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 $dQ/dE = q \beta^{\eta_S} {\cal
R}^{-\alpha}$ and fix the diffusion coefficient $K(R)= K_0\beta^{\eta_T} {\cal
R}^{\delta}$ such as to reproduce the B/C ratio, the MCMC analysis constrains
the source spectral index $\alpha$ to be in the range $2.2-2.5$ for all primary
species up to Fe, regardless of the value of the diffusion slope $\delta$. The
$\eta_S$ low-energy shape of the source spectrum is degenerate with the
low-energy shape $\eta_T$ of the diffusion coefficient: we find
$\eta_S-\eta_T\approx 0$ for p and He data, but $\eta_S-\eta_T\approx 1$ 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
$\eta_S-\eta_T\approx 0-1$ (no need for different slopes $\alpha$). 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.
