halos of the two galaxies meet. Such structures have no well-defined edge, so any definition of their total mass is necessarily somewhat arbitrary. In addition, their dynamical evolution from the Big Bang until the present is substantially more complex than that of a point-mass binary. Thus the mass value returned by the Timing Argument cannot be interpreted without some calibration against consistent dynamical models with extended dark halos.

A first calibration of this type was carried out by @kc91 using simulations of an Einstein-de Sitter CDM cosmogony. Here we use the very much larger Millennium Simulation [@mr_nature] to obtain a more refined calibration based on a large ensemble of galaxy pairs with observable properties similar to those of the Local Group. We find that the standard timing estimate is, in fact, an almost unbiased estimate of the sum of the conventionally defined virial masses of the two large galaxies.

@zaritsky89 attempted to measure the halo mass of the Milky Way alone by measuring radial velocities for its dwarf satellites and assuming the population to be in dynamical equilibrium in the halo potential. They noted, however, that one of the most distant dwarfs, Leo I, has a very large recession velocity 