A TEST OF THICK-TARGET NONUNIFORM IONIZATION AS AN EXPLANATION FOR BREAKS IN SOLAR FLARE HARD X-RAY SPECTRA

Solar nonthermal hard X-ray (HXR) flare spectra often cannot be fitted by a single power law, but rather require a downward break in the photon spectrum. A possible explanation for this spectral break is nonuniform ionization in the emission region. We have developed a computer code to calculate the photon spectrum from electrons with a power-law distribution injected into a thick target in which the ionization decreases linearly from 100% to zero. We use the bremsstrahlung cross section from Haug, which closely approximates the full relativistic Bethe-Heitler cross section, and compare photon spectra computed from this model with those obtained by Kontar et al., who used a step-function ionization model and the Kramers approximation to the cross section. We find that for HXR spectra from a target with nonuniform ionization, the difference (Delta gamma) between the power-law indexes above and below the break has an upper limit between similar to 0.2 and 0.7 that depends on the power-law index d of the injected electron distribution. A broken power-law spectrum with a higher value of Delta gamma cannot result from nonuniform ionization alone. The model is applied to spectra obtained around the peak times of 20 flares observed by the Ramaty High-Energy Solar Spectroscopic Imager from 2002 to 2004 to determine whether thick-target nonuniform ionization can explain the measured spectral breaks. A Monte Carlo method is used to determine the uncertainties of the best-fit parameters, especially on Delta gamma. We find that 15 of the 20 flare spectra require a downward spectral break and that at least six of these could not be explained by nonuniform ionization alone because they had values of Delta gamma with less than a 2.5% probability of being consistent with the computed upper limits from the model. The remaining nine flare spectra, based on this criterion, are consistent with the nonuniform ionization model.