A deeper look into the structure of CDM haloes: Correlations between halo parameters from Einasto fits

We used high resolution dark matter only cosmological simulations to investigate the structural properties of Lambda Cold Dark Matter (CDM) haloes over cosmic time. The haloes in our study range in mass from ∼10¹⁰ to ∼10¹² M, and are resolved with 10⁵ to 10⁷ particles. We fit the spherically averaged density profiles of DM haloes with the three parameter Einasto function. For our sample of haloes, the Einasto shape parameter, α, is uncorrelated with the concentration, c, at fixed halo mass, and at all redshifts. Previous reports of an anticorrelation are traced to fitting degeneracies, which our fits are less sensitive to due to our higher spatial resolution. However, for individual haloes the evolution in α and c is anticorrelated: at redshift z = 7, α 0.4 and decreases with time, while c 3 and increases with time. The evolution in structure is primarily due to accretion of mass at larger radii. We suggest that α traces the evolutionary state of the halo, with dynamically young haloes having high α (closer to a top-hat: α⁻¹ = 0), and dynamically relaxed haloes having low α (closer to isothermal: α = 0). Such an evolutionary dependence reconciles the increase of α versus peak height, ν, with the dependence on the slope of the power spectrum of initial density fluctuations found by previous studies.