Acquisition of angular momentum by tidal torques in expanding, spherical-symmetric density perturbations - an analysis of different approximations

The evolution of expanding, spherical-symmetric density perturbations is reviewed, mainly in the context of an Einstein-de Sitter universe, according to an exact theory and to a first-order and zeroth-order approximation. Then, following Ryden and Gunn (1987) and Ryden (1988), we model inhomogeneities as central peaks surrounded by secondary perturbations, and review and extend (according to a number of different approximations) the analytic expressions of the rms torque acting on a thin spherical mass shell, and of the angular momentum thus acquired. In particular, two extreme physical situations have been analysed: (i) the core of density perturbations, or more generally homogeneous density perturbations; and (ii) the envelope of density perturbations, or more generally density perturbations with halos reduced to the Hubble flow. Though in early times the torque grows in proportion to t2/3 and the angular momentum in proportion to t5/3, different approximations lead to different results even before density perturbations decouple strongly from the Hubble flow. An interpretation of the results is consistent with a suggestion by Peebles (1969), that physical processes leading to the torques under consideration are switched off during the above-mentioned strong decoupling. After this epoch, a given approximation might have mathematical features which are not in contradiction with the physical meaning of the problem, but no physical meaning in itself; from a physical point of view, any approximation should be smoothed, or truncated. Additional support to this conclusion comes from a qualitative estimate of the angular momentum, and then of the spin parameter, related to the whole density perturbations under a number of simplifying assumptions; accordingly, the acquisition of angular momentum appears to end at late rather than at early stages of strong decouling. The related values of the spin parameter are λ greater-than or equivalent to 0.02, which is consistent with λ greater-than or equivalent to 0.05 found by both Barnes and Efstathiou (1987) using numerical computations based on N-body simulations, and Heavens and Peacock (1988) using analytical approximations. The results are also in agreement with current estimations of the Milky Way angular momentum.