$\Lambda$CDM structure formation model [e.g. @nfw97]. Thus if we place tight restrictions on the $V_{max}$ values of our galaxies, we will obtain a sample of Local Group analogues with a narrow range of $M_{tr}$ values. If, in addition, we force the parameters which enter in the Timing Argument (the pair separation and relative radial velocity) to lie in narrow ranges, then the TA mass estimate itself is tightly constrained. The distribution of $A_{200}$ is thus forced to be narrow as a consequence of our selection criteria.

A second effect is that most of the new pairs added by widening the requirement on $V_{max}$ have at least one galaxy with $150{{\rm \,km\,s^{-1}}}\le V_{max} < 200{{\rm \,km\,s^{-1}}}$, thus with relatively low $M_{tr}$. This simply reflects the strong dependence of halo abundance on $V_{max}$. Given that halo mass scales approximately as $V_{max}^3$ it is striking that the addition of so many pairs containing a “low mass” galaxy reduces the median value of $A_{200}$ by just 15%. The low tail of the distribution is more strongly affected, by almost a factor of $2$ at the lower 5% point, but the upper end of the distribution is barely affected at all. This demonstrates that the 