Parametric Evolution Of Power-Law Energy Spectra Of Flare Accelerated Electrons In The Solar Atmosphere

It is well known that solar hard X-ray bursts (HXRs) and solar radio bursts (SRBs) from solar flares both are produced directly by fast electron beams (FEBs) traveling through the solar atmosphere. The observed characteristics of HXRs and SRBs sensitively depend on the energy distribution of FEBs, which are believed commonly to have a power-law energy spectrum. When FEBs propagating in the solar atmosphere, however, their energy spectra can considerably vary due to the interaction with the atmospheric plasmas and this may significantly influence the observational characteristics of the producing HXRs and SRBs. In the present paper, based on flare atmospheric models, we investigate the parametric evolution of power-law spectra of FEBs due to their energy losses when propagating along flaring loops. The results show that an initially single power-law spectrum with a lower-energy cutoff can evolve into a more complex double power-law spectrum or a broken power-law spectrum with multi-breaking knees because of the dependence of the energy loss on the initial energies. The possible effects of the energy-spectral evolution of FEBs on observational characteristics of their HXR flares and SRBs are discussed. The present results are helpful to understand the physics of dynamical spectra of HXRs and SRBs from solar flares.