Statistical Properties of Super-Hot Solar Flares Amir Caspi †1*, Säm Krucker 2,3, Robert P. Lin 2,4,5 † 1 Laboratory for Atmospheric and Space Physics, Univ. of Colorado, Boulder, CO * Formerly at: 2 Space Sciences Laboratory, Univ. of California, Berkeley, CA Inst. of 4D Technologies, School of Engineering, Univ. of Applied Sciences Northwestern Switzerland, Windisch, CH * Formerly at: 4 Department of Physics, Univ. of California, Berkeley, CA School of Space Research, Kyung Hee University, Republic of Korea SH13B-1942

2 Introduction RHESSI has shown that “ super-hot ” (T > 30 MK) thermal plasma appears common in intense, M- & X-class flares. Recent studies of individual X-class events (Caspi & Lin 2010, ApJ 725, L161; Longcope et al. 2010, SolPhys 267, 107) showed that the super-hot component is spectrally & spatially distinct from the ~10-20 MK plasma observed by GOES, suggesting that the two populations are heated by different physical mechanisms. However, it remains unknown why only some flares achieve super-hot temperatures and on what this depends; the origins of super-hot plasma remain poorly understood. We present a survey of 37 M/X flares to investigate: What is the highest temperature achieved during flares? Is there an intrinsic limit to the maximum flare temperature? Does “ super-hot ” imply “ super-energetic? ” Do “hot” and “ super-hot ” flares behave differently?

3 Flare Selection Analysis was restricted to only M- and X-class flares – those most likely to produce super-hot plasma. We required: Good RHESSI coverage of X-ray peak (defined as uninterrupted observation over the full 10 minutes prior to GOES SXR peak) Clearly identifiable HXR (25-50 keV) and SXR (6-12 keV) peaks, occurring in order before the GOES SXR peak Time-series spectra fit reasonably well by the model (below) Imageable with grid 3 (~7 arcsec FWHM) using CLEAN  260 analyzable flares during (234 M, 26 X)  37 flares chosen in simple chronological order (25 M [from 2002], 12 X [from ]) – see Table 1

4 Selected Flares

5 Analysis For each selected flare, we: Accumulate spectra (all detectors excl. 2 & 7) in 20-sec intervals, 1/3-keV energy bins for 10 minutes prior to GOES SXR peak Fit spectrum at each interval with photon model: isothermal continuum, power-law non-thermal continuum, and 2 Gaussian lines (Fe & Fe/Ni complexes) † ; identify max. temperature Image [CLEAN] w/ grids 3-9 (excl. 7) in 6-15 keV energy band (thermally-dominated), 40-sec duration around time of max T Approximate flare volume from area within 50% intensity contour * as V = (4/3)π (A/π) 3/2 Compute source density, thermal energy from fit parameters A sample spectrum (right) and image (inset) are shown for reference. * Area is corrected for point-spread function broadening; volume estimate is good to 1 st order and simulations show it to be a reasonable approximation, within a ~23% uncertainty. † In the A3 shutter state, a 3rd Gaussian is added to approximately correct for a small miscalibration of the thick attenuator response. Spot-check shows correction good to within ~4%.

6 Sample Spectrum/Image Example photon spectrum and model fit; the fit was applied at each interval and the maximum-temperature and maximum-energy intervals were identified. In the A3 (thick+thin) state, the third Gaussian feature is added to approximately correct for a small miscalibration of the thick attenuator response. (Inset) Example image at the time of maximum temperature; the source volume is approximated from the area of >50% intensity.

7 Max. T vs. GOES class Maximum isothermal continuum temperature measured by RHESSI (diamonds) and GOES (crosses) versus GOES class for the 37 analyzed flares, with fit correlations. The RHESSI correlation is significantly (>7σ) steeper than the GOES correlation. Spectral fits with a reduced χ 2 > 2 (open diamonds) are distributed evenly in GOES class and do not significantly skew the correlation.

8 Volume vs. max T Estimated volume derived from the 6-15 keV images cotemporal with, and versus, the maximum RHESSI temperature. The distribution is roughly uniform. In a few cases (square symbols), the images show a complex morphology and suggest multiple sources, skewing the volume measurement which assumes only a single source; note that the largest volumes all suffer from this issue, and most of these also exhibit poor chi-squared values (open symbols) for the spectral fit.

9 Density vs. max T RHESSI thermal electron density cotemporal with, and versus, the maximum RHESSI temperature. 12 of 14 super-hot flares have density ≳ 3.2×10 10 cm -3. The outliers are associated with the uncertain “multiple source” volume measurements. High densities appear necessary (but not sufficient) for super-hot temperatures, consistent with formation due to compression (e.g. Caspi & Lin 2010; Longcope et al. 2010), or thick- target collisional energy loss by non-thermal particles.

10 Energy vs. max T Total energy (assuming T i = T e ) of the RHESSI thermal plasma cotemporal with, and versus, the maximum RHESSI temperature. 13 of 14 super-hot flares exceed ~2.4×10 29 erg at the time of the maximum temperature, versus a significant scatter among cooler flares. (The one super-hot outlier is the “failed eruption” of 2002 May 27 (cf. Ji et al. 2003, ApJ, 595, L135).

11 Energy density vs. max T Thermal energy density of the RHESSI thermal plasma cotemporal with, and versus, the maximum RHESSI temperature. Magnetic field strengths for selected values of equivalent magnetic energy density (B 2 /8π) are shown for reference; these are the minimum field strengths required to contain the thermal plasma (i.e. β < 1). 13 of 14 super-hot flares require B ≳ 100 G in the corona, where the super-hot plasma is located.

12 Max. Energy vs. GOES class Maximum total thermal energy (assuming T i = T e ) of the RHESSI plasma achieved during the flare versus GOES class, with fit correlation. These are instantaneous energies and do not reflect losses (radiative, conductive, etc.), thus the true maximum energy is likely higher. The power-law relationship suggests that GOES class is a good proxy for peak thermal energy, and thus possibly for total energy release.

13 Max. energy density vs. max T Thermal energy density corresponding to the maximum energy versus maximum RHESSI temperature, with reference magnetic field strengths. Super-hot flares have significantly higher maximum energy density, with 13 of 14 exceeding ~970 erg cm -3, equivalent to B ≳ 160 G; excluding the “possible multi-source” outliers (squares) highlights this association more strongly. Strong magnetic fields appear to be strictly necessary (but not sufficient) for the formation of super-hot plasma, consistent with heating by compression of the magnetic field (Caspi & Lin 2010).

15 Discussion Both RHESSI and GOES maximum temperatures show a strong correlation with GOES class. Since the temperature responses of the two instruments are significantly different, this simultaneous correlation suggests that the entire temperature distribution (and underlying physics) may scale with GOES class. The RHESSI correlation is significantly steeper than the GOES correlation, consistent with different formation mechanisms for the two populations (since similar formation would imply similar correlation). The two correlations cross at GOES class of ~C2; if RHESSI plasma is formed directly in the corona (e.g. Caspi & Lin 2010; Longcope et al. 2010), this suggests that the coronal formation mechanism is present in all flares of at least moderate intensity, even those that do not reach super-hot temperatures. This and the above bullet together suggest that the temperature distribution above ~5 MK may be strongly bimodal for all >C flares, not just super-hot/X-class flares. Thermal plasma volume is completely uncorrelated with temperature or GOES class, but high densities ( ≳ 3×10 10 cm -3 ) appear necessary for formation of super-hot plasma. The high density may be either a result of formation (e.g. by the same compression that would heat the plasma) or the cause of it (e.g. a thick target for collisional energy loss by low-energy non-thermal particles, which would not have sufficient energy to reach the chromospheric footpoints).

16 Discussion Strong coronal magnetic fields, exceeding ~200 G, appear necessary (though not sufficient) for the formation of super-hot plasma. This inference is supported by coronal fields inferred from µ-waves during X-class flares (e.g. Asai et al. 2006, PASJ, 58, L1), and is consistent with formation in the corona by compression of reconnected loops (Caspi & Lin 2010), though other explanations are, of course, also possible. The inferred magnetic field strength B ∝ β 1/2 is a strict lower limit since β 0.01, and µ-wave observations (per above) suggest that β ≈ 1.

17 Summary Our analysis of 37 M- and X-class flares has shown that: Maximum RHESSI and GOES temperatures are strongly correlated with GOES class, but the RHESSI correlation is significantly steeper; the (bimodal) temperature distribution likely also scales with GOES class Maximum thermal energy is strongly correlated with GOES class; Super-hot flares are strongly associated with a high electron number density and a high maximum thermal energy density, and thus with strong coronal magnetic fields; super-hot plasma may thus reflect not only higher temperatures, but a higher energy input into the plasma; β ≈ 1 in the super-hot region, suggesting that the plasma is efficiently heated to its physical maximum These correlations and associations that distinguish super-hot and non- super-hot flares may help to constrain models of flare reconnection and subsequent plasma heating.