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Richard W. Nightingale & Markus J. Aschwanden

This study presents detailed analyses of electron temperature, density, and width profiles of 234 coronal loops in the non-equilibrium cooling phase using high-resolution measurements from EUV triple-filter TRACE data. The loop geometries, corrections for projection effects, example data analysis, and histograms of loop parameters such as half lengths, inclination angles, and widths are discussed. Temperature and electron density profiles are analyzed along with the overpressure ratio versus loop half length. Results indicate over-densities and flatter temperature profiles than predicted, suggesting non-equilibrium cooling dynamics in coronal loops during the onset of Solar Cycle 24.

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Richard W. Nightingale & Markus J. Aschwanden

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  1. High-Resolution Measurements of Electron Temperature, Density, and Width Profiles of 234 Coronal Loops in the Non-Equilibrium Cooling Phase ______________________________________ Richard W. Nightingale & Markus J. Aschwanden (nightingale@lmsal.com) Lockheed Martin Advanced Technology Center, Palo Alto, CA 94304 Solar Activity During the Onset of Solar Cycle 24 Workshop In Napa

  2. Outline TRACE 171 Å Coronal Loops In this study we measured the profiles of the electron temperature Te(s), the electron density ne(s), and loop widths w(s) of 243 coronal loops from EUV triple-filter TRACE data. To apply loop scaling laws and hydrodynamic models to these profiles, we show the modeled loop geometry used in order to measure the un-projected full loop length and the inclination angle of the loop plane to the vertical. • The statistics of the measured loop parameters are presented. • The average overpressure of the loops can be determined from these parameters. • This can be interpreted as a natural consequence of the non-equilibrium cooling phase. • Conclusions Solar Activity During the Onset of Solar Cycle 24 Workshop In Napa

  3. 3D Geometry of Loops The Cartesian coordinates (xi,yi) of a loop segment are fitted with a semi-circular geometry by varying the inclination angle  = -90o, …, +90o of the loop plane. Solar Activity During the Onset of Solar Cycle 24 Workshop In Napa

  4. Corrections for Projection Effects Left panel: the effect of the variable column depth wz(s) measured parallel to the line-of-sight z is illustrated. Right panel: the effect of the inclination angle  of the loop plane on the inferred density scale height is shown. Solar Activity During the Onset of Solar Cycle 24 Workshop In Napa

  5. Example of Data Analysis Run Case 0A observed by TRACE on 1998 May 13, 06:44:35 UT, containing partial images in all three wavelengths (left), highpass-filtered images (second row left), cross-sectional loop profiles in all three filters (middle rows), and temperature (top right), density (middle right), and width profiles (bottom right). Solar Activity During the Onset of Solar Cycle 24 Workshop In Napa

  6. Loop Geometries 12 selected loop cases are shown, where the red curves indicate the traced loop segments and the blue curves show the projections of the fitted 3D semi-circular loop geometry models. The heliographic grid has a spacing of 1o in longitude and latitude, while the inferred inclination angles of the loop planes are as indicated. Solar Activity During the Onset of Solar Cycle 24 Workshop In Napa

  7. Temperature Profiles Te (s) Same 12 selected cases are shown as in the last figure, with the x-axis of each panel spanning over the entire loop length and with a low-order (quadratic) polynomial fit also indicated. Solar Activity During the Onset of Solar Cycle 24 Workshop In Napa

  8. Electron Density Profiles ne(s) Same 12 (plus 4 more) selected cases are shown as in the previous 2 figures, with the x-axis of each panel spanning the entire loop length and with a low-order (quadratic) polynomial fit also indicated. Solar Activity During the Onset of Solar Cycle 24 Workshop In Napa

  9. Loop Width Profiles w(s) Same 12 selected cases are shown as in the previous 3 figures, with the x-axis of each panel spanning over the entire loop length and with a low-order (quadratic) polynomial fit also indicated. Solar Activity During the Onset of Solar Cycle 24 Workshop In Napa

  10. Loop Geometries 56 ± 47 Mm 0.67 ± 0.23 Histograms for all 243 coronal loop cases are shown of loop half lengths L, detected fraction of loop segments qsegm, loop plane inclination angles , and loop widths w. 22 ± 18o 1.44 ± 0.33 Mm Solar Activity During the Onset of Solar Cycle 24 Workshop In Napa

  11. Temperatures and Electron Densities 109.0±0.2 cm-3 1.18 ± 0.30 MK Histograms for all 243 cases of average loop temperatures Tavg, mean temperature variations within a loop <T(s) - Tavg>, average electron densities navg, and mean density variations within a loop <n(s) - navg>. 3.4 x 108 cm-3 0.11± 0.05 Solar Activity During the Onset of Solar Cycle 24 Workshop In Napa

  12. Overpressure Ratio Versus Loop Half Length The average loop pressure, from the ideal gas law, is p = 2nekBTe. From equilibrium models (e.g., Rosner et al. 1978 and Serio et al. 1981) the (average) loop pressure is supposed to obey the following (equilibrium) scaling law, pRTV = (Te/1400)3 /L. The overpressure factor q = p/pRTV versus the loop half length L is plotted for the 243 loops observed with TRACE for this study. The predicted peak temperature Tp(q) before the loops cool down is indicated. Solar Activity During the Onset of Solar Cycle 24 Workshop In Napa

  13. TRACE reveals over-densities and flatter temperature profiles than predicted by RTV (Aschwanden, Nightingale, & Alexander 2000) Solar Activity During the Onset of Solar Cycle 24 Workshop In Napa

  14. TRACE loops were observed to appear with a time delay between the 195 Å (1.5 MK) and 171 Å (1.0 MK) filters, which was interpreted in terms of a (non-equilibrium) cooling phase (Winebarger et al. 2003). Solar Activity During the Onset of Solar Cycle 24 Workshop In Napa

  15. Non-Equilibrium Cooling Jakimiec et al. (1992): Aschwanden & Tsiklauri (2008): Flares Loops Solar Activity During the Onset of Solar Cycle 24 Workshop In Napa

  16. Conclusions: EUV loops with under-pressure (compared to RTV) are observed in the heating phase (<20%), while the majority of EUV loops observed with overpressure are progressing through the cooling phase (~80%). 1) Most loops are in anon-equilibrium state(>90%). 2) We interpret the observed overpressure as a natural consequence of the non-equilibrium cooling phase. Applying a non-equilibrium scaling law, we predict that the loops were heated to soft X-ray temperatures up to Te < 15 MK prior to their cooling to EUV wavelengths. We estimate a median loop lifetime of 10 minutes to 1 hour for our sample of TRACE loops, using an approximate temporal scaling law of lifetime ~ 10 [min] (L/10 Mm)2. This work was supported by NASA in part under the TRACE contract NAS5-38099. Solar Activity During the Onset of Solar Cycle 24 Workshop In Napa

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