 25 keV and occulted footpoints as indicated by having the 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 ranges, and X-ray imaging to study the spatial relation between soft and hard X-rays.

Spectral Analysis

We performed two kinds of spectral analysis: a thermal spectrum (see CHIANTI) plus the usual ad hoc broken power-law model to describe the accelerated electrons, and a thermal spectrum plus a kappa-distribution spectral model for the 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 is δ = κ. In the thin-target case, we expect δ = 1.15κ - 0.83 (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 3).

Figure 3: SDO/AIA 131 Å emission and RHESSI X-ray at 6-14 keV (red) and 22-30 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 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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