Non-linear evolution of the angular momentum of protostructures from tidal torques

We discuss the non-linear evolution of the angular momentum L acquired by protostructures, like protogalaxies and protoclusters, due to tidal interactions with the surrounding matter inhomogeneities. The primordial density distribution is assumed to be Gaussian, and the non-linear dynamics of the collisionless mass fluid is followed using Lagrangian perturbation theory. For a cold dark matter spectrum, the inclusion of the leading-order Lagrangian correction terms results in a value of the rms ensemble average 〈L,2〉1/2 which is only a factor of 1.3 higher than the corresponding linear estimate, irrespective of the scale. Consequently, the predictions of linear theory are rather accurate in quantifying the evolution of the angular momentum of protostructures before collapse sets in. In the Einstein-de Sitter universe, the initial torque is a good estimate for the tidal torque over the whole period during which the object is spun up.