deletions | additions       diff --git a/Comparison.tex b/Comparison.tex  index 7b141ec..a156fbc 100644  --- a/Comparison.tex  +++ b/Comparison.tex 
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\item Disk model - In this model, 2-5 satellites are placed randomly between 0 and 200 kpc from the origin on the xy plane and then randomly given a z coordinate randomly between -10 and 10 kpc. All satellites are assigned a 3D velocity of 100 km/s such that each satellite is in circular motion about the host. The model is randomly rotated and viewed along the z axis.  \item Corotating oppositely-aligned pairs (COP) model - Here, each host is restricted to exactly two satellites. Once the first satellite is randomly placed on the xy plane, the placing of the second satellite is restricted such thatthe  $\alpha$ when the system is viewed along the z axis is less than $10^{\circ}$. From there, each satellite is assigned a z cooridate between -10 and 10 kpc and the system is subject to random rotation and viewed along the z axis. \item M31 model - This model is based on the position and velocities of the 13 M31 satellites belonging to the co-rotating plane identified in \citet{Ibata_2013}. The three dimensional positions of the satellites are taken from \citet{McConnachie_2012} and the line-of-sight velocities are compiled from \citet{McConnachie_2012} and \citet{2013ApJ...768..172C}. Note that we only consider the 13 satellites exhibiting coherent rotation; the two satellites aligned with the planar structure but with couter-aligned line-of-sight velocities are considered part of the isotropic background. We assign proper motions to the satellites to place them in circular orbits around the host, and select 2-5 satellites to mock observe (this selection is random, i.e. independent of the luminosities of the true M31 satellites). The system is then randomly rotated and viewed along the z axis.