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According to the current concordance cosmological model, the dark matter (DM)particles are collision-less and produce self-gravitating structures with acentral cusp which, generally, is not observed. The observed density tends to acentral plateau or core, explained within the cosmological model through thegravitational feedback of baryons on DM. This mechanism becomes inefficientwhen decreasing the galaxy stellar mass so that in the low-mass regime (Mstar<< 10**6 Msun) the energy provided by the baryons is insufficient to modifycusps into cores. Thus, if cores exist in these galaxies they have to reflectdepartures from the collision-less nature of DM. Measuring the DM massdistribution in these faint galaxies is extremely challenging, however, theirstellar mass distribution can be characterized through deep photometry. Here weprovide a way of using only the stellar mass distribution to constrain theunderlying DM distribution. The so-called Eddington inversion method allows usto discard pairs of stellar distributions and DM potentials requiring(unphysical) negative distribution functions in the phase space. In particular,cored stellar density profiles are incompatible with the Navarro, Frenk, andWhite (NFW) potential expected from collision-less DM if the velocitydistribution is isotropic and the system spherically symmetric. Through acase-by-case analysis, we are able to relax these assumptions to consideranisotropic velocity distributions and systems which do not have exact cores.In general, stellar distributions with radially biased orbits are difficult toreconcile with NFW-like potentials, and cores in the baryon distribution tendto require cores in the DM distribution.

Can cuspy dark matter dominated halos hold cored stellar mass distributions?