https://sprg.ssl.berkeley.edu/~tohban/wiki/index.php?title=Slowly_but_surely_towards_the_huge_amount_of_energy_I&feed=atom&action=historySlowly but surely towards the huge amount of energy I - Revision history2024-03-29T05:14:12ZRevision history for this page on the wikiMediaWiki 1.16.0https://sprg.ssl.berkeley.edu/~tohban/wiki/index.php?title=Slowly_but_surely_towards_the_huge_amount_of_energy_I&diff=10705&oldid=prevSchriste at 17:10, 22 August 20182018-08-22T17:10:58Z<p></p>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>|second_author = Tomasz Mrozek, Sylwester Ko&#322;oma&#324;ski</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>|second_author = Tomasz Mrozek, Sylwester Ko&#322;oma&#324;ski</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>|publish_date = 31 October 2011</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>|publish_date = 31 October 2011</div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>|next_nugget = <del class="diffchange diffchange-inline">H&alpha; and Hard X-rays</del></div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>|next_nugget=<ins class="diffchange diffchange-inline">{{#ask: [[Category:Nugget]] [[RHESSI Nugget Index::163]]}}</ins></div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>|previous_nugget = [<del class="diffchange diffchange-inline">http</del>:<del class="diffchange diffchange-inline">//sprg.ssl.berkeley.edu/~tohban/wiki/index.php/Quasi-Periodic_Pulsations</del>:<del class="diffchange diffchange-inline">_Fermi/GBM_Results Quasi-Periodic Pulsations</del>: <del class="diffchange diffchange-inline">Fermi/GBM Results</del>]</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>|previous_nugget=<ins class="diffchange diffchange-inline">{{#ask: </ins>[<ins class="diffchange diffchange-inline">[Category</ins>:<ins class="diffchange diffchange-inline">Nugget]] [[RHESSI Nugget Index</ins>::<ins class="diffchange diffchange-inline">161]</ins>]<ins class="diffchange diffchange-inline">}}</ins></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>}}</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>}}</div></td></tr>
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</table>Schristehttps://sprg.ssl.berkeley.edu/~tohban/wiki/index.php?title=Slowly_but_surely_towards_the_huge_amount_of_energy_I&diff=4729&oldid=prevHhudson at 14:25, 31 October 20112011-10-31T14:25:06Z<p></p>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>|second_author = Tomasz Mrozek, Sylwester Ko&#322;oma&#324;ski</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>|second_author = Tomasz Mrozek, Sylwester Ko&#322;oma&#324;ski</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>|publish_date = 31 October 2011</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>|publish_date = 31 October 2011</div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>|next_nugget = <del class="diffchange diffchange-inline">Slowly II</del></div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>|next_nugget = <ins class="diffchange diffchange-inline">H&alpha; and Hard X-rays</ins></div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>|previous_nugget = Quasi-Periodic Pulsations: Fermi/GBM Results</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>|previous_nugget = <ins class="diffchange diffchange-inline">[http://sprg.ssl.berkeley.edu/~tohban/wiki/index.php/Quasi-Periodic_Pulsations:_Fermi/GBM_Results </ins>Quasi-Periodic Pulsations: Fermi/GBM Results<ins class="diffchange diffchange-inline">]</ins></div></td></tr>
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</table>Hhudsonhttps://sprg.ssl.berkeley.edu/~tohban/wiki/index.php?title=Slowly_but_surely_towards_the_huge_amount_of_energy_I&diff=4724&oldid=prevHhudson: some tidying-up2011-10-31T12:41:55Z<p>some tidying-up</p>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>|title = Slowly but surely towards the huge amount of energy I</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>|title = Slowly but surely towards the huge amount of energy I</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>|number = 162</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>|number = 162</div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>|first_author = Urszula <del class="diffchange diffchange-inline">Bak</del>-St&#281;&#347;licka</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>|first_author = Urszula <ins class="diffchange diffchange-inline">B&#261;k</ins>-St&#281;&#347;licka</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>|second_author = Tomasz Mrozek, Sylwester Ko&#322;oma&#324;ski</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>|second_author = Tomasz Mrozek, Sylwester Ko&#322;oma&#324;ski</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>|publish_date = 31 October 2011</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>|publish_date = 31 October 2011</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>|next_nugget = Slowly II</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>|next_nugget = Slowly II</div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>|previous_nugget = <del class="diffchange diffchange-inline">[http://sprg.ssl.berkeley.edu/~tohban/wiki/index.php/</del>Quasi-<del class="diffchange diffchange-inline">Periodic_Pulsations</del>:<del class="diffchange diffchange-inline">_Fermi</del>/<del class="diffchange diffchange-inline">GBM_Results]</del></div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>|previous_nugget = Quasi-<ins class="diffchange diffchange-inline">Periodic Pulsations</ins>: <ins class="diffchange diffchange-inline">Fermi</ins>/<ins class="diffchange diffchange-inline">GBM Results</ins></div></td></tr>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>The decay phase of an LDE may last more than a day. </div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>The decay phase of an LDE may last more than a day. </div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>Some LDEs may also have an unusually long rising phase that may lasts more than 30 minutes. </div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>Some LDEs may also have an unusually long rising phase that may lasts more than 30 minutes. </div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>We refer to this type of LDE as a slow long-duration <del class="diffchange diffchange-inline">events </del>(<del class="diffchange diffchange-inline">SLDEs</del>). During the <del class="diffchange diffchange-inline">rising </del>phase of an SLDE there is no typical impulsive phase [[#References|[1]]]. </div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>We refer to this type of LDE as a <ins class="diffchange diffchange-inline">"</ins>slow long-duration <ins class="diffchange diffchange-inline">event" </ins>(<ins class="diffchange diffchange-inline">SLDE</ins>). </div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>Instead of short pulses we observe a gradual increase of hard X-ray (HXR) emission and/or a smooth, broad (several minutes long) bursts of HXR emission </div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>During the <ins class="diffchange diffchange-inline">rise </ins>phase of an SLDE there is no typical impulsive phase [[#References|[1]]]. </div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>(see Figure 1).</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>Instead of short pulses<ins class="diffchange diffchange-inline">, </ins>we observe a gradual increase of hard X-ray (HXR) emission and/or a smooth, broad (several minutes long) bursts of HXR emission (see Figure 1).</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>RHESSI's [http://sprg.ssl.berkeley.edu/~tohban/nuggets/?page=article&article_id=1 first X-class flare] was just such an event.</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>RHESSI's [http://sprg.ssl.berkeley.edu/~tohban/nuggets/?page=article&article_id=1 first X-class flare] was just such an event.</div></td></tr>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div> Observed change of thermal energy = adiabatic expansion – conductive cooling – radiative cooling + heating rate</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div> Observed change of thermal energy = adiabatic expansion – conductive cooling – radiative cooling + heating rate</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>Knowing the change of the <del class="diffchange diffchange-inline">LTS </del>thermal energy and the values of the three cooling processes we can calculate how efficiently the <del class="diffchange diffchange-inline">LTS </del>was heated. As an additional parameter describing the temporal evolution of the heating rate we <del class="diffchange diffchange-inline">calculated </del>the characteristic time, tau, of the decrease of the heating rate (E<sub>H</sub>) after it reaches its maximum value:</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>Knowing the change of the <ins class="diffchange diffchange-inline">loop-top </ins>thermal energy and the values of the three cooling processes we can calculate how efficiently the <ins class="diffchange diffchange-inline">source </ins>was heated.</div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>As an additional parameter describing the temporal evolution of the heating rate<ins class="diffchange diffchange-inline">. </ins>we <ins class="diffchange diffchange-inline">calculate </ins>the characteristic time, <ins class="diffchange diffchange-inline">&</ins>tau<ins class="diffchange diffchange-inline">;s</ins>, of the decrease of the heating rate (E<sub>H</sub>) after it reaches its maximum value:</div></td></tr>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>[[File:162f1.5.png|thumb|center|600px|</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>[[File:162f1.5.png|thumb|center|600px|</div></td></tr>
</table>Hhudsonhttps://sprg.ssl.berkeley.edu/~tohban/wiki/index.php?title=Slowly_but_surely_towards_the_huge_amount_of_energy_I&diff=4720&oldid=prevTomekMrozek at 18:20, 26 October 20112011-10-26T18:20:50Z<p></p>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>[[File:162f1.png|thumb|center|700px|'''Figure 1''':</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>[[File:162f1.png|thumb|center|700px|'''Figure 1''':</div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>RHESSI light curves (6-12 keV, 25-50 keV) for two LDE flares: Left: a long (50 min) rise phase and Right: a short (<del class="diffchange diffchange-inline">15 </del>min) rise phase.</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>RHESSI light curves (6-12 keV, 25-50 keV) for two LDE flares: Left: a long (50 min) rise phase and Right: a short (<ins class="diffchange diffchange-inline">10 </ins>min) rise phase.</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>Note that SOL2002-04-21 (left) was RHESSI's first X-class flare observation.</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>Note that SOL2002-04-21 (left) was RHESSI's first X-class flare observation.</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>]]</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>]]</div></td></tr>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>These studies provided us with the basic observational characteristics of SLDEs:</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>These studies provided us with the basic observational characteristics of SLDEs:</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div><li> most SLDEs occur in high or mid-high structures,</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins class="diffchange diffchange-inline">::</ins><li> most SLDEs occur in high or mid-high structures,</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div><li> loop-top sources are characterized by low temperature (T<10 MK), low density (N ≈ 10<sup>10</sup> cm<sup>−3</sup>) and large size (r > 7 × 10<sup>8</sup> cm),</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins class="diffchange diffchange-inline">::</ins><li> loop-top sources are characterized by low temperature (T<10 MK), low density (N ≈ 10<sup>10</sup> cm<sup>−3</sup>) and large size (r > 7 × 10<sup>8</sup> cm),</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div><li> the heating rate of plasma is small, below 1 erg cm<sup>−3</sup>s<sup>−1</sup> and,</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins class="diffchange diffchange-inline">::</ins><li> the heating rate of plasma is small, below 1 erg cm<sup>−3</sup>s<sup>−1</sup> and,</div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div> </div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins class="diffchange diffchange-inline">::<li> the heating rate decreases very slowly with time after reaching its maximum value.</ins></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div><del style="color: red; font-weight: bold; text-decoration: none;"><li> the heating rate decreases very slowly with time after reaching its maximum value.</del></div></td><td colspan="2"> </td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>A detailed analysis of SLDEs in the hard X-ray range requires high spectral resolution, much better than the resolution provided by the [http://soi.stanford.edu/results/SolPhys200/Kosugi/index.html Yohkoh/HXT]. </div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>A detailed analysis of SLDEs in the hard X-ray range requires high spectral resolution, much better than the resolution provided by the [http://soi.stanford.edu/results/SolPhys200/Kosugi/index.html Yohkoh/HXT]. </div></td></tr>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>Our study [[#References|[3]]] dealt with six SLDEs, with the following results:</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>Our study [[#References|[3]]] dealt with six SLDEs, with the following results:</div></td></tr>
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<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div><li><b>The character of the loop-top emission:</b> we find a thermal component to be dominant, however for four of the six events we observed significant non-thermal emission </div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins class="diffchange diffchange-inline">::</ins><li><b>The character of the loop-top emission:</b> we find a thermal component to be dominant, however for four of the six events we observed significant non-thermal emission </div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div><li> <b>The heating rate of the plasma:</b> the values obtained are not high, usually below 10 erg cm<sup>3</sup>s<sup>-1</sup>,</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins class="diffchange diffchange-inline">::</ins><li> <b>The heating rate of the plasma:</b> the values obtained are not high, usually below 10 erg cm<sup>3</sup>s<sup>-1</sup>, but larger than those obtained from the earlier SXT observations. This difference is caused by the fact that SXT had less sensitivity to higher-temperature plasma (> 10 MK). </div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>but larger than those obtained from the earlier SXT observations. </div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div></div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>This difference is caused by the fact that SXT had less sensitivity to higher-temperature plasma (> 10 MK). </div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div><li><b>The time evolution of the heating rate:</b> the long duration of the rise phase of an SLDE is consistent with a very slow decrease of the heating rate during this phase. In most cases the characteristic time &tau; is larger than 1000 s. </div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins class="diffchange diffchange-inline">::</ins><li><b>The time evolution of the heating rate:</b> the long duration of the rise phase of an SLDE is consistent with a very slow decrease of the heating rate during this phase. In most cases the characteristic time &tau; is larger than 1000 s. </div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div><li> <b>The total thermal energy released during the rise phase:</b> the low limit of the total energy released during the rising phase was calculated under the following assumptions: (a) the heating rate is constant throughout the entire rise phase and equal to its minimum measured value, (b) the loop-top volume was calculated from the mean area of the source, A, as seen in images, assuming a sphere with a constant volume during the whole rise phase. For the analyzed events we obtained at least about 10<sup>31</sup> erg as the total thermal energy released during the rise phase.</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins class="diffchange diffchange-inline">::</ins><li> <b>The total thermal energy released during the rise phase:</b> the low limit of the total energy released during the rising phase was calculated under the following assumptions: (a) the heating rate is constant throughout the entire rise phase and equal to its minimum measured value, (b) the loop-top volume was calculated from the mean area of the source, A, as seen in images, assuming a sphere with a constant volume during the whole rise phase. For the analyzed events we obtained at least about 10<sup>31</sup> erg as the total thermal energy released during the rise phase.</div></td></tr>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>== Conclusions ==</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>== Conclusions ==</div></td></tr>
</table>TomekMrozekhttps://sprg.ssl.berkeley.edu/~tohban/wiki/index.php?title=Slowly_but_surely_towards_the_huge_amount_of_energy_I&diff=4715&oldid=prevWikisysop: /* References */2011-10-26T15:23:09Z<p><span class="autocomment">References</span></p>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>== References ==</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>== References ==</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>[1] <del class="diffchange diffchange-inline">[</del>[http://adsabs.harvard.edu/abs/2000ASPC..206..221H "Hard X-rays from 'Slow LDEs'"]</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>[1] [http://adsabs.harvard.edu/abs/2000ASPC..206..221H "Hard X-rays from 'Slow LDEs'"]</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>[2] [http://adsabs.harvard.edu/abs/2005SoPh..231...95B "Investigation of X-Ray Flares with Long Rising Phases"]</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>[2] [http://adsabs.harvard.edu/abs/2005SoPh..231...95B "Investigation of X-Ray Flares with Long Rising Phases"]</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>[3] [http://adsabs.harvard.edu/abs/2011SoPh..271...75B "Energy Release During Slow Long-Duration Flares Observed by RHESSI"]</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>[3] [http://adsabs.harvard.edu/abs/2011SoPh..271...75B "Energy Release During Slow Long-Duration Flares Observed by RHESSI"]</div></td></tr>
</table>Wikisysophttps://sprg.ssl.berkeley.edu/~tohban/wiki/index.php?title=Slowly_but_surely_towards_the_huge_amount_of_energy_I&diff=4714&oldid=prevWikisysop: added anchors to references2011-10-26T15:22:35Z<p>added anchors to references</p>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>The decay phase of an LDE may last more than a day. </div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>The decay phase of an LDE may last more than a day. </div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>Some LDEs may also have an unusually long rising phase that may lasts more than 30 minutes. </div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>Some LDEs may also have an unusually long rising phase that may lasts more than 30 minutes. </div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>We refer to this type of LDE as a slow long-duration events (SLDEs). During the rising phase of an SLDE there is no typical impulsive phase [1]. </div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>We refer to this type of LDE as a slow long-duration events (SLDEs). During the rising phase of an SLDE there is no typical impulsive phase <ins class="diffchange diffchange-inline">[[#References|</ins>[1<ins class="diffchange diffchange-inline">]]</ins>]. </div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>Instead of short pulses we observe a gradual increase of hard X-ray (HXR) emission and/or a smooth, broad (several minutes long) bursts of HXR emission </div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>Instead of short pulses we observe a gradual increase of hard X-ray (HXR) emission and/or a smooth, broad (several minutes long) bursts of HXR emission </div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>(see Figure 1).</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>(see Figure 1).</div></td></tr>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>]]</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>]]</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>Chronologically the first studies of SLDEs were based on [http://solar.physics.montana.edu/sxt/ Yohkoh/SXT] images [2]. </div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>Chronologically the first studies of SLDEs were based on [http://solar.physics.montana.edu/sxt/ Yohkoh/SXT] images <ins class="diffchange diffchange-inline">[[#References|</ins>[2<ins class="diffchange diffchange-inline">]]</ins>]. </div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>These studies provided us with the basic observational characteristics of SLDEs:</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>These studies provided us with the basic observational characteristics of SLDEs:</div></td></tr>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>== Results ==</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>== Results ==</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>Our study [[#<del class="diffchange diffchange-inline">ref_3 </del>3]] dealt with six SLDEs, with the following results:</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>Our study [[#<ins class="diffchange diffchange-inline">References|[</ins>3<ins class="diffchange diffchange-inline">]</ins>]] dealt with six SLDEs, with the following results:</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><li><b>The character of the loop-top emission:</b> we find a thermal component to be dominant, however for four of the six events we observed significant non-thermal emission </div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><li><b>The character of the loop-top emission:</b> we find a thermal component to be dominant, however for four of the six events we observed significant non-thermal emission </div></td></tr>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>== References ==</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>== References ==</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>[1] [http://adsabs.harvard.edu/abs/2000ASPC..206..221H "Hard X-rays from 'Slow LDEs'"]</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>[1] <ins class="diffchange diffchange-inline">[</ins>[http://adsabs.harvard.edu/abs/2000ASPC..206..221H "Hard X-rays from 'Slow LDEs'"]</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>[2] [http://adsabs.harvard.edu/abs/2005SoPh..231...95B "Investigation of X-Ray Flares with Long Rising Phases"]</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>[2] [http://adsabs.harvard.edu/abs/2005SoPh..231...95B "Investigation of X-Ray Flares with Long Rising Phases"]</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>[3] [http://adsabs.harvard.edu/abs/2011SoPh..271...75B "Energy Release During Slow Long-Duration Flares Observed by RHESSI"]</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>[3] [http://adsabs.harvard.edu/abs/2011SoPh..271...75B "Energy Release During Slow Long-Duration Flares Observed by RHESSI"]</div></td></tr>
</table>Wikisysophttps://sprg.ssl.berkeley.edu/~tohban/wiki/index.php?title=Slowly_but_surely_towards_the_huge_amount_of_energy_I&diff=4713&oldid=prevWikisysop: /* Results */2011-10-26T14:45:53Z<p><span class="autocomment">Results</span></p>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>== Results ==</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>== Results ==</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>Our study <del class="diffchange diffchange-inline"><ref>Hudson & McKenzie 2000</ref> </del>dealt with six SLDEs, with the following results:</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>Our study <ins class="diffchange diffchange-inline">[[#ref_3 3]] </ins>dealt with six SLDEs, with the following results:</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><li><b>The character of the loop-top emission:</b> we find a thermal component to be dominant, however for four of the six events we observed significant non-thermal emission </div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><li><b>The character of the loop-top emission:</b> we find a thermal component to be dominant, however for four of the six events we observed significant non-thermal emission </div></td></tr>
</table>Wikisysophttps://sprg.ssl.berkeley.edu/~tohban/wiki/index.php?title=Slowly_but_surely_towards_the_huge_amount_of_energy_I&diff=4712&oldid=prevWikisysop: /* Results */ added reference2011-10-26T14:43:55Z<p><span class="autocomment">Results: </span> added reference</p>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>== Results ==</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>== Results ==</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>Our study <del class="diffchange diffchange-inline">(</del>ref<del class="diffchange diffchange-inline">. [3]) </del>dealt with six SLDEs, with the following results:</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>Our study <ins class="diffchange diffchange-inline"><</ins>ref<ins class="diffchange diffchange-inline">>Hudson & McKenzie 2000</ref> </ins>dealt with six SLDEs, with the following results:</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><li><b>The character of the loop-top emission:</b> we find a thermal component to be dominant, however for four of the six events we observed significant non-thermal emission </div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><li><b>The character of the loop-top emission:</b> we find a thermal component to be dominant, however for four of the six events we observed significant non-thermal emission </div></td></tr>
</table>Wikisysophttps://sprg.ssl.berkeley.edu/~tohban/wiki/index.php?title=Slowly_but_surely_towards_the_huge_amount_of_energy_I&diff=4711&oldid=prevWikisysop: /* Results */2011-10-26T14:39:38Z<p><span class="autocomment">Results</span></p>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>Our study (ref. [3]) dealt with six SLDEs, with the following results:</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>Our study (ref. [3]) dealt with six SLDEs, with the following results:</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div><li><b>The character of the loop-top emission:</b> we find a thermal component to be <del class="diffchange diffchange-inline">dominant </del>dominant, however for four of the six events we observed significant non-thermal emission </div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><li><b>The character of the loop-top emission:</b> we find a thermal component to be dominant, however for four of the six events we observed significant non-thermal emission </div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><li> <b>The heating rate of the plasma:</b> the values obtained are not high, usually below 10 erg cm<sup>3</sup>s<sup>-1</sup>,</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><li> <b>The heating rate of the plasma:</b> the values obtained are not high, usually below 10 erg cm<sup>3</sup>s<sup>-1</sup>,</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>but larger than those obtained from the earlier SXT observations. </div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>but larger than those obtained from the earlier SXT observations. </div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>This difference is caused by the fact that <del class="diffchange diffchange-inline">the </del>SXT had less sensitivity to higher-temperature plasma (> 10 MK). </div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>This difference is caused by the fact that SXT had less sensitivity to higher-temperature plasma (> 10 MK). </div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div><li><b>The time evolution of the heating rate:</b> the long duration of the rise phase of an SLDE is consistent with a very slow decrease of heating rate during this phase. In most cases the characteristic time &tau; is larger than 1000 s. </div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><li><b>The time evolution of the heating rate:</b> the long duration of the rise phase of an SLDE is consistent with a very slow decrease of <ins class="diffchange diffchange-inline">the </ins>heating rate during this phase. In most cases the characteristic time &tau; is larger than 1000 s. </div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div><li> <b>The total thermal energy released during the rise phase:</b> the low limit of the total energy released during the rising phase was calculated under the following assumptions: (a) the heating rate is constant <del class="diffchange diffchange-inline">through </del>the entire rise phase and equal to its minimum measured value, (b) loop-top volume was calculated from mean area of the source, A, as seen in images, <del class="diffchange diffchange-inline">and </del>assuming a sphere<del class="diffchange diffchange-inline">, and assumed to be </del>constant during the whole rise phase. For the analyzed events we obtained at least about 10<sup>31</sup> erg as the total thermal energy released during the rise phase.</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><li> <b>The total thermal energy released during the rise phase:</b> the low limit of the total energy released during the rising phase was calculated under the following assumptions: (a) the heating rate is constant <ins class="diffchange diffchange-inline">throughout </ins>the entire rise phase and equal to its minimum measured value, (b) <ins class="diffchange diffchange-inline">the </ins>loop-top volume was calculated from <ins class="diffchange diffchange-inline">the </ins>mean area of the source, A, as seen in images, assuming a sphere <ins class="diffchange diffchange-inline">with a </ins>constant <ins class="diffchange diffchange-inline">volume </ins>during the whole rise phase. For the analyzed events we obtained at least about 10<sup>31</sup> erg as the total thermal energy released during the rise phase.</div></td></tr>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>== Conclusions ==</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>== Conclusions ==</div></td></tr>
</table>Wikisysophttps://sprg.ssl.berkeley.edu/~tohban/wiki/index.php?title=Slowly_but_surely_towards_the_huge_amount_of_energy_I&diff=4710&oldid=prevWikisysop: /* Data Analysis */2011-10-26T14:37:07Z<p><span class="autocomment">Data Analysis</span></p>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>== Data Analysis ==</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>== Data Analysis ==</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>For our analysis we selected six limb or near-the-limb SLDEs, with rise phases <del class="diffchange diffchange-inline">lasted </del>between 25 <del class="diffchange diffchange-inline">– </del>150 min. </div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>For our analysis we selected six limb or near-the-limb SLDEs, with rise phases <ins class="diffchange diffchange-inline">lasting </ins>between 25 <ins class="diffchange diffchange-inline">to </ins>150 min. </div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>RHESSI light curves, GOES/SXI with the RHESSI contours, and the RHESSI spectrum (for the flare with the longest rising phase) are shown in Figure 2. </div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>RHESSI light curves, GOES/SXI with the RHESSI contours, and the RHESSI spectrum (for the flare with the longest rising phase) are shown in Figure 2. </div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>The images were reconstructed with the PIXON algorithm. </div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>The images were reconstructed with the PIXON algorithm. </div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>We used time intervals of 20 – 40 s and narrow energy intervals of 1 – 2 keV. </div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>We used time intervals of 20 – 40 s and narrow energy intervals of 1 – 2 keV. </div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>In our analysis we <del class="diffchange diffchange-inline">were </del>concentrated on coronal sources, so-called loop-top sources only. </div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>In our analysis we concentrated on coronal sources, so-called loop-top sources only. </div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>For each <del class="diffchange diffchange-inline">observed </del>such source we estimated size (area projected on image) and altitude above the photosphere. <del class="diffchange diffchange-inline">In the next step </del>we performed a spectroscopic analysis, using the standard RHESSI software, to obtain the physical parameters. </div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>For each such source we estimated <ins class="diffchange diffchange-inline">the </ins>size (area projected on image) and altitude above the photosphere. <ins class="diffchange diffchange-inline">Next, </ins>we performed a spectroscopic analysis, using the standard RHESSI software, to obtain the physical parameters. </div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>These parameters were used as an input data for calculation of the heating rate. </div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>These parameters were used as an input data for <ins class="diffchange diffchange-inline">a </ins>calculation of the heating rate. </div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>It was assumed that a change <del class="diffchange diffchange-inline">of </del>thermal energy of a loop-top source is due to expansion, radiation, conduction (cooling processes) and heating<del class="diffchange diffchange-inline">:</del></div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>It was assumed that a change <ins class="diffchange diffchange-inline">in the </ins>thermal energy of a loop-top source is due to expansion, radiation, conduction (cooling processes) and heating<ins class="diffchange diffchange-inline">. Expressed in the form of an equation,</ins></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div> Observed change of thermal energy = adiabatic expansion – conductive cooling – radiative cooling + heating rate</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div> Observed change of thermal energy = adiabatic expansion – conductive cooling – radiative cooling + heating rate</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>Knowing the change of LTS thermal energy and values of the three cooling processes we can calculate how efficiently the LTS was heated. As an additional parameter describing temporal evolution of the heating rate we calculated the characteristic time <del class="diffchange diffchange-inline">τ </del>of the decrease of heating rate (E<sub>H</sub>) after it reaches its maximum value:</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>Knowing the change of <ins class="diffchange diffchange-inline">the </ins>LTS thermal energy and <ins class="diffchange diffchange-inline">the </ins>values of the three cooling processes we can calculate how efficiently the LTS was heated. As an additional parameter describing <ins class="diffchange diffchange-inline">the </ins>temporal evolution of the heating rate we calculated the characteristic time<ins class="diffchange diffchange-inline">, tau, </ins>of the decrease of <ins class="diffchange diffchange-inline">the </ins>heating rate (E<sub>H</sub>) after it reaches its maximum value:</div></td></tr>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>[[File:162f1.5.png|thumb|center|600px|</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>[[File:162f1.5.png|thumb|center|600px|</div></td></tr>
</table>Wikisysop