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We use three different cosmological dark matter simulations to study how theorientation of the angular momentum vector (AM) in dark matter haloes evolvewith time. We find that haloes in this kind of simulations are constantlyaffected by a spurious change of mass, which translates into an artificialchange in the orientation of the AM. After removing the haloes affected byartificial mass change, we found that the change in the orientation of the AMvector is correlated with time. The change in its angle and direction (i.e. theangle subtended by the AM vector in two consecutive timesteps) that affect theAM vector has a dependence on the change of mass that affects a halo, the timeelapsed in which the change of mass occurs and the halo mass. We create aMonte-Carlo simulation that reproduces the change of angle and direction of theAM vector. We reproduce the angular separation of the AM vector since a lookback time of 8.5 Gyrs to today ( $\rm \alpha$) with an accuracy ofapproximately 0.05 in $\rm cos(\alpha)$. We are releasing this Monte-Carlosimulation together with this publication. We also create a Monte Carlosimulation that reproduces the change of the AM modulus. We find that haloes indenser environments display the most dramatic evolution in their AM direction,as well as haloes with a lower specific AM modulus. These relations could beused to improve the way we follow the AM vector in low-resolution simulations.

Angular momentum evolution in Dark Matter haloes: a study of the Bolshoi and Millennium simulations