Prospects for Galactic and stellar astrophysics with asteroseismology of
  giant stars in the $\it{TESS}$ Continuous Viewing Zones and beyond
  The NASA-$\it{TESS}$ mission presents a treasure trove for understanding the
stars it observes and the Milky Way, in which they reside. We present a first
look at the prospects for Galactic and stellar astrophysics by performing
initial asteroseismic analyses of bright ($G < 11$) red giant stars in the
$\it{TESS}$ Southern Continuous Viewing Zone (SCVZ). Using three independent
pipelines, we detect $\nu_{\mathrm{max}}$ and $\Delta\nu$ in 41% of the 15,405
star parent sample (6,388 stars), with consistency at a level of $\sim 2\%$ in
$\nu_{\mathrm{max}}$ and $\sim 5\%$ in $\Delta\nu$. Based on this, we predict
that seismology will be attainable for $\sim 3\times10^{5}$ giants across the
whole sky, subject to improvements in analysis and data reduction techniques.
The best quality $\it{TESS}$-CVZ data, for 5,574 stars where pipelines returned
consistent results, provide high quality power spectra across a number of
stellar evolutionary states. This makes possible studies of, for example, the
Asymptotic Giant Branch bump (AGBb). We demonstrate that mixed $\ell=1$ modes
and rotational splitting are cleanly observed in the 1-year data set. By
combining $\it{TESS}$-CVZ data with $\it{TESS}$-HERMES, $\it{SkyMapper}$,
APOGEE and $\it{Gaia}$ we demonstrate the potential for Galactic archaeology
studies using the data, which provides good age precision and accuracy that
reproduces the age of high $\mathrm{[\alpha/Fe]}$ stars and relationships
between mass and kinematics from studies based on $\it{Kepler}$. Better quality
astrometry and simpler target selection than the $\it{Kepler}$ sample makes
this data ideal for studies of the local star formation history and evolution
of the Galactic disc. These results provide a strong case for detailed
spectroscopic follow-up in the CVZs to complement that which has been (or will
be) collected by current surveys. [Abridged]
