deletions | additions       diff --git a/subsection_LogR_gamma_relation_Using__.tex b/subsection_LogR_gamma_relation_Using__.tex  index e3c09f0..b609e37 100644  --- a/subsection_LogR_gamma_relation_Using__.tex  +++ b/subsection_LogR_gamma_relation_Using__.tex 
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\subsection{LogR-$\gamma$ \subsection{Normalization of LogR-gamma  relation} Using As tried by George, we can "normalize" the imposed T-$\rho$ power-law for each model with the known values of T($\Delta$) from the previous curvature work.  In  the simplified relations case of z=3.211 adopting Becker et al 2011 values:  T($\Delta$=2.6)=18400.  While for the foreground Ly-$\alpha$ at z=2.553:  T($\Delta$=5.7)=28600.   Fixing these values of T($\Delta$) and the values of $\gamma$ corresponding to each model  we canthen  compute the logR statistics expected T0 values :  for the z=3.211 forest:  T0=T($\Delta$)/$\Delta^{\gamma -1}$=18400/$2.6^{\gamma -1}$  and for the foreground  at z=2.553  T0=28600/$5.7^{\gamma -1}$  For  each redshift (let's start from one ..the one already simulation we can then impose a new power-law using the T0 value  computed by George z=3.211). This should correspond as above but maintaining the $\gamma $ value and the density field corresponding  to each model. Again we can compute logR and find a new logR-$\gamma$ relation.   So, for example  the orange circles 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 a power law with $\gamma\sim 1.5$ but with different values of T0: T0= 12000 for the foreground Ly-$\alpha$ and T0=11500 for the Ly-$\beta$ at higher redshift.   The only difference between the new logR-$\gamma$ relation and the previous one (presented in Section 1.2) is  in the preliminary tests. values of T0 of the foreground Ly-$\alpha$ and the Ly-$\beta$ at higher redshift .   Because the LogR-$\gamma$ relation is not sensitive to the T0 value of Ly-$\beta$, any difference in the slope ($\Delta$slope) of logR-$\gamma$ relation or in its normalization($\Delta$Norm) will be due to a change in the value of T0 of the foreground Lyman-$\alpha$.