THE RELATIVE TIMING OF MICROWAVES AND X-RAYS FROM SOLAR-FLARES

We investigate the observed delay of microwaves relative to hard X-rays from solar flares. There are two different types of observed microwave delays which must be explained. In the first set of observations, cross-correlations of the hard X-rays and microwaves from flares which exhibit rapid time variation show that microwaves lag X-rays by ∼0.25 s. Since this time scale is of order the collisional time for the electrons, a time-dependent formulation is needed. For various solar flare models, we calculate the evolution of distributions of electrons numerically, and from this we determine the expected microwave and hard X-ray emission. We find that for reasonable thick-target model parameters and for injected electron distributions which are separable in time, energy, pitch angle, and position, the observed delay cannot be explained by magnetic trapping of electrons in the corona. The observed delay can be accounted for if higher energy microwave producing electrons are accelerated later than lower energy hard X-ray producing electrons. In the second set of observations, the peak flux time for simple impulsive spikes is observed to occur about 1-3 s earlier in hard X-rays than in microwaves. These time scales are much larger than collisional time scales, so we use the steady state relations for the microwave to X-ray ratio developed in an earlier work. We apply these to flares whose spectral indices are known throughout the course of the flare. We find that the flux during the rising phase of the flares can be explained well in terms of the thick-target model, but during the decay phase the thick-target model predicts too little microwave flux. A number of possibilities for this excess microwave flux are explored including spectral hardening, magnetic trapping, and thermal synchrotron and free-free emission.