Line-of-sight mass estimator and the masses of the Milky Way and Andromeda Galaxy
The total mass of a galaxy group, such as the Milky Way (MW) and the Andromeda Galaxy (M 31), is typically determined from the kinematics of satellites within their virial zones. Bahcall and Tremaine (1981) proposed the $v^2r$ estimator as an alternative to the virial theorem. In this work, we extend their approach by incorporating the three-dimensional spatial distribution of satellites within the system to improve the reliability and accuracy of galaxy mass estimates. Applying this method to a comprehensive dataset of Local Group satellites based on recent, high-precision distance measurements, we estimate the total mass of the MW to be $(7.9 \pm 2.3) \times 10^{11}$ $M_\odot$ and that of M~31 to be $(15.5 \pm 3.4) \times 10^{11}$ $M_\odot$. The effectiveness of the method is constrained by the precision of distance measurements, making it particularly well suited for the Local Group, but challenging to apply to more distant systems.