A Virial Core in the Sculptor Dwarf Spheroidal Galaxy
The projected virial theorem is applied to the case of multiple stellar populations in the nearby dwarf spheroidal galaxies. As each population must reside in the same gravitational potential, this provides strong constraints on the nature of the dark matter halo. We derive necessary conditions for two populations with Plummer or exponential surface brightnesses to reside in a cusped Navarro-Frenk-White (NFW) halo. We apply our methods to the Sculptor dwarf spheroidal, and show that there is no NFW halo compatible with the energetics of the two populations. The dark halo must possess a core radius of ~120 pc for the virial solutions for the two populations to be consistent. This conclusion remains true, even if the effects of flattening or self-gravity of the stellar populations are included.