D. Maurin et al.: Systematic uncertainties on the cosmic-ray transport parameters The surprising result is that the value for α B/C + O is quite resilient to any slope obtained for δ . This is odd, since it leaves the propagated slope γ = α + δ quite uncon- strained, leading to either 2.6 (Model II) or 3.2 (Model III). This indicates that in Model III, pure diffusive transport (i.e. γ = α + δ ) has not yet been reached at TeV/n ener- gies. The dependence of the transport parameters with the source parameters α and η$_{S}$ are very different. We checked that the transport parameters do not significantly depend on the source parameter α (in particular, δ is unaffected). Still, correlations exist between the source and the other transport parameters (see Paper I), and from Table 3, we can estimate that they affect their best-fit values at most by a few ten percent. On the other hand, Fig. 1 shows that the transport pa- rameters (including δ ) are quite sensitive to the low-energy source spectrum parameterised by η$_{S}$ . In any case, this does not allow reconciliation of Model III with small δ . Taking a sizeable range for η$_{S}$ always lead to δ ≳ 0 . 6. This is even worse for Model I (no reacceleration). At variance, Model II (no convection) is very sensitive to η$_{S}$ . However, η$_{S}$ is con- strained by primary fluxes measurements, and by no means could it span the range shown in Fig. 1. When this con- straint is considered, the best-fit δ for Model II turns out to be 0 . 35. Given the sensitivity of the latter to η$_{S}$ and the possible bias in low-energy data (because of the solar mod- ulation), this is consistent with a Kolmogorov spectrum. If the constraint of the primary flux is taken into account, the uncertainty on the transport parameters (associated to the source parameter η$_{S}$ ) can be estimated as ∼ 10 − 20%. The puzzling point is that, although Model III is pre- ferred over Model II on a statistical basis, the latter seems to agree more with the expected theoretical value of δ . This is more of further if we consider the quantity γ = α + δ , the asymptotic slope reached in the purely diffusive regime. The TRACER experiment finds γ ≈ 2 . 65 for all nu- clei (Ave et al. 2008), whereas the best-fit slope from high- energy H and He data is γ ≈ 2 . 85 (Donato et al. 2009). From the propagated slope’s point of view, Model II is again favoured over Model III, since the former leads to γ = 2 . 59, whereas the latter leads to 3 . 25 (read off Table 4). If Model III is confirmed, as already emphasised above, this would mean that even high-energy data have not reached the purely diffusive transport yet. The source parameters α and η$_{S}$ are not completely free. They can be fitted directly on primary elemental fluxes (see Paper I). If we determine simultaneously the transport and source parameters from a fit on B/C + O HEAO-3 data, we obtain the best-fit values gathered in Table 4. For Models II and III, η B/C + O S is not far from η best S found from the B/C fit (see Fig. 1). For Model II, using the above constraint ( η B/C + O S = 1 . 24) selects the diffusion slope δ B/C + O = 0 . 35, close to the Kolmogorov spectrum for the turbulence. We now turn to the effect of the low-energy shape of the diffusion coefficient. Assuming different diffusion schemes lead to different forms of the spatial and momentum diffu- sion coefficient (Schlickeiser 2002). Recently, Ptuskin et al. (2006) also argue that the form of the spatial diffusion coef- ficient can change at low energy, due to the possibility that the nonlinear MHD cascade sets the power-law spectrum of turbulence. We first consider several theoretically-motivated diffu- sion forms given in the literature. They mostly differ at low energy, so that it is useful to rewrite Eq. (5) as 6. Influence of the low-energy diffusion coefficient 5.3. Fitting α and η$_{S}$ using a primary flux 5.4. Summary for the source effect Note 4. The data used are IMP7-8, Voyager 1&2, ACE, HEA0-3, Spacelab, and CREAM04 for the B/C ratio, and HEAO-3 for the oxygen flux. Table 4. Best-fit values from a simultaneous fit on B/C and O. Fig. 1. From top to bottom: best-fit values of K$_{0}$ , δ , V$_{a}$ , V$_{c}$ , and the associated χ $^{2}$/d.o.f. as a function of η$_{S}$ [see Eq. (9)]. Here, γ = α + δ = 2 . 65. The vertical grey-dotted line is a guideline for the results at the default configuration η$_{S}$ = − 1. K ( E ) = β η$_{T}$ · K$_{0}$ R δ . (10) 5 -4 -2 0 2 4 ] -1   Myr 2 [kpc 0 K -2 10$^{-1}$ 10  (source) S Influence of  -4 -2 0 2 4 0.5 1 Model III Model II (no conv.) Model I (no reac.) Model 0 (pure diff.) -4 -2 0 2 4 ] -1  [km s a V 20 40 60 80 -4 -2 0 2 4 ] -1  [km s c V 5 10 15 20 S -4 -2 0 2 4 /d.o.f 2 1 10 Model η ( B/C + O ) S α ( B/C + O ) δ ( B/C + O ) χ 2 $_{min}$/ d.o.f. 0 − 0 . 82 2.22 0.41 25.3 I − 1 . 23 2.23 0.98 9.23 II 1 . 24 2.24 0.35 3.62 III 1 . 56 2.30 0.95 2.31