Dark matter halos and evolution of bars in disk galaxies: Collisionless models revisited

We construct and evolve three one-parameter families and one two-parameter family of steady-state models of stellar disks embedded in live dark matter (DM) halos in order to study the dynamical and secular phases of bar evolution. These models are tested against those published in the literature in order to extend them and to include the gaseous component in the follow-up paper. Specifically, we are interested in the angular momentum, J, redistribution in the disk-halo system during these two evolutionary phases without distinguishing between the resonant and non-resonant effects. We confirm the previous results and quantify for the first time the dual role that the DM halos play in the bar evolution: more centrally concentrated halos dilute the dynamical processes of the initial bar growth, such as the spontaneous bar instability and the vertical buckling instability, and slow down the J transfer, while facilitating it in the secular phase. The rate of J transfer in the disk and the halo is followed up in order to identify sites and times of peak activity in J emission and absorption. Within the corotation radius, R _cr, the disk J remains nearly constant in time, as long as R _cr stays within the disk - a sign that the lost angular momentum to the outer disk and the halo is being compensated by an influx of fresh J due to the outward motion of R _cr. We demonstrate that this is feasible as long as the bar slowdown dominates the loss of J inside R _cr. Next, we find that in some models the bar pattern speed stalls for prolonged time periods, i.e., the bar exhibits a constant rate of tumbling when R _cr is located outside the disk. This phenomenon appears concurrent with the near absence of J transfer between the disk and the halo, and is associated with the halo emitting J at the corotation resonance and absorbing it at the inner Lindblad resonance. Furthermore, we confirm that stellar bars generally display the corotation-to-bar size ratios in the range of ∼ 1-1.4, but only between the times of the first buckling and R _cr leaving the disk. Hence, the corotation-to-disk size ratio emerges as an important dynamic discriminator between various stages of barred disk evolution. Finally, we analyze a number of correlations between the basic parameters of a barred disk and a halo, some already reported in the literature and some new.