We present the first all-sky view of the Sagittarius (Sgr) dwarf galaxy mapped by M-giant star tracers detected in the complete Two Micron All Sky Survey (2MASS). Near-infrared photometry of Sgr's prominent M-giant population permits an unprecedentedly clear view of the center of Sgr. The main body is fitted with a King profile of limiting major-axis radius 30°—substantially larger than previously found or assumed—beyond which is a prominent break in the density profile from stars in the Sgr tidal tails; thus the Sgr radial profile resembles that of Galactic dwarf speroidal (dSph) satellites. Adopting traditional methods for analyzing dSph light profiles, we determine the brightness of the main body of Sgr to be MV = -13.27 (the brightest of the known Galactic dSph galaxies) and the total Sgr mass-to-light ratio to be 25 in solar units. However, we regard the latter result with suspicion and argue that much of the observed structure beyond the King-fit core radius (224') may be outside the actual Sgr tidal radius as the former dwarf spiral/irregular satellite undergoes catastrophic disruption during its last orbits. The M-giant distribution of Sgr exhibits a central density cusp at the same location as, but not due to, the old stars constituting the globular cluster M54. A striking trailing tidal tail is found to extend from the Sgr center and arc across the south Galactic hemisphere with approximately constant density and mean distance varying from ~20 to 40 kpc. A prominent leading debris arm extends from the Sgr center northward of the Galactic plane to an apogalacticon ~45 kpc from the Sun and then turns toward the north Galactic cap (NGC), from where it descends back toward the Galactic plane, becomes foreshortened, and, at brighter magnitudes, covers the NGC. The leading and trailing Sgr tails lie along a well-defined orbital plane about the Galactic center. The Sun lies within a kiloparsec of that plane and near the path of leading Sgr debris; thus, it is possible that former Sgr stars are near or in the solar neighborhood. We discuss the implications of this new view of the Sgr galaxy and its entrails for the character of the Sgr orbit, mass, mass-loss rate, and contribution of stars to the Milky Way halo. The minimal precession displayed by the Sgr tidal debris along its inclined orbit supports the notion of a nearly spherical Galactic potential. The number of M giants in the Sgr tails is at least 15% that contained within the King limiting radius of the main Sgr body. The fact that M giants, presumably formed within the past few gigayears in the Sgr nucleus, are nevertheless so widespread along the Sgr tidal arms not only places limits on the dynamical age of these arms but also poses a timing problem that bears on the recent binding energy of the Sgr core and that is most naturally explained by recent and catastrophic mass loss. Sgr appears to contribute more than 75% of the high-latitude, halo M giants, despite substantial reservoirs of M giants in the Magellanic Clouds. No evidence of extended M-giant tidal debris from the Magellanic Clouds is found. Generally good correspondence is found between the M-giant, all-sky map of the Sgr system and all previously published detections of potential Sgr debris, with the exception of Sgr carbon stars, which must be subluminous compared with counterparts in other Galactic satellites in order to resolve the discrepancy.
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