Bo\"otes III is a Tidally Disrupting Ultra-Faint Dwarf Galaxy on an Eccentric Polar Orbit

We present updated systemic properties of the ultra-faint dwarf galaxy Bo\"otes III from the Southern Stellar Stream Spectroscopic Survey (S$^5$). We identify 21 high-probability members and measure a velocity dispersion of $\sigma_{v} = 1.69^{+1.03}_{-0.85}$ km s$^{-1}$, about six times smaller than the previously reported $10.7 \pm 3.5$ km s$^{-1}$, and a mean metallicity of [Fe/H] $= -2.34 \pm 0.11$. The revised dispersion brings Bo\"otes III in line with other tidally disrupting dwarfs such as Antlia II and Crater II. Orbit integrations in a Milky Way (MW) + Large Magellanic Cloud (LMC) potential confirm a highly eccentric ($e \approx 0.8$), polar ($i \approx 89.5^\circ$) orbit with a recent pericentric passage $\sim 0.14$ Gyr ago at $r_{\rm peri} \approx 9.5$ kpc. Bo\"otes III is thus likely actively tidally disrupting, as its tidal radius at pericenter, $r_t \approx 164$ pc, is only $\sim 0.35$ of its half-light radius. The unusually low dispersion also implies that Bo\"otes III has either lost most of its dark matter to tides or hosts a cored inner density profile, making it a probe of the nature of dark matter. Simulated tidal streams are broadly consistent with the Styx stellar stream, though the predicted track and kinematics are sensitive to the MW halo mass, LMC mass, and solar velocity. Bo\"otes III overlaps the Typhon stream in integrals-of-motion space but has a much lower mean metallicity, suggesting the two are not the same system but may have had a common group infall origin. Sagittarius-stream contamination prevents a direct tidal-tail detection, so deep spectroscopic follow-up remains essential, both to confirm Styx as a genuine stream and to establish it as Bo\"otes III's tidal tail.