  We present a spectroscopic study of the tidal tails and core of the Milky Way
satellite Tucana III, collectively referred to as the Tucana III stream, using
the 2dF+AAOmega spectrograph on the Anglo-Australian Telescope and the IMACS
spectrograph on the Magellan/Baade Telescope. In addition to recovering the
brightest 9 previously known member stars in the Tucana III core, we identify
22 members in the tidal tails. We observe strong evidence for a velocity
gradient of 8.0 km/s/deg (or 18.3 km/s/kpc over at least 3$^{\circ}$ (or 1.3
kpc) on the sky. Based on the continuity in velocity we confirm that the Tucana
III tails are real tidal extensions of Tucana III. The large velocity gradient
of the stream implies that Tucana III is likely on a radial orbit. We
successfully obtain metallicities for 4 members in the core and 12 members in
the tails. We find that members close to the ends of the stream tend to be more
metal-poor than members in the core, indicating a possible metallicity gradient
between the center of the progenitor halo and its edge. The spread in
metallicity suggests that the progenitor of the Tucana III stream is a dwarf
galaxy rather than a star cluster. Furthermore, we find that with the precise
photometry of the Dark Energy Survey data, there is a discernible color offset
between metal-rich disk stars and metal-poor stream members. This
metallicity-dependent color offers a more efficient method to recognize
metal-poor targets and will increase the selection efficiency of stream members
for future spectroscopic follow-up programs on stellar streams.
