A Dynamical Model for the Orbit of the Andromeda Galaxy M31 and the Origin of the Local Group of Galaxies

In a dynamical model for the origin of the Magellanic Clouds and their large orbital angular momenta around the Galaxy, we consider that a primordial gas-rich Andromeda galaxy collided with our similar Galaxy in an oblique sense some 10 Gyr ago and it left the latter following the Hubble expansion law approximately. A huge gaseous halo was hydrodynamically compressed at their closest approach and driven to form a number of dwarf members, including the Large Magellanic Cloud (LMC) and Small Magellanic Cloud (SMC), of the Local Group of Galaxies (LGG) and scatter them on the orbital plane of these two mass-dominant galaxies. In order to see the reality of this model, we reexamine the two-dimensional sky distribution of the LGG members and the Magellanic Stream, we confirm an earlier and widely-discussed idea that they align along two similar great circles, each with an angular width of ∼30◦, and the planes of these circles are approximately normal to the line joining the present position of the sun and the Galactic center. Further we make a three-dimensional distribution map of these objects, and observe it from various directions. A well-defined plane of finite thickness is found, within which most of the member galaxies are confined, supporting the existence of the above circles on the sky. Thus we could determined the orbital elements of M31 relative to the Galaxy through reproducing the well-studied dynamics of the LMC and SMC around the Galaxy. The expected proper motion of M31 is (μl, μb) = (38 μas yr ,−49 μas yr). Probable orbital motions of the other dwarfs are also determined, and the expected proper motion for each object is given to compare with observations in near future.