Dark matter cores and cusps: the case of multiple stellar populations in dwarf spheroidals

A number of dwarf spheroidal (dSph) galaxies are known to contain a more extended, metal-poor population with a flattish velocity dispersion profile, and a more concentrated, metal-rich population with a velocity dispersion declining with radius. The two populations can be modelled with Michie-King distribution functions (DFs) in the isothermal and in the sharply truncated limits, respectively. We argue that the truncation of the metal-rich population can be traced back to the spatial distribution of the star-forming gas. Suppose δ is the exponent of the first non-constant term in the Taylor expansion of the total potential at the centre (δ= 1 for Navarro-Frenk-White or NFW haloes, δ= 2 for cored haloes). Then, we show that the ratio of the half-light radii of the populations R^δ/2_{h, 2}/R_{h, 1}^δ/2 must be smaller than the ratio of the line-of-sight velocity dispersions σ_{los, 2}(R_{h, 2})/σ_{los, 1}(R_{h, 1}).

Specializing to the case of the Sculptor dSph, we develop a technique to fit simultaneously both populations with Michie-King DFs. This enables us to determine the mass profile of the Sculptor dSph with unprecedented accuracy in the radial range 0.2 < r < 1.2 kpc. We show that cored halo models are preferred over cusped halo models, with a likelihood ratio test rejecting NFW models at any significance level higher than 0.05 per cent. Even more worryingly, the best-fitting NFW models require concentrations with c ≲ 20, which is not in the cosmologically preferred range for dwarf galaxies. We conclude that the kinematics of multiple populations in dSphs provides a substantial new challenge for theories of galaxy formation, with the weight of available evidence strongly against dark matter cusps at the centre.