A dark matter profile to model diverse feedback-induced core sizes of ΛCDM haloes

We analyse the cold dark matter density profiles of 54 galaxy haloes simulated with Feedback In Realistic Environments (FIRE)-2 galaxy formation physics, each resolved within $0.5{{\ \rm per\ cent}}$ of the halo virial radius. These haloes contain galaxies with masses that range from ultrafaint dwarfs ($M_\star \simeq 10^{4.5}\, \mathrm{M}_{\odot }$) to the largest spirals ($M_\star \simeq 10^{11}\, \mathrm{M}_{\odot }$) and have density profiles that are both cored and cuspy. We characterize our results using a new, analytic density profile that extends the standard two-parameter Einasto form to allow for a pronounced constant density core in the resolved innermost radius. With one additional core-radius parameter, r_c, this three-parameter core-Einasto profile is able to characterize our feedback-impacted dark matter haloes more accurately than other three-parameter profiles proposed in the literature. To enable comparisons with observations, we provide fitting functions for r_c and other profile parameters as a function of both M_⋆ and M_⋆/M_halo. In agreement with past studies, we find that dark matter core formation is most efficient at the characteristic stellar-to-halo mass ratio M_⋆/M_halo ≃ 5 × 10^-3, or $M_{\star } \sim 10^9 \, \mathrm{M}_{\odot }$, with cores that are roughly the size of the galaxy half-light radius, r_c ≃ 1-5 kpc. Furthermore, we find no evidence for core formation at radii $\gtrsim 100\ \rm pc$ in galaxies with M_⋆/M_halo < 5 × 10^-4 or $M_\star \lesssim 10^6 \, \mathrm{M}_{\odot }$. For Milky Way-size galaxies, baryonic contraction often makes haloes significantly more concentrated and dense at the stellar half-light radius than DMO runs. However, even at the Milky Way scale, FIRE-2 galaxy formation still produces small dark matter cores of ≃ 0.5-2 kpc in size. Recent evidence for a ~2 kpc core in the Milky Way's dark matter halo is consistent with this expectation.