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RESIK Solar X-ray flare element abundances on a non-isothermal assumption

Solar X-ray spectra from the RESIK crystal spectrometer on the {\em CORONAS-F} spacecraft (spectral range $3.3-6.1$~Å) are analyzed for thirty-three flares using a method to derive abundances of Si, S, Ar, and K, emission lines of which feature prominently in the spectra. For each spectrum, the method first optimizes element abundances then derives the differential emission measure as a function of temperature based on a procedure given by Sylwester et al. and Withbroe. This contrasts with our previous analyses of RESIK spectra in which an isothermal assumption was used. The revised abundances (on a logarithmic scale with $A({\rm H}) = 12$) averaged for all the flares in the analysis are $A({\rm Si}) = 7.53 \pm 0.08$ (previously $7.89 \pm 0.13$), $A({\rm S}) = 6.91 \pm 0.07$ ($7.16 \pm 0.17$), $A({\rm Ar}) = 6.47 \pm 0.08$ ($6.45 \pm 0.07$), and $A({\rm K}) = 5.73 \pm 0.19$ ($5.86 \pm 0.20$), with little evidence for time variations of abundances within the evolution of each flare. Our previous estimates of the Ar and K flare abundances are thus confirmed by this analysis but those for Si and S are reduced. This suggests the flare abundances of Si and Ar are very close to the photospheric abundance or solar proxies, while S is significantly less than photospheric and the K abundance is much higher than photospheric. These estimates differ to some extent from those in which a single enhancement factor applies to elements with first ionization potential less than 10~eV.