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Solar Flare Element Abundances from the Solar Assembly for X-rays (SAX) on MESSENGER

X-ray spectra in the range $1.5-8.5$~keV have been analyzed for 526 large flares detected with the Solar Assembly for X-rays (SAX) on the Mercury {\em MESSENGER} spacecraft between 2007 and 2013. For each flare, the temperature and emission measure of the emitting plasma were determined from the spectrum of the continuum. In addition, with the SAX energy resolution of 0.6 keV (FWHM) at 6~keV, the intensities of the clearly resolved Fe-line complex at 6.7~keV and the Ca-line complex at 3.9~keV were determined, along with those of unresolved line complexes from S, Si, and Ar at lower energies. Comparisons of these line intensities with theoretical spectra allow the abundances of these elements relative to hydrogen to be derived, with uncertainties due to instrument calibration and the unknown temperature distribution of the emitting plasma. While significant deviations are found for the abundances of Fe and Ca from flare to flare, the abundances averaged over all flares are found to be enhanced over photospheric values by factors of $1.66 \pm 0.34$ (Fe), $3.89~\pm~0.76$ (Ca), $1.23~\pm~0.45$ (S), $1.64~\pm~0.66$ (Si), and $2.48~\pm~0.90$ (Ar). These factors differ from previous reported values for Fe and Si at least. They suggest a more complex relation of abundance enhancement with the first ionization potential (FIP) of the element than previously considered, with the possibility that fractionation occurs in flares for elements with a FIP of less than $\sim$7~eV rather than $\sim10$~eV.