Implications of the Soft X-Ray versus Hard X-Ray Temporal Relationship in Solar Flares

Abstract

We have calculated the time profiles of spatially integrated hard X-ray (30-500 keV) and soft X-ray (1-8 Å) emission in both thick-target electron-heated models, and bulk heated thermal models, of the impulsive phase of solar flares. For the thermal model, we find a serious difficulty: the time profiles of the 30-500 keV hard X-ray emission do not peak at the same time as those for the higher energy component (40-500 keV) of this emission, a result that manifestly disagrees with the observations. In the thick-target model, however, the hard X-ray light curves at all energies >30 keV peak at the same time, lending considerable support to this model.

Observations also suggest that the relationship between the hard X-ray and soft X-ray emission is that of "derivativity," that is, the hard X-ray time profile corresponds not so much to the instantaneous soft X-ray flux, but rather its temporal derivative. We have explored the relationship between the hard X-ray (30-500 keV) and soft X-ray (1-8 Å) time profiles in the thick-target model. Typically we find that the temporal derivative of the soft X-ray emission does indeed correspond well to the instantaneous soft X-ray emission, particularly during the rise phase of the event. The cause of this behavior is a combination of heating and density enhancement processes, and we assess the relative roles of each process for a variety of simple hard X-ray time profiles, ranging from short (5 s rise time) to long (60 s rise-time). As expected, temperature enhancements dominate the behavior for the shortest bursts, with density enhancements becoming important for bursts of greater than approximately 15 s duration. It also appears that some other form of gradual heating (e.g., slow reconnection) persists through the decay phase of the event.