We use three different cosmological dark matter simulations to study how the orientation of the angular momentum vector ( AM ) in dark matter haloes evolve with time .
We find that haloes in this kind of simulations are constantly affected by a spurious change of mass , which translates into an artificial change in the orientation of the AM .
After removing the haloes affected by artificial mass change , we found that the change in the orientation of the AM vector is correlated with time .
The change in its angle and direction ( i.e .
the angle subtended by the AM vector in two consecutive timesteps ) that affect the AM vector has a dependence on the change of mass that affects a halo , the time elapsed in which the change of mass occurs and the halo mass .
We create a Monte-Carlo simulation that reproduces the change of angle and direction of the AM vector .
We reproduce the angular separation of the AM vector since a look back time of 8.5 Gyrs to today ( \alpha ) with an accuracy of approximately 0.05 in cos ( \alpha ) .
We are releasing this Monte-Carlo simulation together with this publication .
We also create a Monte Carlo simulation that reproduces the change of the AM modulus .
We find that haloes in denser environments display the most dramatic evolution in their AM direction , as well as haloes with a lower specific AM modulus .
These relations could be used to improve the way we follow the AM vector in low-resolution simulations .