The Quantitative Relation of the Time Profiles of Intensities in the Well-connected Solar Energetic Particle Events

In this work, the quantitative relation of the intensity time profiles in the well-connected energetic particle events has been identified. Focusing on the propagation processes of energetic protons in the energy channels of about 13-64 MeV, solar energetic particle (SEP) events observed by STEREO A, STEREO B, and SOHO have been studied. The intensities observed by the spacecraft with the best magnetic connection to the source region tend to rise the fastest and have the highest peak intensities. In the cases without multiple injections or significant acceleration of particles by interplanetary shocks, particle intensities with the highest peaks are fitted by using a solution of the diffusion equation, and the time profiles of particle intensities could be described by two parameters. By fitting 59 energetic proton events, we find that the two parameters satisfy a power-law model in different events, and the distribution of peak time is also obtained. The power-law model helps one to obtain a quantitative relation of SEP intensities with the fitting function, and the distribution of peak time could provide a basis for determining the magnetic connection between the spacecraft and the source region.