A discrete chemo-dynamical model of the dwarf spheroidal galaxy
  Sculptor: mass profile, velocity anisotropy and internal rotation
  We present a new discrete chemo-dynamical axisymmetric modeling technique,
which we apply to the dwarf spheroidal galaxy Sculptor. The major improvement
over previous Jeans models is that realistic chemical distributions are
included directly in the dynamical modelling of the discrete data. This avoids
loss of information due to spatial binning and eliminates the need for hard
cuts to remove contaminants and to separate stars based on their chemical
properties. Using a combined likelihood in position, metallicity and
kinematics, we find that our models naturally separate Sculptor stars into a
metal-rich and a metal-poor population. Allowing for non-spherical symmetry,
our approach provides a central slope of the dark matter density of $\gamma =
0.5 \pm 0.3$. The metal-rich population is nearly isotropic (with
$\beta_r^{red} = 0.0\pm0.1$) while the metal-poor population is tangentially
anisotropic (with $\beta_r^{blue} = -0.2\pm0.1$) around the half light radius
of $0.26$ kpc. A weak internal rotation of the metal-rich population is
revealed with $v_{max}/\sigma_0 = 0.15 \pm 0.15$. We run tests using mock data
to show that a discrete dataset with $\sim 6000$ stars is required to
distinguish between a core ($\gamma = 0$) and cusp ($\gamma = 1$), and to
constrain the possible internal rotation to better than $1\,\sigma$ confidence
with our model. We conclude that our discrete chemo-dynamical modelling
technique provides a flexible and powerful tool to robustly constrain the
internal dynamics of multiple populations, and the total mass distribution in a
stellar system.
