Line-of-Sight Velocity Projection Impact on the Local Group Mass

The mass of the Local Group (LG), comprising the Milky Way (MW), 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 examine two limiting cases: the \underline{minor infall} model -- ignoring perpendicular velocities to the LoS directions) and the \underline{major infall} model -- assuming purely radial motion towards 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 derive a refined LG mass of $M_{\mathrm{LG}} = (2.99 \pm 0.60) \times 10^{12}\, M_\odot$. This finding aligns with predictions from the $\Lambda$CDM model, timing arguments, and independent mass estimates, resolving previous discrepancies. Our analysis highlights the importance of correcting for velocity anisotropy and offers a robust framework for dynamical mass estimation in galaxy groups.