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\subsection{Constant gamma variation, T0-$\gamma$ degeneracy} At this point we should know more or less the extent of the effect on the logR-$\gamma$ relation due to the variation of the value of T0 in the foreground Ly-$\alpha$ forest.  We need now to investigate the effect of a variation of the parameter $\gamma$ in the foreground forest .  So in order to compute the new logR values for each model we can keep the same density field ( so still we are adopting the corresponding density fields of the original relation) and apply an uniform variation in the $\gamma$ value of the foreground forest. Uniform means that, for example, $\Delta\gamma$ is set to 0.2 between foreground and Ly-$\beta$ for all the points.  So, for example the logR for the model D15 is computed using again the density field of this simulation for both the redshifts z=2.553 and z=3.211 . We impose this time different values of $\gamma$ for the foreground Ly-$\alpha$ ($\gamma_{\alpha}\sim 1.3$) and for the Ly-$\beta$ power laws ( $\gamma_{\beta}\sim 1.5$). The values of T0 are maintained the same as in Section 1.3 : T0= 12000 for the foreground Ly-$\alpha$ and T0=11500 for the Ly-$\beta$ at higher redshift.   % If we maintain the normalization with the known T($\Delta$) values changing $\gamma$ for the foreground of each model will determine also a variation in the T0 value in the foreground Ly-$\alpha$ .  %So , to avoid degeneracy we   %However at this point we will have already tested the effect of varying T0 in the foreground Ly-$\alpha$ ..  %In fact we can change $\gamma$ as above and compute the new T0 value obtained maintaining the normalization, once quantified , for each point we can test how much this variation in T0 would affect the relation repeating the experiment in Section 1.3 varying only the value of T0 in the foreground forest.  Comparing the reference logR-$\gamma$ relation with the new one obtained by varying $\gamma$ (but not T0) for the foreground Ly-$\alpha$ we could quantify, in a crude way, the effect due to the change of $\gamma$ .