Spatial and temporal invariance in the spectra of energetic particles in gradual solar events

We show evidence of spatial and temporal invariance in the energy spectra of similar to 1-100 MeV protons from large gradual solar energetic particle (SEP) events. Nearly identical spectra are seen over longitude intervals of up to 160 degrees, and the intensities at all energies decline with e-folding time constants of 6-18 hr for periods of similar to 3 days. The region of the invariant spectra is associated with acceleration on the eastern flank of the shock wave driven out from the Sun by a coronal-mass ejection (CME). The quasi-parallel shock in this region changes only slowly with time, and a quasi equilibrium is established for particles stored on field lines in the expanding volume between the shock and the Sun. On the western flank of the shock, the SEP event is more dynamic. Here, the nearly quasi-perpendicular shock produces harder spectra that change more rapidly with time as regions of the shock with varying speed and angle sweep across the observer's field line. Gradual SEP events arise from large CMEs with sufficient speeds to generate shocks that are fast enough to accelerate particles. In our study, shocks with transit speed >750 km s(-1) always accelerate particles, while those with speeds of 500-750 km s(-1) sometimes do. However, invariant spectra seem to occur in all gradual SEP events as a consequence of the structure and topology of the CME and shock.