The Barycentric Region of the Local Group: Present Extent, Membership Dependence, and Uncertainty Growth

Abstract

The Local Group (LG) barycentre is used as a kinematic reference in studies of LG dynamics, but the uncertainty in its inferred position and its dependence on theadopted galaxy membership are not always quantified together. We propagate observationally motivated uncertainties for the Milky Way (MW), M31, M33, and theLarge Magellanic Cloud (LMC) through an evaluation ensemble of N = 1000 Monte Carlo realizations. The resulting present-day uncertainty region is highly flattened,with principal-axis scales of (54.8, 7.7, 0.2) kpc. The projections are consistent with unimodality under the Hartigan dip test (p ≥ 0.99), although the distribution ismildly skewed. The median barycentre lies 452 kpc from the Galactic centre, with a distance dispersion of 55 kpc and angular dispersions of approximately 0.8◦. Relativeto a MW+M31 definition, adding M33 or the LMC shifts the median barycentre by approximately 53 and 27 kpc, respectively. When the sampled barycentres are propagated ballistically, the radius enclosing 68% of realizations grows from 55 kpc at the present epoch to 103 kpc after 5 Gyr and 202 kpc after 10 Gyr. These rates describeuncertainty propagation under an isolated-system assumption, not physical motion or degradation of the centre of mass itself. On an independent evaluation ensemble, the calibrated dynamical model reproduces the reference MW–M31 merger fraction and median merger time reasonably well, although the M33 merger chronology remains discrepant. The results show that the inferred LG barycentre depends materially on the adopted membership and that its future positional uncertainty grows substantially when propagated from present-day uncertainties.