Manifold spirals, disc-halo interactions, and the secular evolution in N-body models of barred galaxies

The manifold theory of barred-spiral structure provides a dynamical mechanism explaining how spiral arms beyond the ends of galactic bars can be supported by chaotic flows extending beyond the bar's corotation zone. We discuss its applicability to N-body simulations of secularly evolving barred galaxies. In these simulations, we observe consecutive 'incidents' of spiral activity, leading to a time-varying disc morphology. Besides disc self-excitations, we provide evidence of a newly noted excitation mechanism related to the 'off-centring' effect: particles ejected in elongated orbits at major incidents cause the disc centre-of-mass to recoil and be set in a wobble-type orbit with respect to the halo centre of mass. The time-dependent m = 1 perturbation on the disc by the above mechanism correlates with the excitation of new incidents of non-axisymmetric activity beyond the bar. At every new excitation, the manifolds act as dynamical avenues attracting particles which are directed far from corotation along chaotic orbits. The fact that the manifolds evolve morphologically in time, due to varying non-axisymmetric perturbations, allows to reconcile manifolds with the presence of multiple patterns and frequencies in the disc. We find a time-oscillating pattern speed profile_p(R) at distances R between the bar's corotation, at resonance with the succession of minima and maxima of the non-axisymmetric activity beyond the bar. Finally, we discuss disc thermalization, i.e. the evolution of the disc velocity dispersion profile and its connection with disc responsiveness to manifold spirals.