deletions | additions       diff --git a/subsection_The_Liu_Quasar_Pair__.tex b/subsection_The_Liu_Quasar_Pair__.tex  index 21344bf..5a6d51b 100644  --- a/subsection_The_Liu_Quasar_Pair__.tex  +++ b/subsection_The_Liu_Quasar_Pair__.tex 
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The choice to use projected separations $r_{p} < {100h_{70}}^{-1}$ kpc to refine the sample space – remove chance superpositions. ${100h_{70}}^{-1}$ is the Hubble constant, which accounts for /is a measure of the expansion rate of the Universe ( more details in \cite{Huchra_1992}). Lui further observes that most pairs with separation greater than 100 kpc are found to be closely separated but not interacting with one another. Selecting those with separation less than 100 kpc helps remove these points that are not a part of our sample space. It is surprising to note that 100 kpc is larger than the thresholds used in other galaxy pair studies namely (as cited in \cite{Liu_2011}), but Lui does not explain why 100 kpc is used as the threshold.  Lui further Justifies the use a LOS velocity offset $ \Delta v < 600 km.s^{-1}$ as a method to further refine the desired sample space. Plotting the distribution of $\Delta v$ of AGN pairs (Figure 2 provided in Liu) shows us that that most AGN pairs in the catalogue are found within the $300 ≲ \Delta v < 600 km.s^{-1} $interval. Even so, Lui et all al  further states that $Delta v$ range within which the pair is still interacting depends on the environment – there could be a chance that some data point were erroneously cut from the sample. Visual inspection of SDSS images for spectroscopically selected images further removes 34 AGN pairs from the parent sample. This means that strongly interacting AGN pairs can have $\Delta v$ very large.