D. Maurin et al.: Systematic uncertainties on the cosmic-ray transport parameters Fig. 7. Best-fit B/C ratio for standard Model II (thick red) and III (thick black) using the reference setting (solid and thin dashed lines are for the cross-section sets W03 and GAL09). The special best-fit Models O/I and III/II are also plotted in thin grey lines (light and dark shade respec- tively). The best-fit curves for these four relevant configura- tions are shown in Fig. 7. From this graphic view, we can see that Model II matches the data best at very-low en- ergy, Model III at intermediate energies, and Models O/I and III/II at high energy. While we found that a system- atic bias in HEAO-3 data would not change the ordering of which is the best model (see Sect. 8), we see from Fig. 7 that a more complicated pattern in the data may be more effective in changing which model is best. To summarise, when a standard scheme for the diffu- sion coefficient is assumed, Model III is always preferred over Model II. However, the latter seems to agree more with theoretical expectations for δ . Model II is also more consistent with the measured propagated slope γ = α + δ . Because of this oddity, we may not be able to give a defi- nite answer about the value of δ . This is further complicated when η$_{T}$ is left free; in that case, best models are always without convection, and even the pure diffusive model is redeemed (although both have difficulty reproducing the B/C peak at GeV/n energies). We see that many uncer- tainties show up at GeV/n energies. As also illustrated by the various predictions for various δ in Fig 7, the higher the energy, the closer we can expect to reach the purely diffu- sive regime. As a result, high-energy B/C data are desired to unambiguously pinpoint the value of δ . In the past years, we have promoted and used a model favouring both convection and reacceleration (e.g., Maurin et al. 2001, 2002, and subsequent studies) from sta- tistical criteria. The main and known problem of this model lies in its uncomfortably high value for δ ( δ ∼ 0 . 8). Such a model is also preferred in the present study. In addition, we found that the high value for δ is extremely resilient to any change in the setting, which leaves us with several alterna- tives: assume that there are complicated biases in the data that conspire to give high δ in such models, that this high Acknowledgements. We thank W. R. Webber for providing us with the nuclear production cross-sections discussed in Webber et al. (2003) and for useful suggestions. We also thank C. Combet for a careful reading of the paper. A. P. is grateful for financial support from the Swedish Research Council (VR) through the Oskar Klein Centre. We acknowledge the support of the French ANR (grant ANR-06- CREAM). Finally, the starting point of the paper was a comparison between systematic uncertainties (generated by uncertain- ties in the input ingredients) and statistical uncertainties for the values of the transport parameters. That the for- mer can be larger than the latter shows that many efforts are still needed in CR physics, especially for the production cross-sections, before one can take full advantage of any sta- tistical analysis, as performed in Papers I and II with an MCMC technique. Some of these issues may be resolved as new data on cosmic-ray nuclei are being released ( cream , pamela , tracer ). This study has limitations. For instance, we only varied the source and diffusion parameters according to simple pa- rameterisations. More complicated dependences could have been inspected. However, it is worth recalling that it may be dangerous to introduce too many ad hoc prescriptions, be- cause the statistical meaning—already unclear when com- paring the different classes of models—becomes less and less obvious as the number of parameters and models tested increase. In the framework of homogeneous and isotropic diffusion coefficients, a maybe more important issue is the question of the Galactic wind. A constant wind was cho- sen because of the simplicity of the solutions (of the cor- responding diffusion equation). On the one hand, Galactic winds are ubiquitous. On the other, as shown in this study, constant wind cannot accommodate a realistic slope of the diffusion coefficient. A linear wind may provide different re- sults. We are implementing a numerical solver in our prop- agation code to inspect this issue. Another possibility that cannot be ruled out is that the HEAO-3 data suffer from non-trivial systematics. value of δ is real (in that case it needs to be explained theo- retically), or that any model with convection should be ex- cluded (which contradicts the fact that winds are observed in many galaxies). Even if we adopt the last alternative, no firm conclusions can be drawn on the value of δ . Indeed, if the statistical analysis is relaxed, a large category of mod- els are redeemed, attaining any value for δ between 0.3 and 0.9. These models may be purely diffusive, with convection and/or reacceleration, and are very sensitive to the shape of the low-energy diffusion coefficient (which is not prescribed theoretically for the moment). Data at higher energy are needed to solve this question. More constraints can also be obtained by combining several secondary-to-primary ratios (e.g., Webber 1997a,b). This is left for a later study. References Ahn, H. S., Allison, P. S., Bagliesi, M. 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Conclusion  (GeV/n) k/n E -1 10 1 10 2 10 3 10 B/C ratio 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 =250 MV) - Garcia-Munoz et al. 1987 IMP7-8 ( =225 MV) - Lukasiak 1999 Voyager1&2 ( =225 MV) - De nolfo et al. 2006 ACE 97-98 ( =250 MV) - Engelmann et al. 1990 HEAO-3 ( =200 MV) - Swordy et al. 1990 Spacelab ( =425 MV) - Ahn et al. 2008 CREAM 04 ( Model III (SA) /d.o.f=1.47) 2 =0.86, ( Model II (SA) /d.o.f=4.73) 2 =0.23, ( =-1.30) T Model III/II ( /d.o.f=2.26) 2 =0.51,  ( =-2.61) T Model I/0 ( /d.o.f=3.29) 2 =0.61,  ( TOA =225 MV =250 MV |