Role of galactic bars in the formation of spiral arms: a study through
  orbital and escape dynamics-II
  In the present work we have analysed the effect of dark matter haloes on the
orbital and escape dynamics of stars in barred galaxies. For that, a
three-dimensional gravitational model composed by central bulge, bar, disc and
dark matter halo have been studied from the viewpoint of escape in an open
Hamiltonian system. In addition this model is investigated for the following
dark matter halo profiles viz. oblate and NFW. In both cases, escape mechanism
has been observed near the saddle points corresponding to the bar ends. We
visualise the nature of stellar orbits in the plane of the bar. Further
Poincar\'e surface section maps in several phase planes for different escape
energy values have been plotted to visualise the chaotic and regular domains of
motion. Finally the variation of chaos with the dark matter halo parameters
viz. mass, size, circular velocity and nature has been investigated. Our result
shows that the oblate haloes are preferred to justify the formation of
full-fledged spiral arms and extended dark matter distributions in the giant
spirals than the NFW haloes, only if they host central super massive black
holes (SMBHs). Again, in the absence of SMBHs, the oblate haloes well justify
the formation of less prominent or poor spiral arms and dark matter dominated
cores in the dwarf and LSB galaxies. We also found that, for the NFW haloes,
extreme central baryonic feedback is required to form spiral patterns and such
haloes should preferred for the galaxies with extremely energetic centres.
