Spectral evolution of mildly relativistic electrons in solar flares

Solar flares are a powerful engine capable of accelerating ambient plasma particles to high nonthermal energies. A key characteristic of these particles is their energy spectrum. Numerous studies of nonthermal hard X-ray emission established that a typical spectral evolution of the nonthermal electrons with energies of dozens keV follows a soft-hard-soft pattern in impulsive events and soft-hard-harder pattern in some long-duration events. Here we extend the study of the spectral evolution to the case of flare-accelerated mildly relativistic electrons primarily responsible for the flare microwave emission. We examine the spatially resolved microwave emission observed with the Expanded Owens Valley Solar Array in twelve solar flares and find that they also typically follow a soft-hard-soft spectral evolution. However, the revealed spectral evolution of the mildly relativistic electrons covers the spectral index range from 2-4 to 15 or more and, thus, is much more prominent than for the X-ray-producing electrons. The evolution of the spectral index is closely correlated with the emission flux and does not show any noticeable time delay. The spectral index displays a prominent correlation with the brightness temperature with a pattern similar to all events considered. We conclude that the revealed relationships and the evolutionary pattern is an inherent property of particle acceleration in the solar flares.