Energy Cutoff,Energy Index,and Density of Nonthermal Electrons Responsible for Solar Microwave and HXR Bursts

The purpose of this paper is to investigate the crossing point of the power-law distribution lines calculated during different times of microwave and hard X-ray bursts. A linear correlation between the logarithm of the total density and the energy index of nonthermal electrons described by a power-law is proven to be a necessary condition for the crossing of a group of power-law distribution lines corresponding to the time evolution of the nonthermal electrons during a solar microwave and HXR burst. The common crossing point of these lines may be considered as evidence of a common cutoff energy of the nonthermal electrons responsible for gyrosynchrotron or bremsstrahlung radiation. When the common crossing point is close to the low-energy cutoff, the correlation coefficient is negative, and vice versa. The result may be useful for estimating the cutoff energy as well as the particle acceleration mechanism.