  The Sculptor dwarf spheroidal galaxy contains two distinct stellar
populations: one metal-rich and the other metal-poor. 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 rule out the cuspy
Navarro-Frenk-White (NFW) density profiles predicted for halos and subhalos by
dark matter only simulations of the Lambda Cold Dark Matter (Lambda-CDM)
cosmological model. We present a new theoretical framework to analyse stellar
count and velocity observations in a self-consistent manner based on separable
models, f(E,J)=g(J)h(E), for the distribution function of an equilibrium
spherical system. We use this machinery to analyse 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 Lambda-CDM. Our solution gives a maximum circular
velocity for Sculptor between 20 and 35 km/s. We discuss why some previous
authors came to a different conclusion.
