Velocity Trends in the Debris of Sagittarius and the Shape of the Dark-matter Halo of the Galaxy

Recently, radial velocities have been measured for a large sample of M giants from the 2MASS catalog, selected to be part of the Sgr dwarf leading and trailing streams. Here we present a comparison of their kinematics to models of the Sgr dwarf debris orbiting Galactic potentials, with halo components of varying degrees of flattening and elongation. This comparison shows that the portion of the trailing stream mapped so far is dynamically young and hence does not provide very stringent constraints on the shape of the Galactic dark-matter halo. The leading stream, however, contains slightly older debris, and its kinematics provide for the first time direct evidence that the dark-matter halo of the Galaxy has a prolate shape with an average density axis ratio within the orbit of Sgr close to 5/3. Subject headings: dark-matter – Galaxy: halo, kinematics and dynamics, structure, fundamental parameters