Electron energy and magnetic field derived from solar microwave burst spectra

Microwave bursts during solar flares are known to be sensitive to high-energy electrons and magnetic field, both of which are important ingredients of solar flare physics. This paper presents such information derived from the microwave bursts of the 412 flares that were measured with the Owens Valley Solar Array. We assumed that these bursts are predominantly due to gyrosynchrotron radiation by nonthermal electrons in a single power-law energy distribution to use the simplified formulae for gyrosynchrotron radiation in the data analysis. A second major assumption was that statistical properties of flare electrons derived from this microwave database should agree with an earlier result based on the hard X-ray burst spectrometer on Solar Maximum Mission. Magnetic field information was obtained in the form of a scaling law between the average magnetic field and the total source area, which turns out to be a narrow distribution around ∼400 G. The derived nonthermal electron energy is related to the peak flux, peak frequency, and spectral index, through a multistep regression fit, which can be used for a quick estimate for the nonthermal electron energy from spatially integrated microwave spectral observations.