Simplified expressions for the gyrosynchrotron radiation from mildly relativistic, nonthermal and thermal electrons

Simplified expressions are presented for the gyrosynchrotron radiation from mildly relativistic electrons, both for nonthermal (power-law) and for thermal (Maxwellian) distributions. Expressions are given for the emissivity, absorptivity, effective temperature, frequency of peak brightness, and degree of circular polarization. The expressions are designed for the range from about 10 to about 100 of harmonic numbers, 20 to 80 deg of viewing angle, 3 to 7 electron energy spectral index (nonthermal electrons), and 10 to the 8th to 10 to the 9th K in temperature (thermal electrons). This range generally covers the cases of interest for the 10 keV to 1 MeV electrons that are probably important in solar and stellar flares and possibly in other astrophysical situations. The accuracy of these expressions, within the stated range of validity, is generally much better than a factor of 2, while the values of some of the quantities cover up to 15 orders of magnitude. The simplicity of the expressions should make them useful for semiquantitative investigations of models of astrophysical sources