Buried but not destroyed: the evolution from prompt cusps to NFW haloes

The internal structure of dark matter haloes encodes their assembly history and offers critical insight into the nature of dark matter and structure formation. Analytical studies and high-resolution simulations have recently predicted the formation of ‘prompt cusps’ - steep power-law density profiles that emerge rapidly from the monolithic collapse of primordial peaks. Yet, by $z=0$ most haloes are well described by Navarro-Frenk-White (NFW) density profiles, raising the question of how these early cusps are transformed in a cosmological setting. We address this problem using 64 zoom-in $N$-body simulations of eight haloes, each resimulated with eight different free-streaming wavenumbers to control the abundance of small-scale structure while keeping the large-scale environment fixed. To mitigate numerical discreteness effects, we classify artificial fragments and genuine subhaloes with a physically motivated procedure based on matching subhaloes to their progenitor peaks. At the population level, we demonstrate that haloes initially form prompt cusps, and their profiles subsequently transition towards the NFW form. Our study reveals three distinct pathways by which prompt cusps evolve: major mergers, accretion of artificial fragments, and interactions with large-scale filaments, each having a distinct impact on the inner density profile. In particular, we show that the original power-law cusp remains visible in the profile of particles associated with the primordial peak even when the total halo profile is already NFW-like. This work highlights the imprint of early collapse on present-day halo structure and provides new insights into the origin of the universality of the NFW profile.

💡 Research Summary

This paper presents a comprehensive investigation into the evolutionary pathway connecting the early-forming “prompt cusps” in dark matter haloes to the ubiquitous Navarro-Frenk-White (NFW) profile observed at later times. The central question addressed is how the steep, power-law density profiles (ρ ∝ r^{-12/7}) predicted to form from the monolithic collapse of isolated primordial peaks are transformed within the complex, hierarchical environment of a ΛCDM universe.

To tackle this, the authors employ a sophisticated suite of 64 zoom-in N-body simulations. They select eight target haloes and resimulate each under eight different cosmological initial conditions. The key innovation in their setup is varying the free-streaming wavenumber (effectively controlling the abundance of small-scale structure) while keeping the large-scale environment and tidal fields identical. This allows them to isolate the effects of small-scale physics on halo evolution. A major technical challenge in such high-resolution simulations is contamination by “artificial fragments” – spurious clumps arising from numerical discreteness noise. The team develops a novel, physically motivated algorithm to distinguish these artefacts from genuine subhaloes by linking present-day sub-structures back to their progenitor peaks in the initial density field, significantly enhancing the reliability of their analysis.

The simulations confirm that haloes indeed form with prompt cusp profiles at early times. As they evolve, these profiles systematically transition towards the characteristic NFW form (ρ ∝ r^{-1} at small radii). The study identifies three distinct, concurrent pathways driving this evolution:

1. Major Mergers: Interactions with other haloes of comparable mass cause significant gravitational shocks and violent relaxation, redistributing energy and mass in the inner regions.
2. Accretion of Artificial Fragments: The frequent accretion of numerous small, numerically generated clumps provides a persistent source of dynamical heating, gradually softening the central cusp.
3. Interactions with Large-Scale Filaments: Sustained mass inflow and tidal forces from the cosmic web in which a halo is embedded influence its growth and shape over long periods.

The most profound insight comes from a differential analysis. The authors separate the particles constituting a present-day halo into two components: those that originated from the initial, collapsing primordial peak (“peak material”) and those accreted later from the surroundings (“accreted material”). They then compute the density profile for each component separately. Strikingly, they find that even at late times when the total halo profile has become NFW-like, the density profile of the peak material alone still retains the steep slope of the original prompt cusp. This demonstrates that the prompt cusp is not destroyed or erased but rather becomes embedded or buried within the more broadly distributed later-accreted material. The NFW-like appearance of the total profile is thus an emergent property of this composite system.

In conclusion, this work provides compelling evidence that the memory of a halo’s earliest collapse can survive billions of years of cosmic evolution. The universal NFW profile does not imply a complete erasure of individual formation histories; instead, the imprint of the primordial prompt cusp may persist at the heart of many dark matter haloes. This finding has significant implications for our understanding of halo structure, the origin of profile universality, and for indirect dark matter detection, as preserved prompt cusps could be potent sources of annihilation radiation.