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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 η and the centre of mass offset Δ 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  z  form  correlates with its virial mass  M  vir  and we show that the fraction of its recently accreted mass and the likelihood of it having experienced a recent major merger increase with increasing  M  vir  and decreasing  z  form . We then show that both η and Δ r  increase with increasing  M  vir  and decreasing  z  form , 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 η and Δ 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 Δ 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  Δ 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.

The dynamical state of dark matter haloes in cosmological simulations – I. Correlations with mass assembly history