D. Maurin et al.: Systematic uncertainties on the cosmic-ray transport parameters Table 5. K ( E ) and K$_{pp}$ for different schemes. Note 5. The spatial diffusion coefficient is K$_{xx}$ = β η$_{T}$ · K$_{0}$ · R $^{δ}$. Note 6. Models 0, I, II, and III for L = 4 kpc. SA corresponds to the reference DM used throughout the paper. In the second step, we let η$_{T}$ vary over a wide range in order to draw more general conclusions. A few turbulence schemes are gathered in Table 5. The associated best-fit values of the transport coefficients are presented in Table 6. When only convection is present (Model I), the low-energy form of K ( E ) is irrelevant, as seen in Table 6. For models with reacceleration (Models II and III), it significantly affects almost all parameters. If there is no wind (Model II), the effect is maximum on δ . The model with pure diffusion (Model 0), or with both con- vection and reacceleration (Model III), falls in-between. For Model III, the cases SA and IFM, on the one hand, and LBI and Mix, on the other, give very similar results. This is eas- ily understood as the quantities η SA T = 2 − δ and η IMF T = 1 (respectively η LBI T = 1 − δ and η Mix T = 0) are roughly equal for δ best III ∼ 1. The important result is that Model III is mildly sensitive to the diffusion scheme, with an uncertainty of a few ten percent scatter on all the transport parameters. However, Model II parameters are extremely sensitive to the diffusion scheme (more than a factor of 2 scatter). Depending on The best-fit transport parameters and χ 2 min evolution as a function of η$_{T}$ are plotted in Fig. 2. For η$_{T}$ ≲ − 2, all the models converge slowly towards purely diffusive models (no convection, no reacceleration). But this is at the cost of a bad χ 2 (see bottom panel). Based on the χ 2 criterium, high values of η$_{T}$ ( ≳ 2) are also disfavoured. The four configu- rations have marked minima in their χ 2 $_{min}$, corresponding to η best T ≈ − 2 . 75 , − 2 . 5 , − 0 . 25 , +0 . 25 for Models 0, I, II, and III respectively, for which δ best ≈ 0 . 6 , 0 . 6 , 0 . 4 , 0 . 8. For η$_{T}$ ∼ − 2 . 5, all models point to δ ∼ 0 . 5, close to a Kraichnan spectrum for turbulence. For Model III, for a well-chosen value of η$_{T}$ , the diffusion slope could be decreased at most down to δ = 0 . 5, but such a configuration does not correspond to the minimal χ 2 for We generalise the analysis by allowing for any value of the parameter η$_{T}$ in the diffusion coefficient K ( E ). In doing so, we do not seek to provide sound physical motivations for the range tested. In this section, whatever the value of η$_{T}$ , the diffusion coefficient in momentum space is assumed to follow K$_{pp}$K$_{xx}$ = (4 / 3) p $^{2}$V 2 a / ( δ (4 − δ $^{2}$) (4 − δ )). the case considered, δ is found in the range 0 . 16 − 0 . 38. The hierarchy of χ 2 min among the various models is always conserved. Fig. 2. Same as Fig. 1, but now as a function of η$_{T}$ [see Eq. (10)]. The vertical grey-dotted line is for the default configuration η$_{T}$ = 1 (SA). 6.2. Generalisation to any η$_{T}$ 6.1. Influence of the turbulence scheme Table 6. Best-fit transport parameters based on different low-energy dependence of the diffusion coefficient. Type of turbulence η$_{T}$ K$_{pp}$K$_{xx}$ 4 / 3 p $^{2}$V 2 a LBI Leaky Box Inspired 0 1 δ (4 − δ $^{2}$) (4 − δ ) SA Slab Alfv´ en 1 1 δ (4 − δ $^{2}$) (4 − δ ) IFM Isotropic fast magnetosonic 2 − δ β 1 − δ ln( v $_{V$_{a}$}$) Mix Mixture SA and IFM 1 − δ β 1 − δ ln( v $_{V$_{a}$}$) Type K best 0 × 10 2 δ best V best c V best a χ $^{2}$/d.o.f (kpc $^{2}$Myr − $^{1}$) (km s − $^{1}$) (km s − $^{1}$) 0: LBI 3.48 0.45 . . . . . . 17.5 0: SA 4.08 0.40 . . . . . . 28.8 0: IFM 4.30 0.38 . . . . . . 36.7 0: Mix 3.71 0.43 . . . . . . 23.7 I: LBI 0.40 0.94 13.6 . . . 12.0 I: SA 0.42 0.93 13.5 . . . 11.2 I: IFM 0.42 0.93 13.5 . . . 11.6 I: Mix 0.41 0.94 13.5 . . . 12.0 II: LBI 5.50 0.38 . . . 65.0 1.61 II: SA 9.76 0.23 . . . 73.1 4.73 II: IFM 14.0 0.16 . . . 18.9 6.86 II: Mix 7.13 0.32 . . . 12.8 2.03 III: LBI 0.70 0.78 18.0 47.1 0.87 III: SA 0.48 0.86 18.8 38.0 1.47 III: IFM 0.49 0.85 18.9 45.6 1.25 III: Mix 0.73 0.77 17.8 57.4 0.93 6 -4 -3 -2 -1 0 1 ] -1   Myr 2 [kpc 0 K -2 10$^{-1}$ 10  (transport) T Influence of  -4 -3 -2 -1 0 1 0.5 1 Model III Model II (no conv.) Model I (no reac.) Model 0 (pure diff.) -4 -3 -2 -1 0 1 ] -1  [km s a V 20 40 60 80 -4 -3 -2 -1 0 1 ] -1  [km s c V 5 10 15 20 T -4 -3 -2 -1 0 1 /d.o.f 2 1 10