We use Reuven Ramaty High Energy Solar Spectroscopic Imager (RHESSI) high-resolution imaging and spectroscopy observations from ~6 to 100?keV to determine the statistical relationships between measured parameters (temperature, emission measure, etc.) of hot, thermal plasma in 37 intense (GOES M- and X-class) solar flares. The RHESSI data, most sensitive to the hottest flare plasmas, reveal a strong correlation between the maximum achieved temperature and the flare GOES class, such that "super-hot" temperatures 30?MK are achieved almost exclusively by X-class events; the observed correlation differs significantly from that of GOES-derived temperatures, and from previous studies. A nearly ubiquitous association with high emission measures, electron densities, and instantaneous thermal energies suggests that super-hot plasmas are physically distinct from cooler, ~10-20?MK GOES plasmas, and that they require substantially greater energy input during the flare. High thermal energy densities suggest that super-hot flares require strong coronal magnetic fields, exceeding ~100?G, and that both the plasma β and volume filling factor f cannot be much less than unity in the super-hot region.
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