The Tidal Torque Theory Revisited. I. Protohalo Angular Momentum

Abstract

In the tidal-torque theory, the angular momentum (AM) of dark matter halos arises from the tidal torque suffered by aspherical collapsing patches due to surrounding mass fluctuations. This theory was implemented in the peak model where protohalos are ellipsoidal. However, the adopted delimitation of these objects was doubtful and the protohalo AM was calculated numerically, which complicated the interpretation of the result and compromised its applicability. In addition, the AM of final halos was derived without taking into account non-linear effects. Here, we re-derive the protohalo AM in the peak model, delimiting ellipsoids in the usual natural way and following a novel fully analytic approach that leads to a very simple and practical expression. The predicted AM is shown to fully agree with the results of cosmological simulations. In Paper II, we will apply this model to infer the rotational properties of relaxed halos, accounting for shell-crossing and major mergers.