Dynamical Models for the Sculptor Dwarf Spheroidal in a ΛCDM Universe

The Sculptor dwarf spheroidal galaxy appears to contain two distinct stellar populations of differing metallicity. Several authors have argued that in order for these two populations to reside in the same gravitational potential, the dark matter halo must have a core similar to that observed in the stellar count profile. This would exclude cuspy Navarro–Frenk–White (NFW) density profiles of the kind predicted for halos and subhalos by dark matter-only simulations of the ΛCDM cosmological model. We present a new theoretical framework to analyze observations of stellar count and velocity in a self-consistent manner based on separable models, $f(E,J)=g\left(J\right)h\left(E\right)$, for the distribution function of an equilibrium spherical system. We use this machinery to analyze available photometric and kinematic data for the two stellar populations in Sculptor. We find, contrary to some previous claims, that the data are consistent with populations in equilibrium within an NFW dark matter potential with structural parameters in the range expected in ΛCDM; we find no statistical preference for a potential with a core. Our models allow a maximum circular velocity for Sculptor between 20 and 35 km s⁻¹. We discuss why some previous authors came to a different conclusion.