Cold dark matter haloes in the Planck era: evolution of structural parameters for Einasto and NFW profiles

Abstract: We present the evolution of the structure of relaxed cold dark matter haloes in the cosmology from the Planck satellite. Our simulations cover 5 decades in halo mass, from dwarf galaxies to galaxy clusters. Due to the increased matter density and power spectrum normalization the concentration mass relation in the Planck cosmology has a 20 percent higher normalization at redshift z=0 compared to WMAP cosmology. We confirm that CDM haloes are better described by the Einasto profile; for example, at scales near galaxy half-light radii CDM haloes have significantly steeper density profiles than implied by NFW fits. There is a scatter of 0.2 dex in the Einasto shape parameter at fixed halo mass, adding further to the diversity of CDM halo profiles. The evolution of the concentration mass relation in our simulations is not reproduced by any of the analytic models in the literature. We thus provide a simple fitting formula that accurately describes the evolution between redshifts z=5 to z=0 for both NFW and Einasto fits. Finally, the observed concentrations and halo masses of spiral galaxies, groups and clusters of galaxies at low redshifts are in good agreement with our simulations, suggesting only mild halo response to galaxy formation on these scales.

• The paper analyzes cold dark matter halo structure evolution in the Planck era using N-body simulations, finding a higher concentration-mass relation and superior fits from the Einasto profile compared to NFW.
• The Einasto shape parameter increases with mass and redshift, while the concentration-mass relation evolves significantly, with existing analytic models failing to reproduce the observed evolution.
• These findings have direct implications for cosmological models, gravitational lensing, and galaxy formation, suggesting the importance of incorporating baryonic physics and potentially leveraging machine learning for future research.

Overview of Cold Dark Matter Haloes in the Planck Era

This paper conducts an in-depth analysis of the evolution of cold dark matter (CDM) halo structures in a cosmology defined by the Planck satellite. Utilizing a broad range of numerical N-body simulations that span over five orders of magnitude in halo mass, the study examines CDM haloes from dwarf galaxies to large galaxy clusters within the context of Planck cosmological parameters.

Key Findings

The concentration-mass relation, a fundamental descriptor of halo structure, is observed to have a higher normalization under Planck cosmology compared to WMAP results by approximately 20% at redshift $z=0$. This outcome aligns closely with the WMAP1 results despite substantial variations in cosmological parameters between these frameworks, a phenomenon attributed to the balanced effects of Planck's higher $\Omega_{\text{m}}$ against lower $\sigma_8$, $n$, and $h$.

The research confirms the superiority of the Einasto profile over the Navarro-Frenk-White (NFW) profile in describing the internal density distributions of CDM haloes. The averages over the profile parameters reveal that Einasto profiles consistently fit better over the NFW across all halo mass scales, especially concerning their inner density slopes.

Evolution of Parameters

The investigation of the evolution of the structural parameters from redshift $z=5$ to $z=0$ demonstrates that:

1. Einasto Shape Parameter ($\alpha$): This parameter, crucial for accurately modeling CDM density profiles, tends to increase with halo mass and redshift. Its behavior can be well characterized by the peak height parameter $\nu$, thereby offering a robust characterization of halo structure over vast time spans and scales.
2. Concentration-Mass Relationship: The relation evolves significantly with redshift, showing stronger slopes at lower masses and higher redshifts. However, none of the existing analytic models accurately reproduce the observed evolution, highlighting a novel contribution of the study and underscoring the richness of CDM halo structure evolution under different cosmologies.

These results challenge prior assumptions of a universal form of structural evolution and provide new insights into the dependency of halo profiles on underlying cosmological parameters.

Implications and Conclusion

From a practical standpoint, the findings have direct implications for current cosmological models and simulations, influencing the interpretation of gravitational lensing and the dynamics of galaxy formation. Given the sensitivity of halo structure to underlying cosmological parameters, slight deviations in these models could offer significant clues into the nature of dark matter itself.

In future scenarios, these results pose stimulating questions concerning how precisely baryonic processes affect halo concentrations, as the evident discrepancies between simulation predictions and observational data on a cosmic scale suggest that baryonic physics must be carefully incorporated into dark matter simulations to provide a comprehensive understanding of structure formation. Furthermore, these insights could propel advancements in machine learning and AI methodologies for analyzing complex cosmological simulations, potentially exploring new models that capture a more extensive range of cosmological phenomena.

Ultimately, the study offers valuable contributions and elucidates many subtleties involved in CDM halo structural evolution, laying a foundation for future explorations and challenges in cosmological research.