Constraining the shape of dark matter haloes using only starlight II. Tests of the technique with objects of known gravitational potential

Abstract

Under the collisionless cold dark matter (CDM) paradigm, galaxies with stellar masses below 10**(5-6) Msun are expected to preserve primordial cuspy dark matter (DM) profiles. Because baryonic feedback should be too weak to transform cusps into cores at these masses, such galaxies provide especially sensitive tests of DM physics. If cores are observed in these systems, they could indicate departures from CDM. To address this problem, Sanchez Almeida et al. (2025) introduced the Eddington Inversion Method tool (EIM-tool), a photometry-based diagnostic that avoids the need for long-term spectroscopic observations and is suitable for the analysis of the forthcoming large photometric surveys of galaxies. The method relies on the fact that embedding a stellar distribution with a central core inside a cuspy NFW halo can require a negative phase-space distribution function f, which is physically impossible. By fitting observed stellar surface densities using f as a free parameter, EIM-tool tests whether an assumed gravitational potential is physically consistent with an observed stellar distribution. This paper validates EIM-tool using globular clusters, dwarf spheroidal galaxies (dSphs), and numerical simulations with independently known potentials. Applied to 21 globular clusters, the method rejected NFW cusps in 71\% of cases while consistently favoring cored Schuster-Plummer models, accurately recovering expected core radii. Applied to dSphs, EIM-tool reproduced conclusions from classical dynamical studies: Sculptor and Fornax favored cored halos, whereas Draco remained compatible with a cusp. Tests on EDGE and FIRE simulations further showed that the tool reliably rejects cuspy NFW profiles when the true DM distribution is core-like. Overall, these results establish EIM-tool as a robust and efficient photometric method for distinguishing cored and cuspy DM halos.