Statistical analysis of solar energetic particle rise times using Earth and Mars observations and constraints on particle transport parameters
The propagation of solar energetic particles (SEPs) in interplanetary space is modulated by solar wind turbulence, which significantly influences particle diffusion and energy evolution through scattering processes. Traditional analyses based on absolute flux measurements face inherent difficulties in disentangling source acceleration from subsequent transport, while temporal features such as onset and peak times are less affected and better suited for studying SEP transport. This study establishes a statistical relationship between the rise time of SEP events at different energies using multi-satellite observations at Earth and Mars. We use data from SOHO/ERNE and Tianwen-1/MEPA between November 2020 and March 2025, selecting 75 SEP events at 1 AU and 58 near Mars. For each energy range, onset times are determined by linear fitting, and peak times are extracted via a sliding median filter combined with Savitzky-Golay smoothing; the difference gives the SEP rise time. Comparing with the pure diffusion equation prediction, we examine the statistical behavior of rise time at Earth and Mars. Despite event selection uncertainties, SEP rise time follows a clear power-law relation with energy. The flatter power-law at Mars indicates weaker energy dependence with increasing solar distance. Using these empirical relations, we constrain the rigidity dependence of the parallel mean free path within the parallel diffusion model. Our results show that turbulence scattering at Mars approaches a rigidity-independent regime, reflecting turbulence evolution toward a dissipation-dominated state from Earth to Mars.