Charge-to-mass dependence of heavy ion spectral breaks in large gradual solar energetic particle events

We fit the ∼0.1-500 MeV/nucleon H-Fe spectra in 46 large SEP events surveyed by [1] 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 . We also calculate the low-energy power-law spectral slope γ₁. We find that: 1) γ_a , γ₁, and γ_b are species-independent within a given SEP event, and the spectra steepen with increasing energy; 2) E_B 's are well ordered by Q/M ratio, and decrease systematically with decreasing Q/M, scaling as (Q/M)^α with α varying between ∼0.2-3; 3) α is well correlated with Fe/O at ∼0.16-0.23 MeV/nucleon and CME speed; 4) In most events: α <1.4 and the spectra steepen significantly at higher energy with γ_b -γ_a >3; and 5) Seven out of nine extreme SEP events (associated with faster CMEs and GLEs) are Fe-rich and have α >1.4 with flat spectra at low and high energies yielding γ_b -γ_a <3. The species-independence of γ_a , γ₁, and γ_b and the systematic Q/M dependence of E_B within an event, as well as the range of values for α suggest that the formation of double power-laws in SEP events occurs primarily due to diffusive acceleration at near-Sun CME shocks and not due to scattering in the interplanetary turbulence. In most events, the Q/M-dependence of E_B is consistent with the equal diffusion coefficient condition while the event-to-event variations in a are probably driven by differences in the near-shock wave intensity spectra, which are flatter than the Kolmogorov turbulence spectrum but still weaker compared to that inferred for the extreme events. The weaker turbulence allows SEPs to escape more easily, resulting in weaker Q/M-dependence of E_B , (lower a values) and spectral steepening at higher energies. In extreme events, the flatter spectra at high- and low-energy and stronger Q/M-dependence of E_B (larger α values) occur due to enhanced wave power, which also enables the faster CME shocks to accelerate flare suprathermals more efficiently than ambient coronal ions.