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 Sgr dwarf's orbit that enables us to explore a wider parameter space than is accessible to the N -body models. We conclude that the extant data on the Sgr dwarf are compatible with a wide range of orbital histories. At one extreme the Sgr dwarf initially possesses ～10¹¹ M_⊙ and starts from a Galactocentric distance R _D(0)?200 kpc. At the other extreme the Sgr dwarf starts with ～10⁹ M_⊙ and R _D(0)～60 kpc, similar to its present apocentric distance. In all cases the Sgr dwarf is initially dark matter dominated and the current velocity dispersion of the Sgr dwarf's dark matter is tightly constrained to be 21±2 km s^?1. This number is probably compatible with the smaller measured dispersion of the Sgr dwarf's stars because of (i) the dynamical difference between dark and luminous matter, and (ii) velocity anisotropy.