synchrotron losses, we use the maximum value of $E_{\rm{max,e}}$ as a lower limit for $E_{\rm{max,p}}$.

To reproduce the radio spectral shape, we need a hard index for the electrons $\Gamma_{\rm{e,1}}$ = 1.8 (taking thus $\Gamma_{\rm{e,2}}$ = 2.8), while we keep $\Gamma_{\rm{p}}$ = 2 due to the lack of observational constraints. For a $B$ field between 10 and 20 $\mu$G, the $\gamma$-ray data can only be explained if the total energy in electrons reaches $W_{\rm{e}}$ = (2.5 – 7) $\times$ $10^{49}$ erg, which is clearly unreasonable since that requires a $K_{\rm{e-p}}$ between 0.5 and 1.4. If in order to reduce $W_{\rm{e}}$, we increase $B$ to higher values than expected for the compressed ISM, the $\gamma$-ray data cannot be fitted and the IC spectrum lies one order of magnitude below the data. Even if infrared and optical photon fields with energy density 0.26 eV cm$^{-3}$ each (the same as the CMB value, which is a reasonable estimate 100 pc below the Galactic plane) are added, an unrealistically large $W_{\rm{e}}$ is still required to fit the $\gamma$-ray data.

Another inconsistency of that model is that the values of $E_{\rm{b}}$, $E_{\rm{max,e}}$ and $E_{\rm{max,p}}$ reported in Table \[tab:Phys\_param\] are not consistent with the magnetic field. 