A deeper look into the structure of {\Lambda}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 ($\Lambda$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, $\alpha$, 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 $\alpha$ and $c$ is anti-correlated: at redshift $z=7$,
$\alpha \simeq 0.4$ 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 $\alpha$ traces the evolutionary state of the
halo, with dynamically young haloes having high $\alpha$ (closer to a top-hat:
$\alpha^{-1}=0$), and dynamically relaxed haloes having low $\alpha$ (closer to
isothermal: $\alpha=0$). Such an evolutionary dependence reconciles the
increase of $\alpha$ vs peak height, $\nu$, with the dependence on the slope of
the power spectrum of initial density fluctuations found by previous studies.
