Testing linear-theory predictions of galaxy formation

The angular momentum of galaxies is routinely ascribed to a process of tida l torques acting during the early stages of gravitational collapse, and is predicted from the initial mass distribution using second-order perturbatio n theory and the Zel'dovich approximation. We test this theory for a flat h ierarchical cosmogony using a large N-body simulation with sufficient dynam ic range to include tidal fields, allow resolution of individual galaxies, and thereby expand on previous studies. The predictions of linear collapse, linear tidal torque, and biased-peaks galaxy formation are applied to the initial conditions and compared with results for evolved bound objects. We find relatively good correlation between the predictions of linear theory a nd actual galaxy evolution. Collapse is well described by an ellipsoidal mo del within a shear field, which results primarily in triaxial objects that do not map directly to the initial density field, While structure formation from early times is a complex history of hierarchical merging, salient fea tures are well described by the simple spherical-collapse model. Most notab ly, we test several methods for determining the turnaround epoch, and find that turnaround is successfully described by the spherical-collapse model. The angular momentum of collapsing structures grows linearly until turnarou nd, as predicted, and continues quasi-linearly until shell crossing. The pr edicted angular momentum for well-resolved galaxies at turnaround overestim ates the true turnaround and final values by a factor of similar to 3, with a scatter of similar to 70 per cent, and only marginally yields the correc t direction of the angular momentum vector. We recover the prediction that final angular momentum scales as mass to the 5/3 power. We find that mass a nd angular momentum also vary proportionally with peak height. In view of t he fact that the observed galaxy collapse is a stochastic hierarchical and non-linear process, it is encouraging that the linear theory can serve as a n effective predictive and analytic tool.