Halo Spin from Primordial Inner Motions

We reexamine how angular momentum arises in dark-matter haloes. The standard tidal-torque theory (TTT), in which an ellipsoidal protohalo is torqued up by the tidal field, is an approximation to a mechanism which is more accurate, and that we find to be more pedagogically appealing. In the initial conditions, within a collapsing protohalo, there is a random gravity-sourced velocity field; the spin from it largely cancels out, but with some excess. Velocities grow linearly, giving a sort of conservation of angular momentum (in a particular comoving linear-theory way) until collapse. Then, angular momentum is conserved in physical coordinates. This picture is more accurate in detail than the TTT, which is not literally valid, although it is useful for many predictions. Protohaloes do not uniformly torque up; instead, their inner velocity fields retain substantial dispersion. We also discuss how this picture is applicable to rotating filaments, and the relation between halo mass and spin. We also explain that an aspherical protohalo in an irrotational flow generally has nonzero angular momentum, entirely from its aspherical outskirts.