  The Sagittarius Dwarf Spheroidal galaxy (Sgr) is investigated as a target for
DM annihilation searches utilising J-factor distributions calculated directly
from a high-resolution hydrodynamic simulation of the infall and tidal
disruption of Sgr around the Milky Way. In contrast to past studies, the
simulation incorporates DM, stellar and gaseous components for both the Milky
Way and the Sgr progenitor galaxy. The simulated distributions account for
significant tidal disruption affecting the DM density profile. Our estimate of
the J-factor value for Sgr, $J_{\text{Sgr}}=1.48\times 10^{10}$ M$_\odot^2$
kpc$^{-5}$ ($6.46\times10^{16}\ \text{GeV}\ \text{cm}^{-5}$), is significantly
lower than found in prior studies. This value, while formally a lower limit, is
likely close to the true J-factor value for Sgr. It implies a DM cross-section
incompatibly large in comparison with existing constraints would be required to
attribute recently observed $\gamma$-ray emission from Sgr to DM annihilation.
We also calculate a J-factor value using a NFW profile fitted to the simulated
DM density distribution to facilitate comparison with past studies. This NFW
J-factor value supports the conclusion that most past studies have
overestimated the dark matter density of Sgr on small scales. This, together
with the fact that the Sgr has recently been shown to emit $\gamma$-rays of
astrophysical origin, complicate the use of Sgr in indirect DM detection
searches.
