The Dynamical State of Dark Matter Haloes in Cosmological Simulations I:
  Correlations with Mass Assembly History
  Using a statistical sample of dark matter haloes drawn from a suite of
cosmological N-body simulations of the Cold Dark Matter (CDM) model, we
quantify the impact of a simulated halo's mass accretion and merging history on
two commonly used measures of its dynamical state, the virial ratio eta and the
centre of mass offset Delta r. Quantifying this relationship is important
because the degree to which a halo is dynamically equilibrated will influence
the reliability with which we can measure characteristic equilibrium properties
of the structure and kinematics of a population of haloes. We begin by
verifying that a halo's formation redshift zform correlates with its virial
mass Mvir and we show that the fraction of its recently accreted mass and the
likelihood of it having experienced a recent major merger increases with
increasing Mvir and decreasing zform. We then show that both eta and Delta r
increase with increasing Mvir and decreasing zform, which implies that massive
recently formed haloes are more likely to be dynamically unrelaxed than their
less massive and older counterparts. Our analysis shows that both eta and Delta
r are good indicators of a halo's dynamical state, showing strong positive
correlations with recent mass accretion and merging activity, but we argue that
Delta r provides a more robust and better defined measure of dynamical state
for use in cosmological N-body simulations at z~0. We find that Delta r < 0.04
is sufficient to pick out dynamically relaxed haloes at z=0. Finally, we assess
our results in the context of previous studies, and consider their
observational implications.
