Slowly but surely towards the huge amount of energy II

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|name = Nugget
|name = Nugget
|title = Slowly but surely towards the huge amount of energy II
|title = Slowly but surely towards the huge amount of energy II
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|number = 163
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|number = 164
|first_author = Sylwester Kołomański
|first_author = Sylwester Kołomański
|second_author = Tomasz Mrozek
|second_author = Tomasz Mrozek
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|publish_date = 14 November 2011
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|publish_date = 28 November 2011
|next_nugget = Hα and Hard X-rays
|next_nugget = Hα and Hard X-rays
|previous_nugget = [http://sprg.ssl.berkeley.edu/~tohban/wiki/index.php/Slowly_but_surely_towards_the_huge_amount_of_energy_I]
|previous_nugget = [http://sprg.ssl.berkeley.edu/~tohban/wiki/index.php/Slowly_but_surely_towards_the_huge_amount_of_energy_I]
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== A search for extreme ==
== A search for extreme ==
-
How much energy does a solar flare need to exist? How much energy must be accumulated in magnetic field before a flare starts? And how fast the accumulated energy must be released? Should it be discharged in short time during flare initial (impulsive) stage? Or should it leak continuously throughout entire flare duration? These are one of the basic questions in solar physics. Answers will help us to understand solar and stellar flares.
+
How much energy does a solar flare need to exist? How much energy must be accumulated in magnetic field before a flare starts? And how fast the accumulated energy must be released? Should it be discharged in short time during the flare initial (impulsive) stage? Or should it leak continuously throughout the entire flare duration? These are ones of the basic questions in solar physics. Answers will help us to understand solar and stellar flares.
-
In our search for the answer we decided to go to extreme. We chose flares which last very long, so-called long duration events. A long duration event (LDE) is a solar flare characterized by a slow decrease in X-ray thermal emission (see Figure 1). This decrease may last from several hours to more than a day. Studies of LDEs based on past solar space missions (Skylab, Yohkoh) resulted inter alia in conclusion is that, without the continuous energy input during the whole decay phase, LDEs would decay much faster than observed. If energy is continuously released during many hours of the decay, i.e. LDEs may be extremely energy hungry. But which part of LDE is the best tool to find out how much energy is generated?
+
To answer the questions we decided to go to the extreme in our search. We chose flares that last very long, so-called long duration events. A long duration event (LDE) is a solar flare characterized by a slow decrease in X-ray thermal emission (see Figure 1). This decrease may last from several hours to more than a day. Studies of LDEs based on past solar space missions ([http://en.wikipedia.org/wiki/Skylab Skylab], [http://en.wikipedia.org/wiki/Yohkoh Yohkoh]) resulted inter alia in conclusion that, without the continuous energy input during the whole decay phase, LDEs would decay much faster than observed. If energy is continuously released during many hours of the decay, i.e. LDEs may be extremely energy hungry. But which part of an LDE is the best tool to find out how much energy is generated?
[[File:163f1.jpg|thumb|center|700px|'''Figure 1''':
[[File:163f1.jpg|thumb|center|700px|'''Figure 1''':
-
Comparison of the decay phase for a long duration event (SOL2005-07-30)and a typical flare (SOL2002-08-03)
+
Comparison of the decay phase for a long duration event (SOL2005-07-30) and a typical flare (SOL2002-08-03).
]]
]]
-
Coronal sources called loop-top sources (LTSs) are observed in every flare. LTSs are remarkable X-rays features seen close to a flare loop apex. They form before flare maximum, and in LDEs they may last many hours. LTSs should be located close to the primary energy release site. Thus, they are a very promising tool for analysing of an energy release during the decay phase. The most demanding case for the energy release is the long-lasting X-ray emission from LTSs seen in LDE flares.  If a long-lasting X-ray source is thermal, then it must be continuously heated, because the characteristic radiative cooling time of hot (above 10MK) and dense (≈ 10<sup>10</sup> cm<sup>-3</sup>) plasma is ≈ 1 hour. If an X-ray source is non-thermal then there should be a continuous acceleration of particles, to counteract fast thermalization of non-thermal electrons. The timescale of the thermalization in the sense of momentum loss of electrons is about several seconds.
+
Coronal sources called loop-top sources (LTSs) are observed in every flare. LTSs are remarkable X-rays features seen close to a flare loop apex. They form before the flare maximum, and in LDEs they may last many hours. LTSs should be located close to the primary energy release site. Thus, they are a very promising tool for analysing energy release during the decay phase. The most demanding case for the energy release is long-lasting X-ray emission from LTSs seen in LDE flares.  If a long-lasting X-ray source is thermal, then it must be continuously heated, because the characteristic radiative cooling time of hot (above 10MK) and dense (≈ 10<sup>10</sup> cm<sup>-3</sup>) plasma is ≈ 1 hour. If an X-ray source is non-thermal then there should be a continuous acceleration of particles, to counteract fast thermalization of non-thermal electrons. The timescale of the thermalization in the sense of momentum loss of electrons is about several seconds.
-
Knowing all these we decided to do the search for how much energy can be produced during flares by study LTSs of long duration flares. RHESSI satellite was chosen as a source of observational data because of its high sensitivity and high angular and energy resolutions. A sample of LDEs lasting at least for 7 hours was selected.
+
Knowing all these we decided to do the search for how much energy can be produced during flares by studying LTSs of long duration flares. RHESSI satellite was chosen as a source of observational data because of its high sensitivity and high angular and energy resolutions. A sample of LDEs lasting at least 7 hours was selected.
==How to see a weak source?==
==How to see a weak source?==
-
It is a large difficulty to reconstruct a RHESSI image when an emitting source is weak. And LTSs are weak at very late decay phase indeed. Usually RHESSI image reconstruction is performed for detectors nos. 3–6, 8, 9. However, we were not able to reconstruct any reliable image in a case of very late phase of LDE decay with the use of this standard set of grids. The weak signal was not the problem since by taking integration times up to several minutes we were able to collect enough counts, i.e. about several thousand. The problem may be solved if we remember that when the source size is comparable to the resolution of a particular grid, then the detector records very weak or no modulation of the signal (Hurford et al. 2002). The resulting image obtained for this grid is then dominated by noise. This grid added to the set used for reconstruction introduces noise only. In the worst case we may not get convergence of the reconstruction algorithm. Thus, we used only these grids for which detector recorded significant modulation and reconstructed images showed a definite source in a single detector image.
+
It is a large difficulty to reconstruct a RHESSI image when an emitting source is weak. And LTSs are weak at very late decay phase indeed. Usually RHESSI image reconstruction is performed for detectors nos. 3–6, 8, 9. However, we were not able to reconstruct any reliable image in a case of a very late phase of the LDE decay with the use of this standard set of grids. The weak signal was not the problem since by taking integration times up to several minutes we were able to collect enough counts, i.e. about several thousands. The problem may be solved if we remember that when a source size is comparable to the resolution of a particular grid, then the detector records very weak modulation or even no modulation of the signal ([http://adsabs.harvard.edu/abs/2002SoPh..210...61H Hurford et al. 2002]). The resulting image obtained for this grid is then dominated by noise. This grid added to the set used for reconstruction introduces noise only. In the worst case we may not get convergence of the reconstruction algorithm. Thus, we used only these grids, for which detector recorded significant modulation and reconstructed images showed a definite source in a single detector image.
-
The images used in further analysis were reconstructed with a PIXON algorithm in very narrow (1 keV) energy intervals. With described method of selection of detectors we were able to obtain good quality images up to 20 keV in the early decay and up to 10 keV in very late decay of the LDE flares. It enabled us to obtain reliable fits to observed spectra of loot-top sources.
+
The images used in further analysis were reconstructed with a PIXON algorithm in very narrow (1 keV) energy intervals. With described method of selection of detectors we were able to obtain good quality images up to 20 keV in the early decay and up to 10 keV in the very late decay of the LDE flares. It enabled us to obtain reliable fits to observed spectra of loot-top sources.
==Searching for energy with RHESSI==
==Searching for energy with RHESSI==
-
To find out how effective the energy release and heating processes are at the decay phase of LDEs we calculated the energy balance of the observed LTS based on physical parameters estimated through imaging spectroscopy. Change of thermal energy of a loop-top source is due to some processes which cool and heat plasma of the source. Three major cooling processes where included into our calculations: expansion, radiation and conduction. Knowing the change of LTS thermal energy and values of the three cooling processes we can calculate if and how efficiently the LTS was heated. The equation of energy balance can be written as follows:
+
To find out how effective energy release and heating processes are at the decay phase of LDEs we calculated the energy balance of the observed LTS based on physical parameters estimated through imaging spectroscopy. A change of thermal energy of a loop-top source is due to some processes that cool and heat plasma of the source. Three major cooling processes where included into our calculations: expansion, radiation and conduction. Knowing the change of LTS thermal energy and values of the three cooling processes we can calculate if and how efficiently the LTS was heated. The equation of energy balance can be written as follows:
observed change of thermal energy = adiabatic expansion − conductive cooling − radiative cooling + heating rate
observed change of thermal energy = adiabatic expansion − conductive cooling − radiative cooling + heating rate
-
Having the heating rate EH estimated we are able to calculate the total thermal energy deposited in a LTS during the whole decay of a flare. The calculation was done under following assumptions: '''(a)''' duration of a flare was taken from GOES 1-8 Å lightcurve, '''(b)''' volume was calculated from the mean area of the source as seen in images, assuming a sphere with a constant volume during the whole decay phase. With the first assumption involved one obtain the lower limit of the total thermal energy released during decay of LDEs.
+
Having the heating rate E<sub>H</sub> estimated we are able to calculate the total thermal energy deposited in an LTS during the whole decay of a flare. The calculation was done under the following assumptions: '''(a)''' duration of a flare was taken from GOES 1-8 Å lightcurve, '''(b)''' volume was calculated from the mean area of a source as seen in images, assuming a sphere with a constant volume during the whole decay phase. With the first assumption involved one obtains the lower limit of the total thermal energy released during the decay of LDEs.
[[File:163f2.jpg|thumb|right|500px|'''Figure 2''':
[[File:163f2.jpg|thumb|right|500px|'''Figure 2''':
Line 46: Line 46:
==Slow but energy hungry==
==Slow but energy hungry==
-
Estimated values of heating rates EH are low, usually about 1 erg cm<sup>− 3</sup> s<sup>− 1</sup> at very early stage of decay and may drop below 10<sup>2</sup> erg cm<sup>-3</sup> s<sup>-1</sup>  at the end of decay,  But EH is never equal to zero, i.e. LTSs need to be ‘fed‘ with energy with no interruptions for many hours. Even with such low heating rate an LTS of typical volume of the of 10<sup>28</sup> cm<sup>3</sup> existing for 10 hours needs in total about 10<sup>31</sup> erg of thermal energy to be visible as it is. And 10<sup>31</sup> erg is just the thermal energy released to sustain only long-lasting LTS. Energy released in LDEs surely is not deposited only in loop-top sources and only as a thermal energy. Thus total energy ‘produced’ by LDE during the decay must by larger than 10<sup>31</sup> erg.  This is huge amount of energy which can be higher than energy released during the impulsive phase of a flare (Jiang et al., 2006). This severe requirement should be taken into account when building a model of solar flares. But a flare is not only the decay. Energy is also released during the rise.
+
Estimated values of heating rates E<sub>H</sub> are low, usually about 1 erg cm<sup>− 3</sup> s<sup>− 1</sup> at a very early stage of the decay and may drop below 10<sup>2</sup> erg cm<sup>-3</sup> s<sup>-1</sup>  at the end of the decay,  But E<sub>H</sub> is never equal to zero, i.e. LTSs need to be ‘fed‘ with energy continuously for many hours. Even with such a low heating rate an LTS of typical volume of the of 10<sup>28</sup> cm<sup>3</sup> existing for 10 hours needs in total about 10<sup>31</sup> erg of thermal energy to be visible as it is. And 10<sup>31</sup> erg is just the thermal energy released to sustain only long-lasting LTS. Energy released in LDEs surely is not deposited only in loop-top sources and only as thermal energy. Thus total energy ‘produced’ by an LDE during the decay must be larger than 10<sup>31</sup> erg.  This is huge amount of energy, which can be higher than energy released during the impulsive phase of a flare ([http://adsabs.harvard.edu/abs/2006ApJ...638.1140J Jiang et al., 2006]). This severe requirement should be taken into account when building models of a solar flare. But a flare is not only the decay. Energy is also released during the rise.
==A powerful example==
==A powerful example==
-
As an example of how much energy can be generated during whole flare we took the SOL2007-01-25T07:14 event. This was so-called slow long duration event (SLDE), i.e. it had not only slow decay but also slow rise. In total the flare lasted almost 18 hours (GOES 1-8 Å lightcurve). In the first part of “Slowly but surely towards the huge amount of energy” we estimated that during the rise of the flare there was released at least 1.5×1031 erg of thermal energy. During the decay there was additional 2.2×10<sup>31</sup> erg of thermal energy. Thus in total the event must generated at least about 4×10<sup>31</sup> erg, although it was ‘just’ C6.3 x-ray class flare.
+
As an example of how much energy can be generated during the whole flare we took the SOL2007-01-25T07:14 event. This was so-called slow long duration event (SLDE), i.e. it had not only slow decay but also slow rise. In total the flare lasted almost 18 hours (GOES 1-8 Å lightcurve). In the first part of “[[Slowly but surely towards the huge amount of energy I]]” we estimated that during the rise of the flare there was released at least 1.5×10<sup>31</sup> erg of thermal energy. During the decay there was additional 2.2×10<sup>31</sup> erg of thermal energy. Thus in total the event had to generate at least about 4×10<sup>31</sup> erg, although it was ‘just’ C6.3 x-ray class flare.
==Acknowledgements==
==Acknowledgements==
Line 60: Line 60:
== References ==
== References ==
-
[1] [http://adsabs.harvard.edu/abs/2005SoPh..231...95B "Investigation of X-Ray Flares with Long Rising Phases"]
+
[1] [http://adsabs.harvard.edu/abs/2011A%26A...531A..57K "RHESSI observations of long-duration flares with long-lasting X-ray loop-top sources"]
[2] [http://adsabs.harvard.edu/abs/2011CEAB...35..103M "RHESSI Investigation of X-Ray Coronal Sources During the Decay Phase of Solar Flares: I. Observations"]
[2] [http://adsabs.harvard.edu/abs/2011CEAB...35..103M "RHESSI Investigation of X-Ray Coronal Sources During the Decay Phase of Solar Flares: I. Observations"]
-
[3] [http://adsabs.harvard.edu/abs/2011CEAB...35..115K "RHESSI investigation of X-ray coronal sources during the decay phase of solar flares: II. energy balance"]
+
[3] [http://adsabs.harvard.edu/abs/2011CEAB...35..115K "RHESSI investigation of X-ray coronal sources during the decay phase of solar flares: II. Energy balance"]

Revision as of 15:11, 9 November 2011


Nugget
Number: 164
1st Author: Sylwester Kołomański
2nd Author: Tomasz Mrozek
Published: 28 November 2011
Next Nugget: Hα and Hard X-rays
Previous Nugget: [1]
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Contents

A search for extreme

How much energy does a solar flare need to exist? How much energy must be accumulated in magnetic field before a flare starts? And how fast the accumulated energy must be released? Should it be discharged in short time during the flare initial (impulsive) stage? Or should it leak continuously throughout the entire flare duration? These are ones of the basic questions in solar physics. Answers will help us to understand solar and stellar flares.

To answer the questions we decided to go to the extreme in our search. We chose flares that last very long, so-called long duration events. A long duration event (LDE) is a solar flare characterized by a slow decrease in X-ray thermal emission (see Figure 1). This decrease may last from several hours to more than a day. Studies of LDEs based on past solar space missions (Skylab, Yohkoh) resulted inter alia in conclusion that, without the continuous energy input during the whole decay phase, LDEs would decay much faster than observed. If energy is continuously released during many hours of the decay, i.e. LDEs may be extremely energy hungry. But which part of an LDE is the best tool to find out how much energy is generated?

Figure 1: Comparison of the decay phase for a long duration event (SOL2005-07-30) and a typical flare (SOL2002-08-03).

Coronal sources called loop-top sources (LTSs) are observed in every flare. LTSs are remarkable X-rays features seen close to a flare loop apex. They form before the flare maximum, and in LDEs they may last many hours. LTSs should be located close to the primary energy release site. Thus, they are a very promising tool for analysing energy release during the decay phase. The most demanding case for the energy release is long-lasting X-ray emission from LTSs seen in LDE flares. If a long-lasting X-ray source is thermal, then it must be continuously heated, because the characteristic radiative cooling time of hot (above 10MK) and dense (≈ 1010 cm-3) plasma is ≈ 1 hour. If an X-ray source is non-thermal then there should be a continuous acceleration of particles, to counteract fast thermalization of non-thermal electrons. The timescale of the thermalization in the sense of momentum loss of electrons is about several seconds.

Knowing all these we decided to do the search for how much energy can be produced during flares by studying LTSs of long duration flares. RHESSI satellite was chosen as a source of observational data because of its high sensitivity and high angular and energy resolutions. A sample of LDEs lasting at least 7 hours was selected.


How to see a weak source?

It is a large difficulty to reconstruct a RHESSI image when an emitting source is weak. And LTSs are weak at very late decay phase indeed. Usually RHESSI image reconstruction is performed for detectors nos. 3–6, 8, 9. However, we were not able to reconstruct any reliable image in a case of a very late phase of the LDE decay with the use of this standard set of grids. The weak signal was not the problem since by taking integration times up to several minutes we were able to collect enough counts, i.e. about several thousands. The problem may be solved if we remember that when a source size is comparable to the resolution of a particular grid, then the detector records very weak modulation or even no modulation of the signal (Hurford et al. 2002). The resulting image obtained for this grid is then dominated by noise. This grid added to the set used for reconstruction introduces noise only. In the worst case we may not get convergence of the reconstruction algorithm. Thus, we used only these grids, for which detector recorded significant modulation and reconstructed images showed a definite source in a single detector image.

The images used in further analysis were reconstructed with a PIXON algorithm in very narrow (1 keV) energy intervals. With described method of selection of detectors we were able to obtain good quality images up to 20 keV in the early decay and up to 10 keV in the very late decay of the LDE flares. It enabled us to obtain reliable fits to observed spectra of loot-top sources.

Searching for energy with RHESSI

To find out how effective energy release and heating processes are at the decay phase of LDEs we calculated the energy balance of the observed LTS based on physical parameters estimated through imaging spectroscopy. A change of thermal energy of a loop-top source is due to some processes that cool and heat plasma of the source. Three major cooling processes where included into our calculations: expansion, radiation and conduction. Knowing the change of LTS thermal energy and values of the three cooling processes we can calculate if and how efficiently the LTS was heated. The equation of energy balance can be written as follows:

observed change of thermal energy = adiabatic expansion − conductive cooling − radiative cooling + heating rate

Having the heating rate EH estimated we are able to calculate the total thermal energy deposited in an LTS during the whole decay of a flare. The calculation was done under the following assumptions: (a) duration of a flare was taken from GOES 1-8 Å lightcurve, (b) volume was calculated from the mean area of a source as seen in images, assuming a sphere with a constant volume during the whole decay phase. With the first assumption involved one obtains the lower limit of the total thermal energy released during the decay of LDEs.

Figure 2: The SOL2007-01-25T07:14 long duration event. The upper panel: RHESSI light curves. Vertical lines mark the boundaries of the satellite night (N) and the SAA (S) periods (solid and dashed lines mark the beginnings and ends of the periods, respectively). The light curves were shifted vertically for clarity. The intensity is given in relative units. The lower panel: SoHO/EIT 195 Å images illustrating the decay phase of the flare. Contours show the emission in the 7 − 8 keV range observed with RHESSI.

Slow but energy hungry

Estimated values of heating rates EH are low, usually about 1 erg cm− 3 s− 1 at a very early stage of the decay and may drop below 102 erg cm-3 s-1 at the end of the decay, But EH is never equal to zero, i.e. LTSs need to be ‘fed‘ with energy continuously for many hours. Even with such a low heating rate an LTS of typical volume of the of 1028 cm3 existing for 10 hours needs in total about 1031 erg of thermal energy to be visible as it is. And 1031 erg is just the thermal energy released to sustain only long-lasting LTS. Energy released in LDEs surely is not deposited only in loop-top sources and only as thermal energy. Thus total energy ‘produced’ by an LDE during the decay must be larger than 1031 erg. This is huge amount of energy, which can be higher than energy released during the impulsive phase of a flare (Jiang et al., 2006). This severe requirement should be taken into account when building models of a solar flare. But a flare is not only the decay. Energy is also released during the rise.


A powerful example

As an example of how much energy can be generated during the whole flare we took the SOL2007-01-25T07:14 event. This was so-called slow long duration event (SLDE), i.e. it had not only slow decay but also slow rise. In total the flare lasted almost 18 hours (GOES 1-8 Å lightcurve). In the first part of “Slowly but surely towards the huge amount of energy I” we estimated that during the rise of the flare there was released at least 1.5×1031 erg of thermal energy. During the decay there was additional 2.2×1031 erg of thermal energy. Thus in total the event had to generate at least about 4×1031 erg, although it was ‘just’ C6.3 x-ray class flare.

Acknowledgements

We are grateful to members of our group Urszula Bąk-Stęślicka and Zbigniew Kołtun for their work, inspiring discussions and many critical comments.

References

[1] "RHESSI observations of long-duration flares with long-lasting X-ray loop-top sources"

[2] "RHESSI Investigation of X-Ray Coronal Sources During the Decay Phase of Solar Flares: I. Observations"

[3] "RHESSI investigation of X-ray coronal sources during the decay phase of solar flares: II. Energy balance"

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