Dark matter density profiles of the Milky Way satellite population: reconciling simulations and observations
The cusp-core problem remains a key challenge for the $Λ$CDM model. Historically, comparing inner dark matter halo slopes ($d\logρ/d\log r$) from simulations and observations has suffered from a methodological mismatch: evaluating slopes at different radii creates apparent tensions due to inconsistent definitions rather than genuine physical differences. We rigorously compare dark matter density profiles of Milky Way (MW) dwarf satellites inferred from dynamical modelling against CDM hydrodynamical simulations. Using the NIHAO and FIRE-2 suites ($M_{\star} \sim 10^3$-$10^{11}\,\rm M_\odot$), we confront simulated profiles with dynamical inferences of 16 MW satellites across four methods, strictly within their reliability limits. Crucially, we evaluate simulated slopes at observationally accessible radii, directly comparing profiles at matched stellar mass. Both observed and simulated galaxies exhibit a mass-dependent core-formation trend: inner slopes rise from cuspy values ($\approx -1.5$) at $M_{\star} \sim 10^5\,\rm M_\odot$ to core-like values ($\approx 0$ to $-0.4$) at $M_{\star} \sim 10^8\,\rm M_\odot$. Efficient core formation begins at $M_{\star} \gtrsim 10^6\,\rm M_\odot$ for centrals, where satellites display increased scatter consistent with tidal disruption. Simulated profiles agree with observations within $\lesssim 1σ$ for most systems, outperforming a NFW profile. Furthermore, differing observational models present scatter for a given system comparable to the simulation-to-observation offset. Evaluating dark matter density slopes at fixed physical radii significantly improves agreement between hydrodynamical simulations and dynamical models, revealing no clear tension when comparing profiles at fixed stellar mass, but Willman\,1 remains an unresolved outlier.