Dark Matter Halos and Evolution of Bars in Disk Galaxies: Collisionless
  Models Revisited
  We construct and evolve families of steady-state models of stellar disks
embedded in live 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 include the gaseous component in the
follow up paper. We are interested in the angular momentum (J) redistribution
in the disk-halo system. 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, such as
spontaneous bar instability and vertical buckling instability, and slowdown the
J transfer, while facilitating it in the secular phase. Within the corotation
radius (Rcr), the disk J remains nearly constant, as long as Rcr stays within
the disk -- a sign that the lost J to the outer disk and the halo is being
compensated by an influx of fresh J due to the outward motion of Rcr. This is
feasible as long as the bar slowdown dominates the loss of J inside Rcr. We
find that in some models the bar pattern speed stalls for prolonged time
periods when Rcr is located outside the disk. This phenomenon appears
concurrent with the near absence of J transfer between the disk and the halo.
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 Rcr leaving the disk. 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.
