deletions | additions       diff --git a/subsection_The_Liu_Quasar_Pair__.tex b/subsection_The_Liu_Quasar_Pair__.tex  index bfa8c87..42039ff 100644  --- a/subsection_The_Liu_Quasar_Pair__.tex  +++ b/subsection_The_Liu_Quasar_Pair__.tex 
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The quasar pair catalogue sample used in this project is obtained from Lui et al 2011. The purpose of the Lui's selection criteria is to compile (from the SDSS) a Quasar Pair catalogue of interacting AGN pairs only. (Liu et al 2011)AGN pairs that make up the parent sample are identified optically from the spectroscopic sample of the SDSS DR7. Further selection criteria is applied to refine the parent sample to ensure the study of genuinely interacting AGN pairs rather than chance superpositions. Using line of sight (LOS) velocity differences (or offset) where LOS velocity is the velocity meausured along the line of sight of an observer, and transverse separation - the projected distance within the LOS direction - rp ,Lui selects only AGN pairs that are interacting.  The choice to use projected separations rp < 100h70-1 kpc to refine the sample space – remove pairs that are at low separation but are not interacting - h^-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 Liu lui  does not explain why 100 kpc is used as the threshold.100 kpc is approximately 10 times the effective radius (radius that contains half the total mass) for the typical elliptical galaxy that hosts these quasars.  Lui further Justifies the use a LOS velocity offset (Δv) < 600 km s-1 as a method to further refine the desired sample space. Observing the distribution of (Δv) of AGN pairs (figure (2) provided in Liu) shows us that that most AGN pairs are found within the 300 ≲ (Δv) < 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.   Lui notes that corrections are to be made to the sample due to SDSS’ limitations, as pairs with angular separation ≤ 55” lead to the spectroscopic data of the pair not being captured unless one of the AGN is captured on an overlapping plate (which is not common). .  The correction is done by supplementing the observed pairs (with angular separation≤ 55” ) with modified ([C-1]Np) pairs. The Np pairs are randomly drawn from the sample pairs with separation smaller than 55”. details of this correction are contained in Liu et al 2011.