deletions | additions       diff --git a/Comparison.tex b/Comparison.tex  index 3f2091e..8604f9b 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 that the angle between $\alpha$ when  the position vectors of system is viewed along  the two satellites z-axis  is greater less  than $170^{\circ}$. 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.