The Orbit and Mass of the Sagittarius Dwarf Galaxy
Possible orbital histories of the Sgr dwarf galaxy are explored. A special-purpose N-body code is used to construct the first models of the Milky Way - Sgr Dwarf system in which both the Milky Way and the Sgr Dwarf are represented by full N-body systems and followed for a Hubble time. These models are used to calibrate a semi-analytic model of the Dwarf's orbit that enable us to explore a wider parameter space than is accessible to the N-body models. We conclude that the extant data on the Dwarf are compatible with a wide range of orbital histories. At one extreme the Dwarf initially possesses 10^{11} Solar Mass and starts from a Galactocentric distance 200 kpc. At the other extreme the Dwarf starts with 10^9 Solar Mass and Galactocentric distance 60 kpc, similar to its present apocentric distance. In all cases the Dwarf is initially dark-matter dominated and the current velocity dispersion of the Dwarf's dark matter is tightly constrained to be 21 km/s. This number is probably compatible with the smaller measured dispersion of the Dwarf's stars because of (a) the dynamical difference between dark and luminous matter, and (b) velocity anisotropy.