High Temperatures in Active Regions

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|first_author = Jim McTiernan
|first_author = Jim McTiernan
|publish_date = 16 March 2009
|publish_date = 16 March 2009
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== Introduction ==
== Introduction ==
-
Since RHESSI was launched in February 2002, it has observed thousands of solar flares (more than 46,000 in the latest reprocessing of the RHESSI flare list). It was noticed in 2002 that RHESSI was observing solar emission even when there are no flares present (Ref. 1). The temperature required for this high energy emission is greater than 5 MK, a temperature range that is not often considered for solar active regions, mostly because the instruments used for T measurement of active regions, such as Yohkoh SXT, SOHO EIT or CDS, or didn't have much response to high T. Here we have measured the T for approximately 7000 time intervals from Feb 2002 through August 2006.
+
Since [http://hesperia.gsfc.nasa.gov/hessi/ RHESSI] was launched in February 2002, it has observed thousands of [http://www.scholarpedia.org/article/Solar_activity solar flares] (more than 46,000(!) in the latest reprocessing of the RHESSI flare list). It was immediately noticed in 2002 that RHESSI was observing solar emission even when there are no flares present (Ref. 1). The minimum temperature required for detectability would be about 5 MK, a temperature range that is not often considered for solar active regions.
 +
Most of the instruments previously used for temperature measurements of solar active regions, such as [http://www.lmsal.com/SXT/homepage.html Yohkoh SXT], [http://umbra.nascom.nasa.gov/eit/ SOHO EIT] or [http://solar.bnsc.rl.ac.uk/ CDS], didn't have much response to higher temperatures.  
 +
This Nugget describes measurements of the temperature for approximately 7000 time intervals from Feb 2002 through August 2006 (Ref. 2).
== Background Subtraction and Interval Selection ==  
== Background Subtraction and Interval Selection ==  
-
[[Image:97_jmm_Spd2006_fig1.png|500px|thumb|left|'''Figure 1''':This is the RHESSI 3 to 6 keV count rate for one orbit. The black dashed lines show an interval which was chosen for a temperature measurement. The red line is the expected background level.]]
+
[[Image:97_jmm_Spd2006_fig1.png|400px|thumb|left|'''Figure 1''':This is the RHESSI 3 to 6 keV count rate for one orbit. The black dashed lines show an interval which was chosen for a temperature measurement. The red line is the expected background level.]]
-
Figure 1 shows the RHESSI count rate for a typical orbit for 8 April 2006. (Nothing special about April 2006, it was just a convenient option when the original SPD poster with this calculation was created.) The plot clearly shows a jump at the day-night transitions. That is solar emission. Two things need to be accomplished before we can get a T measurement of the steady-state component that would be related to active regions:
+
Figure 1 shows the RHESSI count rate for a typical orbit for 8 April 2006. (Nothing special about April 2006, it was just a convenient option when the original [http://spd.aas.org/ SPD] poster with this calculation was created.) The plot shows a jump at each [http://en.wikipedia.org/wiki/Terminator_(solar) day-night transition] (terminator). This immediately tells us that the Sun is emitting detectable X-rays.
 +
Two things then need to be accomplished before we can get a temperature measurement of a steady-state component that could be related to active regions:
-
1) Avoid microflares, SAA's, particle events, etc: So for each orbit, an interval of between 1 and 5 minutes was chosen based on the following criteria: No flares or particle events, no attenuators, no data gaps, and at least 5 minutes from the SAA. The intervals chosen have the minimum (daylight) count rate for the orbit, subject to a flatness test that insures that there are no microflares in the intervals, there is one right after, though.
+
1) Avoid [http://sprg.ssl.berkeley.edu/~tohban/nuggets/?page=article&article_id=52 microflares], the [http://en.wikipedia.org/wiki/South_Atlantic_Anomaly SAA], [http://en.wikipedia.org/wiki/Van_Allen_radiation_belt particle events], etc: For each orbit, an interval of between 1 and 5 minutes was chosen based on the following criteria: no flares or particle events, no attenuators, no data gaps, and at least 5 minutes from the SAA. The intervals chosen have the minimum (daylight) count rate for the orbit, subject to a flatness test that insures that there are no microflares in the intervals; the interval in Figure 1 is followed by a microflare.
-
2) Find the background level: You cannot just assume that the background level can be given by the nighttime values before and after spacecraft day. The background level depends on the cosmic ray flux and local particle flux, and it varies with the position of the spacecraft. Figure 2 shows background data.
+
2) Find the background level: You cannot assume that the background can be given by the nighttime values before and after spacecraft day. The background depends on the cosmic ray flux and local particle flux, and it varies with the position of the spacecraft. Figure 2 shows background data, which is calculated from the 5 minute periods before and after daylight for each orbit in the mission.
-
[[Image:97_jmm_Spd2006_fig2.png|500px|thumb|left|'''Figure 2''':This is the RHESSI 3 to 6 keV background level, plotted versus the longitude of the ascending node of the orbit, and orbital phase. The longitude of the ascending
+
[[Image:97_jmm_Spd2006_fig2.png|400px|thumb|right|'''Figure 2''':This is the RHESSI 3 to 6 keV background level, plotted versus the [http://en.wikipedia.org/wiki/Longitude_of_the_ascending_node longitude of the ascending node] of the orbit, and orbital phase. The longitude of the ascending
node is the longitude at which the spacecraft passes over the equator, moving from south to north; the combination of this quantity and the orbital phase gives complete information about the latitude and longitude of the spacecraft. On orbit, a spacecraft follows a series of vertical lines on this plot, going up. ]]
node is the longitude at which the spacecraft passes over the equator, moving from south to north; the combination of this quantity and the orbital phase gives complete information about the latitude and longitude of the spacecraft. On orbit, a spacecraft follows a series of vertical lines on this plot, going up. ]]
-
Here is how we calculate the background level: The count rate has been accumulated during the 5 minute periods before and after daylight for each orbit in the mission. Each spectrum has an energy range from 3 to 300 keV, which is split into 492 energy bands (1/3 keV resolution from 3 to 100 keV and 1 keV resolution from 100 to 300 keV).
+
For the low-latitude regions where most of the temperature measurements were taken, the uncertainty in the background is approximately 1/2 the background rate. For the 3 to 6 keV energy band shown in Figures 1 and 2, this is approximately 1 count per second per detector. The uncertainty is higher for higher latitude regions; e.g., regions which are red in Figure 2.
-
The spectra are then averaged over time, longitude of the ascending node, and orbital phase. The angular ranges are split into 10 degree bins. A 56 day time interval is sufficient to ensure that there are measurements in each angular bin. For each 56-day time intervals, the spectra in each angular bin are averaged, resulting in a 36x36 array, for each of the 492 energy bands. We end up with an array of 492x18x36x36 for each 56-day interval; 492 energy bands, 18 detector segments, 36 bins of ascending node longitude, and 36 bins of orbital phase.  Each of these arrays is stored in an IDL save file.
+
== Measurements ==
-
For a background spectrum for a given time from this database, restore the files accumulated for times that bracket the given time, and interpolate the spectrum over time and position. This can be done for any time or energy band for the whole RHESSI mission, and it is used for the [http://hessi.ssl.berkeley.edu/hessidata/metadata/qlook_spectrum_plot/ RHESSI quicklook spectra].
+
Given a way to choose time intervals and calculate background, we calculate the temperature and emission measure. A total of 8747 time intervals were analyzed, from 14 February 2002 to 2 August 2006. Of these intervals, 6961 had enough counts above the background for a spectrum to be fitted. (The spectra for the fits were accumulated in 1/3 keV energy channels in the energy range from 3 to 30 keV. To be included in the fit, the background-subtracted count rate for a channel was required to be greater than 3 times its uncertainty. Detectors 1,3,4,6,9 were used.)
 +
We also obtained temperature and [http://en.wikipedia.org/wiki/Spectroscopy emission measure] (EM) from the standard soft X-ray photometry from [http://www.swpc.noaa.gov/today.html GOES] for each of the intervals. GOES 10 data were used prior to 16 March 2003, and GOES 12 data were used after.  
-
The uncertainty in the background is the dispersion obtained in each of the angular bins during the averaging process. For the low-latitude regions where most of the temperature measurements were taken, the uncertainty in the background is approximately 1/2 the background rate. For the 3 to 6 keV energy band shown in Figures 1 and 2, this is approximately 1 count per second per detector. The uncertainty is higher for higher latitude regions; e.g., regions which are very dark in Figure 2.
+
The RHESSI temperature is between 6 and 11 MK, and the GOES temperature is usually between 3 and 6 MK. The GOES EM is typically a factor of 50 to 100 times the RHESSI EM. This is consistent with a differential emission measure that decreases with increasing temperature.  
 +
[[Image:97_jmm_Ppr2008_f4.png|300px|thumb|left|'''Figure 3''':RHESSI temperature versus GOES temperature for time intervals before 14 September 2002. The blue dashed line is a linear fit with slope of 0.89. The red dashed line indicates where the two temperatures are equal.]]
-
== Measurements ==
+
[[Image:97_jmm_Ppr2008_f6.png|300px|thumb|right|'''Figure 4''':RHESSI temperature versus GOES temperature for all time intervals. The red dashed line indicates where the two temperatures are equal.]]
 +
 
 +
There is a small problem here, though. From Figure 3, it looks as if the two measurements have some correlation. This is not wildly unexpected; GOES should always measure a temperature lower than RHESSI, since it observes lower energy photons, so there should be some correlation due to that. We don't expect the correlation to be perfect; this would require the distribution of emission measure (DEM) to be a constant for all intervals.
 +
 
 +
In Figure 4, which shows all of the measurements, the rough correlation is gone, and often the GOES T is higher than the RHESSI T. Probably this is due to particles affecting the GOES measurements; we don't have a background subtraction method available for GOES to deal with this sort of problem. This erodes confidence in the GOES measurements -- below an EM (for GOES) of 3x10<math>^{48}</math> cm<math>^{-3}</math>, the GOES temperature is often higher than RHESSI's, and the results are suspect. (This is the C level in the GOES long wavelength channel -- which is typically only seen when the Sun is at its most active.)
 +
 
 +
[[Image:97_jmm_Ppr2008_f7.png|400px|thumb|right|'''Figure 5''':Top: 28-day averages of GOES (red stars) and RHESSI (black diamonds) temperatures. Middle: 28-day averages of GOES and RHESSI EM. Bottom: The black line is the fraction of time intervals that resulted in zero value for RHESSI temperature. The red line is a normalized value of sunspot number.]]
 +
 
 +
Here in Figure 5 is the overall time variation of the RHESSI and GOES temperatures and EMs. The average RHESSI temperature is relatively constant for the mission, with a drop from the 7 to 8 MK range to the 6.5 to 7.5 MK range. The RHESSI EM bounces up and down, but the bounces are superposed on a steady decrease of about one order of magnitude. Some of the bounces are pretty well correlated with the monthly sunspot number, particularly in 2002; the correlation coefficient between RHESSI EM and sunspot number is 0.61. The GOES values start relatively constant, and then become erratic at the start of 2003. (The average GOES temperature does remain lower than the average RHESSI temperature, even though the presence of GOES temperatures higher than RHESSI temperatures for individual intervals makes us distrust the GOES values.) The GOES EM decreases steadily by about 2 orders of magnitude.
 +
 
 +
== Heating? ==
-
Now that we have a way to choose time intervals and calculate background, we can calculate the temperature and emission measure. A total of 8747 time intervals were analyzed, from 14 February 2002 to 2 August 2006. Of these intervals, 6961 had enough counts above the background level for a spectrum to be fitted. (The spectra for the fits were accumulated in 1/3 keV energy channels in the energy range from 3 to 30 keV. To be included in the fit, the background-subtracted count rate for a channel was required to be greater than 3 times its uncertainty. Detectors 1,3,4,6,9 were used.)
+
The proven coronal heating process is the heating by flares that results in hot post-flare loops. Is it possible that all we are seeing is post-flare loops, with no need for [http://solarmuri.ssl.berkeley.edu/~hhudson/cartoons/thepages/Buchlin.html nanoflare] or wave heating or anything fancy? Maybe. The radiative cooling time for a loop of 8 MK and density of 10<math>^9</math>cm<math>^{-3}</math> is about 200 minutes. The conductive cooling time (for a loop length of 10<math>^5</math> km) is about 13 minutes. Using the approximation of total cooling time of <math>\tau_{mix}=(5/3)\tau_r^{7/12}*\tau_c^{5/12}</math> (Ref. 3), we find a cooling time of approximately an hour. If there are flares/microflares occurring more frequently than this, then it's conceivable that all of this is residual heating from those events. We know that there are anywhere from 5 to 90 microflares per day (Ref. 4) so there should be events often enough. Whether a single small microflare can result in enough heat to result in a persistent EM as large as observed is an issue that needs to be addressed by solar heating experts in the future.
-
We also obtained T and EM from GOES data for each of the intervals, for comparisons. GOES 10 data were used prior to 16 March 2003, and GOES 12 data were used after.  
+
== References ==
 +
1. [http://adsabs.harvard.edu/abs/2002SoPh..210..431B Microflares and hot component in solar active regions] by A. Benz and P. Grigis
-
The RHESSI temperature is between 6 and 11 MK, and the GOES temperature is usually between 3 and 6 MK. The GOES $EM$ is typically a factor of 50 to 100 times the RHESSI $EM$. This is consistent with a differential emission measure that decreases with increasing temperature. There is a small problem, though.
+
2. [http://sprg.ssl.berkeley.edu/~jimm/hessi/hsi_teem_2009.pdf RHESSI/GOES Observations of the Non-flaring Sun from 2002 to 2006] by J. McTiernan
-
[[Image:97_jmm_Ppr2008_f4.png|300px|thumb|left|'''Figure 3''':RHESSI temperature versus GOES temperature for time intervals up to 14 September 2002. The blue dashed line is a linear fit with slope of 0.89. The red dashed line indicates where the two temperatures are equal.}
+
3. [http://adsabs.harvard.edu/abs/1995ApJ...439.1034C Cooling of solar flares plasmas. 1: Theoretical considerations] by P. Cargill et al.
-
From Figure 3, it looks as if the two measurements have some correlation. This is not wildly unexpected, GOES should always measure a T lower than RHESSI, since it observes lower energy photons, so there should be some correlation due to that. We don't expect the correlation to be perfect; this would reqiure the slope of the DEM to be a constant for all intervals.  
+
4. [http://adsabs.harvard.edu/abs/2008ApJ...677.1385C RHESSI Microflare Statistics. I. Flare-Finding and Frequency Distributions] by S. Christe et al.
-
[[Image:97_jmm_Ppr2008_f6.png|300px|thumb|left|'''Figure 3''':RHESSI temperature versus GOES temperature for time intervals up to 2 August 2006. The red dashed line indicates where the two temperatures are equal.}
+
[[Category:Nugget]]

Latest revision as of 22:38, 5 June 2009


Nugget
Number: 97
1st Author: Jim McTiernan
2nd Author:
Published: 16 March 2009
Next Nugget: Chree Analysis for Flares
Previous Nugget: The Jakimiec Track
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Contents

Introduction

Since RHESSI was launched in February 2002, it has observed thousands of solar flares (more than 46,000(!) in the latest reprocessing of the RHESSI flare list). It was immediately noticed in 2002 that RHESSI was observing solar emission even when there are no flares present (Ref. 1). The minimum temperature required for detectability would be about 5 MK, a temperature range that is not often considered for solar active regions. Most of the instruments previously used for temperature measurements of solar active regions, such as Yohkoh SXT, SOHO EIT or CDS, didn't have much response to higher temperatures. This Nugget describes measurements of the temperature for approximately 7000 time intervals from Feb 2002 through August 2006 (Ref. 2).

Background Subtraction and Interval Selection

Figure 1:This is the RHESSI 3 to 6 keV count rate for one orbit. The black dashed lines show an interval which was chosen for a temperature measurement. The red line is the expected background level.

Figure 1 shows the RHESSI count rate for a typical orbit for 8 April 2006. (Nothing special about April 2006, it was just a convenient option when the original SPD poster with this calculation was created.) The plot shows a jump at each day-night transition (terminator). This immediately tells us that the Sun is emitting detectable X-rays. Two things then need to be accomplished before we can get a temperature measurement of a steady-state component that could be related to active regions:

1) Avoid microflares, the SAA, particle events, etc: For each orbit, an interval of between 1 and 5 minutes was chosen based on the following criteria: no flares or particle events, no attenuators, no data gaps, and at least 5 minutes from the SAA. The intervals chosen have the minimum (daylight) count rate for the orbit, subject to a flatness test that insures that there are no microflares in the intervals; the interval in Figure 1 is followed by a microflare.

2) Find the background level: You cannot assume that the background can be given by the nighttime values before and after spacecraft day. The background depends on the cosmic ray flux and local particle flux, and it varies with the position of the spacecraft. Figure 2 shows background data, which is calculated from the 5 minute periods before and after daylight for each orbit in the mission.

Figure 2:This is the RHESSI 3 to 6 keV background level, plotted versus the longitude of the ascending node of the orbit, and orbital phase. The longitude of the ascending node is the longitude at which the spacecraft passes over the equator, moving from south to north; the combination of this quantity and the orbital phase gives complete information about the latitude and longitude of the spacecraft. On orbit, a spacecraft follows a series of vertical lines on this plot, going up.

For the low-latitude regions where most of the temperature measurements were taken, the uncertainty in the background is approximately 1/2 the background rate. For the 3 to 6 keV energy band shown in Figures 1 and 2, this is approximately 1 count per second per detector. The uncertainty is higher for higher latitude regions; e.g., regions which are red in Figure 2.

Measurements

Given a way to choose time intervals and calculate background, we calculate the temperature and emission measure. A total of 8747 time intervals were analyzed, from 14 February 2002 to 2 August 2006. Of these intervals, 6961 had enough counts above the background for a spectrum to be fitted. (The spectra for the fits were accumulated in 1/3 keV energy channels in the energy range from 3 to 30 keV. To be included in the fit, the background-subtracted count rate for a channel was required to be greater than 3 times its uncertainty. Detectors 1,3,4,6,9 were used.) We also obtained temperature and emission measure (EM) from the standard soft X-ray photometry from GOES for each of the intervals. GOES 10 data were used prior to 16 March 2003, and GOES 12 data were used after.

The RHESSI temperature is between 6 and 11 MK, and the GOES temperature is usually between 3 and 6 MK. The GOES EM is typically a factor of 50 to 100 times the RHESSI EM. This is consistent with a differential emission measure that decreases with increasing temperature.

Figure 3:RHESSI temperature versus GOES temperature for time intervals before 14 September 2002. The blue dashed line is a linear fit with slope of 0.89. The red dashed line indicates where the two temperatures are equal.
Figure 4:RHESSI temperature versus GOES temperature for all time intervals. The red dashed line indicates where the two temperatures are equal.

There is a small problem here, though. From Figure 3, it looks as if the two measurements have some correlation. This is not wildly unexpected; GOES should always measure a temperature lower than RHESSI, since it observes lower energy photons, so there should be some correlation due to that. We don't expect the correlation to be perfect; this would require the distribution of emission measure (DEM) to be a constant for all intervals.

In Figure 4, which shows all of the measurements, the rough correlation is gone, and often the GOES T is higher than the RHESSI T. Probably this is due to particles affecting the GOES measurements; we don't have a background subtraction method available for GOES to deal with this sort of problem. This erodes confidence in the GOES measurements -- below an EM (for GOES) of 3x1048 cm − 3, the GOES temperature is often higher than RHESSI's, and the results are suspect. (This is the C level in the GOES long wavelength channel -- which is typically only seen when the Sun is at its most active.)

Figure 5:Top: 28-day averages of GOES (red stars) and RHESSI (black diamonds) temperatures. Middle: 28-day averages of GOES and RHESSI EM. Bottom: The black line is the fraction of time intervals that resulted in zero value for RHESSI temperature. The red line is a normalized value of sunspot number.

Here in Figure 5 is the overall time variation of the RHESSI and GOES temperatures and EMs. The average RHESSI temperature is relatively constant for the mission, with a drop from the 7 to 8 MK range to the 6.5 to 7.5 MK range. The RHESSI EM bounces up and down, but the bounces are superposed on a steady decrease of about one order of magnitude. Some of the bounces are pretty well correlated with the monthly sunspot number, particularly in 2002; the correlation coefficient between RHESSI EM and sunspot number is 0.61. The GOES values start relatively constant, and then become erratic at the start of 2003. (The average GOES temperature does remain lower than the average RHESSI temperature, even though the presence of GOES temperatures higher than RHESSI temperatures for individual intervals makes us distrust the GOES values.) The GOES EM decreases steadily by about 2 orders of magnitude.

Heating?

The proven coronal heating process is the heating by flares that results in hot post-flare loops. Is it possible that all we are seeing is post-flare loops, with no need for nanoflare or wave heating or anything fancy? Maybe. The radiative cooling time for a loop of 8 MK and density of 109cm − 3 is about 200 minutes. The conductive cooling time (for a loop length of 105 km) is about 13 minutes. Using the approximation of total cooling time of \tau_{mix}=(5/3)\tau_r^{7/12}*\tau_c^{5/12} (Ref. 3), we find a cooling time of approximately an hour. If there are flares/microflares occurring more frequently than this, then it's conceivable that all of this is residual heating from those events. We know that there are anywhere from 5 to 90 microflares per day (Ref. 4) so there should be events often enough. Whether a single small microflare can result in enough heat to result in a persistent EM as large as observed is an issue that needs to be addressed by solar heating experts in the future.

References

1. Microflares and hot component in solar active regions by A. Benz and P. Grigis

2. RHESSI/GOES Observations of the Non-flaring Sun from 2002 to 2006 by J. McTiernan

3. Cooling of solar flares plasmas. 1: Theoretical considerations by P. Cargill et al.

4. RHESSI Microflare Statistics. I. Flare-Finding and Frequency Distributions by S. Christe et al.

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