Three-dimensional stellar orbits due to off-centered dark matter halo at the center of the disc galaxies

Stellar orbits and the evolution of galaxies are intertwined processes that have long-term implications on each other. This paper studies how stellar orbits at the galaxy’s central region are disturbed by an asymmetric dark matter halo potential. Evidence from the observations and simulations in the Milky Way type galaxy suggests that the center of the dark matter halo could be off-centered by a few parsecs concerning the center of the core. The equations of motion of stars in the core of galaxies are expressed in terms of three-dimensional perturbed potential arising from the offset halo. The central region’s azimuthal variation in the effective potential is obtained and the first-order epicyclic theory is used to solve for the orbits. The magnitude of this perturbation potential grows at small radii and exhibits $m=1$ azimuthal fluctuations. In the central region, within 3 kpc radius, even a small halo offset of 300 pc can cause a surprisingly strong spatial and kinematical lopsidedness. A planar orbit, initially assumed to be in disc plane, tends to leave the plane giving rise to non-planar configuration. Furthermore, as long as the halo offset persists, the central region will stay lopsided. The dark matter halo would significantly impact the dynamic development of this region and could help fuel the active galactic nucleus.