deletions | additions       diff --git a/subsection_The_Liu_Quasar_Pair__.tex b/subsection_The_Liu_Quasar_Pair__.tex  index 7f7d127..08a6f2a 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 $rp < {100h_{70})}^{-1}$ kpc to refine the sample space – remove chance superpositions g - ${100h_{70})}^{-1}$ 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 (Barton et al. 2000; Ellison et al. 2008; Darg et al. 2010), 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 \lsim ≲  \Delta v < 600 km.s^{-1} $interval. Even so, Lui et all further states that Δv 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. Perhaps their spectroscopic profiles do not match those of interacting pairs. What was the criteria for this- is still left unanswered.  Lui also notes possible outliers and common trends in our refined sample space. The surprising, sixteen data points with z> 0.16 ,which seem to be outliers are kept in our sample. They are said to reduce uncertainties at higher red-shifts.