Constraining the History of the Sagittarius Dwarf Galaxy Using Observations of Its Tidal Debris

We present a comparison of semi-analytic models of the phase-space structure of tidal debris with observations of stars associated with the Sagittarius dwarf galaxy (Sgr). We find that many features in the data can be explained by these models. The properties of stars 10-15 degrees away from the center of Sgr --- in particular, the orientation of material perpendicular to Sgr's orbit (c. f. Alard 1996) and the kink in the velocity gradient (Ibata et al 1997) --- are consistent with those expected for unbound material stripped during the most recent pericentric passage ~50 Myrs ago. The break in the slope of the surface density seen by Mateo, Olszewski & Morrison (1998) at ~ b=-35 can be understood as marking the end of this material. However, the detections beyond this point are unlikely to represent debris in a trailing streamer, torn from Sgr during the immediately preceding passage ~0. 7 Gyrs ago, but are more plausibly explained by a leading streamer of material that was lost more that 1 Gyr ago and has wrapped all the way around the Galaxy. The observations reported in Majewski et al (1999) also support this hypothesis. We determine debris models with these properties on orbits that are consistent with the currently known positions and velocities of Sgr in Galactic potentials with halo components that have circular velocities vcirc=140-200 km/s. The best match to the data is obtained in models where Sgr currently has a mass of ~10⁹ Mₛun and has orbited the Galaxy for at least the last 1 Gyr, during which time it has reduced its mass by a factor of 2-3, or luminosity by an amount equivalent to ~10% of the total luminosity of the Galactic halo. These numbers suggest that Sgr is rapidly disrupting and unlikely to survive beyond a few more pericentric passages.