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This study examines the effect of dark matter halos on the orbital and escapedynamics of stars in the central region of barred galaxies. A three-dimensionalgravitational model with a central bulge, bar, disc, and dark matter halo (orsimply dark halo) has been set up and analyzed from the viewpoint of escape inopen Hamiltonian systems for this purpose. Additionally, this model has beenexamined separately for the dark halo profiles: oblate and NFW. In bothcircumstances, an escape mechanism has been identified near the saddle pointsof the phase space, which correspond to the bar ends. The escaping motion ofstars is seen using orbital maps and Poincar\'e surface section maps generatedin various phase planes. Finally, the relationship between chaos and dark haloparameters such as mass, size, circular velocity, and nature has been studied.Our findings suggest that oblate dark halos are preferred over NFW dark halosfor justifying the formation of full-fledged spiral arms and extendeddistribution of dark halos in giant spiral galaxies with supermassive blackholes (SMBHs) at their centers. Again, the oblate dark halos well justify theemergence of less prominent or poor spiral arms and the core-dominateddistribution of dark halos in dwarf and LSB galaxies in the absence of centralSMBHs. On the other hand, extreme central baryonic feedback is required for theNFW halos to generate spiral patterns, and such dark halos should be preferredfor galaxies with extremely energetic centers.

Effect of dark matter halos on the orbital and escape dynamics of barred galaxies