Masses for the Local Group and the Milky Way

We use the very large Millennium Simulation of the concordance ΛCDM 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% 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 current 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× 10 M⊙, or logMLG/M⊙ = 12.72, with an interquartile range of [12.58, 12.83] and a 5% to 95% range of [12.26, 13.01]. Thus a 95% lower confidence limit on the true mass of the Local Group is 1.81× 10 M⊙. 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× 10 M⊙ with a 95% lower confidence limit of 0.80× 10 M⊙.