The Three Dimensional Structural Shape of the Gravitational Potential in the Local Group

The Local Group is a small galaxy cluster with the membership of 62 nearby galaxies including the Milky Way and M31. Although the Local Group has yet to be virialized, it interacts with the surrounding matter as one gravitationally bound system. To understand the formation and evolution of the Local Group as well as its member galaxies, it is important to reconstruct the gravitational potential field from the surrounding matter distribution in the local cosmic web. By measuring the anisotropy in the spatial distribution of the Local Group galaxies, which is assumed to be induced by the local gravitational tidal field , we resolve the three dimensional structure of the gravitational potential in the vicinity of the Milky Way smoothed on the Local Group mass scale. Our results show that (i) the minor principal axis of the Local Group tidal field is in the equatorial direction of alpha_{p}=15^{h}00^{m} and delta_{p}=20^{d}; (ii) it has a prolate shape with axial ratio of 0.5 +/- 0.13; (iii) the global tides in the Local Group is quite strong, which may provide a partial explanation for the low abundance of dwarf galaxies in the Local Group.