  In this paper, we use the outer-galactic HI scale height data as well as the
observed rotation curve as constraints to determine the halo density
distribution of the Andromeda galaxy (M31). We model the galaxy as a
gravitationally-coupled system of stars and gas, responding to the external
force-field of a known Hernquist bulge and the dark matter halo, the density
profile of the latter being characterized by four free parameters. The
parameter space of the halo is optimized so as to match the observed HI
thickness distribution as well as the rotation curve on an equal footing,
unlike the previous studies of M31 which were based on rotation curves alone.
We show that an oblate halo, with an isothermal density profile, provides the
best fit to the observed data. This gives a central density of 0.011 M_sun
/pc^3, a core radius of 21 kpc, and an axis ratio of 0.4. The main result from
this work is the flattened dark matter halo for M31, which is required to match
the outer galactic HI scale height data. Interestingly, such flattened halos
lie at the most oblate end of the distribution of halo shapes found in recent
cosmological simulations.
