Testing linear-theory predictions of galaxy formation

The angular momentum of galaxies is routinely ascribed to a process of tidal torques acting during the early stages of gravitational collapse, and is predicted from the initial mass distribution using second-order perturbation theory and the Zel’dovich approximation. We have tested this theory for a flat hierarchical cosmogony using a large N -body simulation with sufficient dynamic 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 to evolved bound objects. We find relatively good correlation between the predictions of linear theory and actual galaxy evolution. Collapse is well described by an ellipsoidal model within a shear field, which results primarily in triaxial objects which do not map directly to the initial density field. While structure formation from early times is a complex history of hierarchical merging, salient features are well described by the simple spherical-collapse model. Most notably, we test several methods for determining the turnaround epoch, and find that turnaround is succesfully described by the spherical collapse model. The angular momentum of collapsing structures grows linearly until turnaround, as predicted, and continues quasi-linearly until shell crossing. The predicted angular momentum for well-resolved galaxies at turnaround overestimates the true turnaround and final values by a factor of ∼ 3 with a scatter of ∼ 70 percent, and only marginally yields the correct 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 and angular momentum also vary proportionally with peak height. In view of the fact that the observed galaxy collapse is a stochastic hierarchical and non-linear process, it is encouraging that the linear theory can serve as an effective predictive and analytic tool.