1. Statistical Properties of Hot Thermal Plasmas in M/X Flares Using RHESSI Fe & Fe/Ni Line * and Continuum Observations Amir Caspi †1,2, Sam Krucker 2, Robert P. Lin 1,2 † cepheid@ssl.berkeley.edu; http://sprg.ssl.berkeley.edu/~cepheid/spd2007/cepheid@ssl.berkeley.eduhttp://sprg.ssl.berkeley.edu/~cepheid/spd2007/ 1 Department of Physics, University of California, Berkeley, CA 94720 2 Space Sciences Laboratory, University of California, Berkeley, CA 94720 * (Fe & Fe/Ni line analysis not shown here)

2. Introduction Hard X-ray emission from “super-hot” thermal plasma (T > 30MK) was first observed in solar flares by Lin et al. (1981), and has since been observed in a handful of large flares. The origins of such hot plasma remain poorly understood. We present the first results from a study investigating the following questions: What is the highest temperature achieved during flares, and when does it occur? Is there an intrinsic limit to the maximum flare temperature, and if so, on what does it depend? Does “super-hot” imply “super-energetic?” Do “super-hot” flares behave differently than merely “hot” flares?

3. Flare Selection Since 2002, RHESSI has observed over 500 flares of GOES class M and X, which are the most likely candidates for “super-hot” temperatures (GOES class is often used as a proxy for flare temperature). For analysis, we selected flares as follows: Flare occurred during 2002 to 2005 Good coverage of X-ray peak (currently defined as uninterrupted observation over the full 10 minutes prior to GOES SXR peak) Imageable with grid 3 (~7 arcsec FWHM) using CLEAN Clearly identifiable HXR (25-50 keV) and SXR (6-12 keV) peaks, occurring before the GOES SXR peak (in order: HXR, SXR [RHESSI], SXR [GOES]) Time-series spectra are fit reasonably well by the model (below)  260 analyzable flares (234 M-class, 26 X-class)

4. Selected Flares Heliocentric positions of the selected flares are shown; flares already processed (results at right) are highlighted in red.

5. Sample Image/Spectrum Top: a sample CLEAN image using grids 3-9 (ex. 7); the contour (at 50% of peak pixel flux) is used to approximate the source volume Bottom: a sample spectrum with the model fit; the instrumental artifact is included for attenuator state A3

6. Methodology For each selected flare, we perform the following analysis: Image [CLEAN] w/ grids 3-9 (excl. 7) in 6-15 keV energy band (thermally-dominated), 40-sec duration at GOES SXR peak time Approximate flare volume based on area enclosed by 50% CLEAN contour * (contour at 50% of peak pixel flux) Obtain spectra (all grids excl. 2 & 7) in 20-sec intervals for the 10 minutes prior to GOES SXR peak; identify HXR/SXR peaks Fit each interval between the HXR/SXR peak times with: isothermal continuum, power-law non-thermal continuum, 2 Gaussian lines (Fe & Fe/Ni complexes) † Compute source density, thermal energy from fit parameters A sample image and spectrum are shown for reference. * This approximation is fairly crude but gives a first-order estimate; we will improve this estimate by using visibility-based imaging algorithms and forward-modeling of the source. † In the A3 shutter state, a 3rd Gaussian is added to model an instrumental artifact which is not yet accounted for in the spectral response matrix.

7. First Results Preliminary analysis has been completed for 37 flares from the initial set of 260 (~14% of the sample set), and first results are given below. The results will likely change somewhat as we improve the analytical method and continue analysis on the entire sample set.

8. Max. Temp. vs. GOES class The maximum isothermal plasma temperature occurring during the flare (from spectral fitting) versus GOES class. There appears to be a (very) rough power-law correlation.

9. Density/Vol. vs. GOES class The density (at the time of maximum temperature) and estimated source volume vs. GOES class. Densities are derived from the emission measure & estimated source volume, assuming a unity filling factor. There appears to be no correlation for either quantity, although this may change as we improve the volume estimation technique.

10. Energy vs. GOES class Total thermal energy and thermal energy density (at time of maximum temperature) vs. GOES class. Energies are derived from the emission measure and estimated source volume, assuming a unity filling factor and ion/electron thermal equilibrium. There appears to be a (very) rough power-law correlation for energy, and possibly (loose) upper/lower limits for energy density. Magnetic energy densities for various field strengths are shown for reference; for large flares, this suggests the field strength at the looptop (the location of the thermal emission) must be ~200G or higher in order to confine the thermal plasma within the loop.

11. Emission Measure vs. Max T The isothermal emission measure at the time of (and plotted against) the maximum temperature observed by RHESSI. No correlation can be inferred, but there may be loose upper/lower limits on the EM at maximum temperature.

12. Density/Vol. vs. Max. T The density (at the time of maximum temperature) and estimated source volume vs. the maximum temperature observed by RHESSI. Densties are derived as before (see left). There appears to be no correlation for either quantity, although this may change as we improve the volume estimation technique.

13. Energy vs. Max. T Total thermal energy and thermal energy density (at time of maximum temperature) vs. maximum temperature observed by RHESI. Energies are derived as before (see left). No correlation can be inferred, but there may be loose upper/lower limits for the energy and energy density for a given maximum temperature.

14. Summary We selected 260 M/X-class flares for analysis to characterize thermal flare plasmas and investigate the properties of “super-hot” flares. Preliminary analysis has been completed on 37 flares: “Super-hot” plasma temperatures appear to be a common feature of X- class flares, but may be uncommon for M-class flares. Maximum flare temperature and thermal energy may be power-law correlated with GOES class (a proxy for lower bulk plasma temperature), while energy density may show upper/lower limits Emission measure is not clearly correlated with maximum temperature, but upper/lower limits may exist; similarly for energy density Density and source volume do not appear to show any correlation or limits vs. GOES class or maximum temperature; however, this may change as we improve the imaging method and volume estimation technique. We anticipate that these results will change as we analyze the rest of the sample set and improve our analytical method.

15. Ongoing/Future Work These are only first results - there remains a lot more to be done. We plan to: Complete analysis on the remaining 223 selected flares Utilize visibility-based imaging algorithms and forward-modeling of source sizes to improve the estimates of source volume Improve the criteria for flare selection and time-interval selection (for spectral fitting) to reduce possible selection bias Separate occulted from on-disk flares to explore characteristics as a function of population Use the Fe & Fe/Ni line complex ratio (already being fit) as another diagnostic of maximum flare temperature and analyze its behavior alongside the continuum temperature measurements Explore differential emission measure fitting to examine the behavior of temperature distributions with GOES class, etc. Use imaging spectroscopy on spatially-separate sources to reduce spectral ambiguity (of source-integrated spectra) and examine the behaviors of multiple spatial locations within flares RHESSI data is vast, rich, and flexible - there are many ways to analyze it…this is just the tip of the proverbial iceberg!