deletions | additions       diff --git a/Comparison to Toy Models.tex b/Comparison to Toy Models.tex  index 584a017..1aaa252 100644  --- a/Comparison to Toy Models.tex  +++ b/Comparison to Toy Models.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 subjected to a random rotation and oberved along the z direction, i.e. the z direction is taken to be the line of sight and the xy plane is taken to be the plane of the sky.  \item ``Dumbell" Corotating oppositely-aligned pairs  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 the position vectors of the two satellites is greater than $170^{\circ}$. From there, each satellite is assigned a z cooridate between -10 and 10 kpc and the model procceeds as in the disk model. \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.