deletions | additions       diff --git a/Comparison to Toy Models.tex b/Comparison to Toy Models.tex  index 7693054..d847554 100644  --- a/Comparison to Toy Models.tex  +++ b/Comparison to Toy Models.tex 
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As mentioned previously, the argument that the disk model fails to adequetely describe the data depends on the extent to which the selection cuts adequately exclude edge-on and out-of-phase disks from our SDSS sample, if such things exist. This argument can be summarized by the claim that it would be difficult to observationally distinguish an edge-on rotating disk from a dumbbell rotating in the line-of-sight direction. Previously, we had assigned a charactaristic velocity of 100 km/s to the satellites and only cut on satellites whos 1D velocity offset was less than $\sqrt{2} \times 25$ km/s. Since the toy model is essentially scale-free, this is best viewed as cutting on satellites that have a 1D velocity offset less than $\sqrt{2} \times 25\%$ of the charactaristic 3D velocity for satellites of the host.   Figure \ref{fig:vel_limit} shows how the shape of the 90\% isotropic disk sample changes wihen the velocity threshold chenges. The lines in the figure span from cutting on 10\% of the 3D velocity to cutting on 80\% of the 3D velocity. Overplotted is the SDSS data; it is apparent that reproducing the lack of signal at $\sim 20^{\circ} \, \lt \alpha \, \lt \sim 60^{\circ}$, or correspondingly the sharpness of the upturn at very small $\alpha$, requires a very high velocity threshold, cutting on 60-80\% of the characteristic velocity. Since we impose a cut of $\sqrt{2} \times 25$ km/s on our data, this would lead us to hypothesize a characteristic velocity of ~ 60 $\sim 60$  km/s or lower for our satellite population. If this is the case, then we would expect the systems selected to be sufficiently edge-on to account for the lack of signal detected at $\alpha \sim 30^{\circ}$