Paper detail

p, He, and C to Fe cosmic-ray primary fluxes in diffusion models: Source and transport signatures on fluxes and ratios

The propagated fluxes of proton, helium, and heavier primary cosmic-ray species (up to Fe) are a means to indirectly access the source spectrum of cosmic rays. We check the compatibility of the primary fluxes with the transport parameters derived from the B/C analysis, but also if they bring further constraints. Proton data are well described in the simplest model defined by a power-law source spectrum and plain diffusion. They can also be accommodated by models with, e.g., convection and/or reacceleration. There is no need for breaks in the source spectral indices below $\sim 1$ TeV/n. Fits on the primary fluxes alone do not provide physical constraints on the transport parameters. If we let free the source spectrum $dQ/dE = q β^{η_S} {\cal R}^{-α}$ and fix the diffusion coefficient $K(R)= K_0β^{η_T} {\cal R}^δ$ such as to reproduce the B/C ratio, the MCMC analysis constrains the source spectral index $α$ to be in the range $2.2-2.5$ for all primary species up to Fe, regardless of the value of the diffusion slope $δ$. The $η_S$ low-energy shape of the source spectrum is degenerate with the low-energy shape $η_T$ of the diffusion coefficient: we find $η_S-η_T\approx 0$ for p and He data, but $η_S-η_T\approx 1$ for C to Fe primary species. This is consistent with the toy-model calculation in which the shape of the p/He and C/O to Fe/O data is reproduced if $η_S-η_T\approx 0-1$ (no need for different slopes $α$). When plotted as a function of the kinetic energy per nucleon, the low-energy p/He ratio is shaped mostly by the modulation effect, whereas primary/O ratios are mostly shaped by their destruction rate.