ABSTRACT
We fit ∼0.1–500 MeV nucleon−1 H–Fe spectra in 46 large solar energetic particle (SEP) events with the double power-law Band function to obtain a normalization constant, low- and high-energy parameters γ
a and γ
b, and break energy E
B, and derive the low-energy spectral slope γ
1. We find that: (1) γ
a, γ
1, and γ
b are species-independent and the spectra steepen with increasing energy; (2) E
B decreases systematically with decreasing Q/M scaling as (Q/M)
α
; (3) α varies between ∼0.2–3 and is well correlated with the ∼0.16–0.23 MeV nucleon−1 Fe/O; (4) in most events, α < 1.4, γ
b–γ
a > 3, and O E
B increases with γ
b–γ
a; and (5) in many extreme events (associated with faster coronal mass ejections (CMEs) and GLEs), Fe/O and 3He/4He ratios are enriched, α ≥ 1.4, γ
b–γ
a < 3, and E
B decreases with γ
b–γ
a. The species-independence of γ
a, γ
1, and γ
b and the Q/M dependence of E
B within an event and the α values suggest that double power-law SEP spectra occur due to diffusive acceleration by near-Sun CME shocks rather than scattering in interplanetary turbulence. Using γ
1, we infer that the average compression ratio for 33 near-Sun CME shocks is 2.49 ± 0.08. In most events, the Q/M dependence of E
B is consistent with the equal diffusion coefficient condition and the variability in α is driven by differences in the near-shock wave intensity spectra, which are flatter than the Kolmogorov turbulence spectrum but weaker than the spectra for extreme events. In contrast, in extreme events, enhanced wave power enables faster CME shocks to accelerate impulsive suprathermal ions more efficiently than ambient coronal ions.
