Gyrosynchrotron emission generated by nonthermal electrons with energy spectra of a broken power law

Latest observational reports of solar flares reveal some uncommon features of microwave spectra, such as unusually hard (or even positive) spectra, and/or a super-high peak frequency. For a better understanding of these features, we conduct a parameter study to investigate the effect of broken-power-law spectra of energetic electrons on microwave emission on the basis of gyrosynchrotron mechanism. The electron broken-power-law energy distribution is characterized by three parameters, the break energy ($E_B$), the power-law indices below ($\delta_1$) and above ($\delta_2$) the break energy. We find that with the addition of the $\delta_2$ component of the electron spectra, the total flux density can increase by several times in the optically-thick regime, and by orders of magnitude in the optically-thin regime; the peak frequency ($\nu_p$) also increases and can reach up to tens of GHz; and the degree of polarization ($r_c$) decreases in general. We also find that (1) the variation of the flux density is much larger in the optically-thin regime, and the microwave spectra around the peak frequency manifest various profiles with the softening or soft-hard pattern; (2) the parameters $\delta_1$ and $E_B$ affect the microwave spectral index ($\alpha$) and the degree of polarization ($r_c$) mainly in the optically-thick regime, while $\delta_2$ mainly affects the optically-thin regime. The results are helpful in understanding the lately-reported microwave bursts with unusual spectral features and point out the demands for a more-complete spectral coverage of microwave bursts, especially, in the high-frequency regime, say, $>10-20$ GHz.