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Note 5. The spatial diffusion coefficient is K$_{xx}$ = β η$_{T}$ · K$_{0}$ · R $^{δ}$. 

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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. 

## 6.1. Influence of the turbulence scheme 

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 

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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. 

## 6.2. Generalisation to any η$_{T}$ 

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 )). 2 

The best-fit transport parameters and χ 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 

