Local Group analogue the separation and relative radial velocity of the two galaxies can be combined with the age of the Universe (taken to be 13.6 Gyr) to obtain a Timing Argument mass estimate $M_{TA}$ (Equations (1) to (3)). The true mass of the pair $M_{tr}$ is harder to define because of the extended and complex mass distributions predicted by the $\Lambda$CDM model. The mass of an individual dark halo is often taken to be $M_{200}$ the mass within a sphere of mean density 200 times the critical value, so a natural choice for $M_{tr}$ is the sum of $M_{200}$ for the two galaxies. The Millennium Simulation database only lists $M_{200}$ for Type 0 galaxies, those at the centre of the main subhalo of each friends-of-friends particle group. Many of our LG analogues lie within a single FOF group. One of the pair is then a Type 1 galaxy, the central object of a subdominant subhalo, and so has no listed value for $M_{200}$. In such cases we have gone back to the particle data for the simulation in order to measure $M_{200}$ directly also for these galaxies.

An alternative convention is to define $M_{tr}$ as the sum of the 