Spectral properties of large gradual solar energetic particle events -   II -Systematic Q/M-dependence of heavy ion spectral breaks
  We fit the $\sim$0.1-500 MeV/nucleon H-Fe spectra in 46 large SEP events surveyed by Desai et al. (2016) with the double power-law Band function to obtain a normalization constant, low- and high-energy parameters $\gamma_a$ and $\gamma_b$; and break energy $E_B$. We also calculate the low-energy power-law spectral slope $\gamma_1$. We find that: 1) $\gamma_a$, $\gamma_1$, and $\gamma_b$ 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)$^\alpha$ with $\alpha$ varying between $\sim$0.2-3; 3) $\alpha$ is well correlated with Fe/O at $\sim$0.16-0.23 MeV/nucleon and CME speed; 4) In most events: $\alpha<$1.4, the spectra steepen significantly at higher energy with $\gamma_b$-$\gamma_a >$3; and 5) Seven out of 9 extreme SEP events (associated with faster CMEs and GLEs) are Fe-rich, have $\alpha >$1.4, have flatter spectra at low and high energies with $\gamma_b$-$\gamma_a <$3. The species-independence of $\gamma_a$, $\gamma_1$, and $\gamma_b$ and the systematic Q/M dependence of $E_B$ within an event, as well as the range of values for $\alpha$ 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 $\alpha$ 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. 
M. I. Desai, G. M. Mason, M. A. Dayeh, R. W. Ebert, D. J. McComas, G.   Li, C. M. S. Cohen, R. A. Mewaldt, N. A. Schwadron, ...
physics.space-ph astro-ph.SR