Interpretation of a correlation between the flux densities of extended hard X-ray and microwave solar bursts

The demonstrated correlation between the observed 100-keV X-ray flux density and the 3.75- or 9.4-GHz microwave flux density of solar bursts is interpreted in terms of a source model for the extended bursts in which microwave emission comes from thin shells at increasing heights for decreasing frequencies. The model consists of a hemisphere containing a uniform density of radiating (gyrosynchrotron) electrons in a dipole magnetic field decreasing rapidly with increasing radius. An approximate analytical treatment of the model is used to deduce expressions for the emitted fluxes in terms of model parameters. Numerical calculations based on one set of model parameters of emission fluxes are then presented which demonstrate that the same population of electrons can account for both the X-ray and the microwave observations.