Earth-mass haloes and the emergence of NFW density profiles

Abstract: We simulate neutralino dark matter ($\chi$DM) haloes from their initial collapse, at $\sim$ earth mass, up to a few percent solar. Our results confirm that the density profiles of the first haloes are described by a $\sim r^{-1.5}$ power-law. As haloes grow in mass, their density profiles evolve significantly. In the central regions, they become shallower and reach on average $\sim r^{-1}$, the asymptotic form of an NFW profile. Using non-cosmological controlled simulations, we observe that temporal variations in the gravitational potential caused by major mergers lead to a shallowing of the inner profile. This transformation is more significant for shallower initial profiles and for a higher number of merging systems. Depending on the merger details, the resulting profiles can be shallower or steeper than NFW in their inner regions. Interestingly, mergers have a much weaker effect when the profile is given by a broken power-law with an inner slope of $-1$ (such as NFW or Hernquist profiles). This offers an explanation for the emergence of NFW-like profiles: after their initial collapse, $r^{-1.5}$ $\chi$DM haloes suffer copious major mergers, which progressively shallows the profile. Once an NFW-like profile is established, subsequent merging do not change the profile anymore. This suggests that halo profiles are not universal but rather a combination of (1) the physics of the formation of the microhaloes and (2) their early merger history -- both set by the properties of the dark matter particle -- as well as (3) the resilience of NFW-like profiles to perturbations.