Early Evolution of Spin Direction in Dark Matter Halos and the Effect of the Surrounding Large-scale Tidal Field* †

It is usually assumed that the angular momentum (AM) of dark matter halos arises during the linear stages of structure formation, as a consequence of the coupling between the proto-haloes' shape and the tidal field produced by their surrounding density perturbations. This approach, known as linear tidal torque theory (TTT), has been shown to make fairly good predictions about the mean evolution of both the AM amplitude and orientation up to approximately the time when the proto-haloes collapse. After this point, proto-haloes are increasingly affected by non-linear processes that are not taken into account by the model. However, it has been seen in numerical simulations that, even at very early stages, the AM of proto-haloes is systematically reoriented towards perpendicularity with respect to the forming cosmic filaments, in contradiction with the fixed direction expected from the TTT. In this work we present a novel analytical approach that introduces an anisotropic scaling factor to the standard TTT equations, which allows the AM orientation to change in time, even during the linear regime. The amplitude and direction of this shift depend on the large scale tidal field around the forming proto-haloes. Our results significantly improve the predictions for the AM direction up to the time of protohalo collapse and, in some cases, even further in time.