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 MichieKing 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 d is the exponent of the first non-constant term in the Taylor expansion of the total potential at the centre (d= 1 for NavarroFrenkWhite or NFW haloes, d= 2 for cored haloes). Then, we show that the ratio of the half-light radii of the populations Rd/2h, 2/Rh, 1d/2 must be smaller than the ratio of the line-of-sight velocity dispersions slos, 2(Rh, 2)/slos, 1(Rh, 1).