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We present a comparison of semi-analytic models of the phase-space structureof tidal debris with observations of stars associated with the Sagittariusdwarf galaxy (Sgr). We find that many features in the data can be explained bythese 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 themost recent pericentric passage ~50 Myrs ago. The break in the slope of thesurface density seen by Mateo, Olszewski & Morrison (1998) at ~ b=-35 can beunderstood as marking the end of this material. However, the detections beyondthis point are unlikely to represent debris in a trailing streamer, torn fromSgr during the immediately preceding passage ~0.7 Gyrs ago, but are moreplausibly explained by a leading streamer of material that was lost more that 1Gyr ago and has wrapped all the way around the Galaxy. The observationsreported in Majewski et al (1999) also support this hypothesis. We determinedebris models with these properties on orbits that are consistent with thecurrently known positions and velocities of Sgr in Galactic potentials withhalo components that have circular velocities v_circ=140-200 km/s. The bestmatch to the data is obtained in models where Sgr currently has a mass of ~10^9M_sun and has orbited the Galaxy for at least the last 1 Gyr, during which timeit has reduced its mass by a factor of 2-3, or luminosity by an amountequivalent to ~10% of the total luminosity of the Galactic halo. These numberssuggest that Sgr is rapidly disrupting and unlikely to survive beyond a fewmore pericentric passages.Comment: 19 pages, 5 figures, accepted to Astronomical Journa

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