Gyrosynchrotron Emission Generated by Nonthermal Electrons with the Energy Spectra of a Broken Power Law

Abstract

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 brokenpower-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 (δ 1 ) and above (δ 2 ) the break energy. We find that with the addition of the δ 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 (ν 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 δ 1 and E B affect the microwave spectral index (α) and the degree of polarization (r c ) mainly in the optically-thick regime, while δ 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.

Evolution of Flare-Accelerated Electrons Quantified by Spatially Resolved Analysis

“…The greater hardening of the MW-derived δ can then be reconciled by a hardening of the spectrum of the injected electrons only above E bk , or by a sustained increase in time of E bk itself. This would be in line with the recent study of Wu et al (2019), which conducted the detailed simulation of the GS emission from the electrons with double power-law energy distribution and found that the increased high-energy electrons specified by the second spectral index result in a harder spectral index in the MW flux density spectrum, even if the total number of electrons does not change significantly.…”

The First Flare Observation with a New Solar Microwave Spectrometer Working in 35–40 GHz

“…In addition, spectra with unusual shapes, such as flat or continuous rising even at frequencies above tens of GHz, have been reported (White et al 1992;Ramaty et al 1994;Kaufmann et al 2004;Silva et al 2007;Zhou et al 2010;Nagnibeda et al 2013;Song et al 2016). Wu et al (2019) found with GS simulations that the turnover frequency can reach up to tens of GHz, being sensitive to the abundance of energetic electrons of hundreds keV to a few MeV. These studies indicate the necessity of a full spectral coverage of the centimetermillimeter wavelength to better understanding solar flares.…”

The Mouse That Squeaked: A Small Flare from Proxima Cen Observed in the Millimeter, Optical, and Soft X-Ray with Chandra and ALMA

“…If our prediction of an orders-of-magnitude larger SXR-millimeter scaling relationship for M-dwarf flares compared to solar flares holds, the relationship of particle to thermal emission in M-dwarf flares might also differ. Simulations of 5-100 GHz flux densities resulting from optically thin gyrosynchrotron emission find a dependence on the high-energy electron density and cutoff energy (Wu et al 2019). Millimeter emission currently remains one of the few direct probes of the accelerated particle environment in M-dwarf flares (MacGregor et al 2021).…”