The Tidal Torque Theory Revisited. II. Rotational Halo Properties

Abstract The peak model of structure formation was built more than 50 yr ago with the aim to address the origin of dark matter halo rotation in the tidal torque theory. Paradoxically, it has allowed one to explain and reproduce all halo properties found in cosmological simulations except their rotation, which remains to be understood. With the present two papers, we remedy this anomaly. In Paper I, we derived the angular momentum (AM) of protohalos centered on triaxial peaks of suited scale, taking into account that, to leading order, their density profile is smooth and homogeneous. Here we use that result to derive the AM of these objects, accounting for the fact that their actual density profile is slightly outward decreasing and lumpy so that they do not collapse monolithically at once, but progressively from inside out, undergoing mergers during the process. By monitoring in detail their resulting mass and AM growth, we characterize the spin distribution of the final halos and the precise mass and radial distribution of their inner mean specific AM. The results obtained explain and reproduce the rotational properties of simulated halos.