A deeper look into the structure of ΛCDM haloes: correlations between halo parameters from Einasto fits

Abstract

We used high resolution dark matter only cosmological simulations to investigate the structural properties of Lambda Cold Dark Matter ($Λ$CDM) haloes over cosmic time. The haloes in our study range in mass from $\sim 10^{10}$ to $\sim 10^{12} \mathrm{M}_\odot$, and are resolved with $10^5$ to $10^7$ 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 anti-correlation 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 anti-correlated: at redshift $z=7$, $α\simeq 0.4$ and decreases with time, while $c\simeq 3$ 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 $α$ vs peak height, $ν$, with the dependence on the slope of the power spectrum of initial density fluctuations found by previous studies.