Cored galaxies in cuspy dark matter halos

Aims. We investigate the constraints placed on the inner stellar density profile from the photometric data of dwarf spheroidal and ultra-faint dwarf galaxies. Our aim is to clarify the conditions in which cored stellar profiles require dark matter halos that are also cored, deviating from the cuspy profiles expected for cold dark matter halos. Methods. We considered a variety of spherically symmetric stellar profiles, which we classified as ‘strong’ or ‘weak’ cores and cusps according to the behaviour of the slope ( b 0 ) and logarithmic slope ( γ 0 ) at their centres. We explored which profiles lead to unphysical negative distribution functions when embedded in a cuspy halo, while treating the isotropic and anisotropic kinematics separately. Results. We find that weakly cored stellar profiles in 3D (i.e. b 0 ≠ 0, γ 0 = 0) can be consistent with cuspy dark matter profiles, but strong 3D cores ( b 0 = γ 0 = 0) are not. However, both weak and strong 3D cores yield nearly indistinguishable inner profiles in projection, which implies that ruling out a dark matter cusp from photometric data alone is highly challenging. As an example, we studied the profiles of ultra-faint dwarf galaxies and found that they are consistent with both weak and strong 3D cores. This result is not solely applicable to the limited numbers of stars in these systems, since we reached the same conclusion even for Fornax, one of the most luminous and best-studied dwarf spheroidal companions of the Milky Way. Conclusions. We conclude that based on current data and analysis techniques, cored surface density profiles in nearby dwarf galaxies cannot be taken as strong evidence against the presence of cuspy dark matter halos.