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We present a new discrete chemo-dynamical axisymmetric modeling technique,which we apply to the dwarf spheroidal galaxy Sculptor. The major improvementover previous Jeans models is that realistic chemical distributions areincluded directly in the dynamical modelling of the discrete data. This avoidsloss of information due to spatial binning and eliminates the need for hardcuts to remove contaminants and to separate stars based on their chemicalproperties. Using a combined likelihood in position, metallicity andkinematics, we find that our models naturally separate Sculptor stars into ametal-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 tangentiallyanisotropic (with $\beta_r^{blue} = -0.2\pm0.1$) around the half light radiusof $0.26$ kpc. A weak internal rotation of the metal-rich population isrevealed with $v_{max}/\sigma_0 = 0.15 \pm 0.15$. We run tests using mock datato show that a discrete dataset with $\sim 6000$ stars is required todistinguish between a core ($\gamma = 0$) and cusp ($\gamma = 1$), and toconstrain the possible internal rotation to better than $1\,\sigma$ confidencewith our model. We conclude that our discrete chemo-dynamical modellingtechnique provides a flexible and powerful tool to robustly constrain theinternal dynamics of multiple populations, and the total mass distribution in astellar system.

A discrete chemo-dynamical model of the dwarf spheroidal galaxy Sculptor: mass profile, velocity anisotropy and internal rotation