Line-of-sight velocity projection impact on Local Group mass determinations

The mass of the Local Group (LG), which includes the Milky Way, Andromeda (M31), and their satellites, is crucial for validating galaxy formation and cosmological models. Traditional virial mass estimates, which rely on line-of-sight (LoS) velocities and simplified infall assumptions, are prone to systematic biases due to unobserved velocity components and anisotropic kinematics. Using the TNG cosmological simulation, we examined two limiting cases: the minor infall model – which ignores velocities perpendicular to LoS directions – and the major infall model – which assumes purely radial motion toward the center of mass (CoM). Our simulations demonstrate that geometric corrections are vital: the minor infall model underestimates the true mass, while the major infall model overestimates it. By applying these calibrated corrections to observed dwarf galaxy kinematics within 1 Mpc of the LG’s CoM, we derived a refined LG mass of M_LG = (2.99 ± 0.60) × 10¹² M . This finding resolves previous discrepancies as it aligns with predictions from the Λ cold dark matter model, timing arguments, and independent mass estimates. Our analysis highlights the importance of correcting for velocity anisotropy and offers a robust framework for dynamical mass estimations of galaxy groups.