Masses for the Local Group and the Milky Way

We use the very large Millennium Simulation of the concordance Λ cold dark matter cosmogony to calibrate the bias and error distribution of Timing Argument estimators of the masses of the Local Group and of the Milky Way. From a large number of isolated spiral-spiral pairs similar to the Milky Way/Andromeda system, we find the interquartile range of the ratio of timing mass to true mass to be a factor of 1.8, while the 5 and 95 per cent points of the distribution of this ratio are separated by a factor of 5.7. Here, we define true mass as the sum of the `virial' masses, M₂₀₀, of the two dominant galaxies. For present best values of the distance and approach velocity of Andromeda, this leads to a median likelihood estimate of the true mass of the Local Group of 5.27 × 10¹²M_solar or logM_LG/M_solar = 12.72, with an interquartile range of [12.58, 12.83] and a 5-95 per cent range of [12.26, 13.01]. Thus, a 95 per cent lower confidence limit on the true mass of the Local Group is 1.81 × 10¹²M_solar. A timing estimate of the Milky Way's mass based on the large recession velocity observed for the distant satellite Leo I works equally well, although with larger systematic uncertainties. It gives an estimated virial mass for the Milky Way of 2.43 × 10¹²M_solar with a 95 per cent lower confidence limit of 0.80 × 10¹²M_solar.