Acquisition of angular momentum by tidal torques in expanding, spherical-symmetric density perturbations: an analysis of different approximations. 3

The evolution of expanding, spherical-symmetric density perturbations is improved and extended to all kinds of high-density (Omega0 greater than or approximately = 0.1) Friedmann universes made of dust only, according to an exact theory and to a first-order and zeroth-order approximation. Then inhomogeneities are modeled as central peaks surrounded by secondary perturbations, and the effects of spin growth on the expansion are investigated, concerning the expression of the rms torque acting on a thin spherical mass shell and the angular momentum thus acquired. Though in early times the angular momentum grows in proportion to t5/3, all the approximations used to lead to a gain of spin in proportion to t from a given time on, at least during the linear stages of evolution; in all cases, the torque attains a maximum value and then decreases later. The comparison of the results with those related to excluding the effects of spin growth on the expansion, discloses that considerable differences in both radius and torque, and to a lesser extent in angular momentum, occur at a given time for any approximation. The angular momentum of the whole density perturbation is calculated for different masses and peak heights, at the beginning of strong decoupling from the Hubble flow (bar-delta = 1). A dissipation by a factor 4-6 (consistent with the result of numerical simulations) has to occur during nonlinear evolution, if typical values of the spin parameter in the range 0.05-0.07 are wanted. Then the transition from linear to nonlinear regime appears to be the physical mechanism which makes spin growth turn off. In addition, more dissipation has to occur for lower masses and vice versa, in order to pass from J proportional to M5/3 found using a mass-peak height correlation by Ryden and Gunn (1987) to J proportional to M7/4 deduced for spiral galaxies by, e.g. Brosche (1977) and Fall (1983).