Kinematical asymmetry in the dwarf irregular galaxy WLM and a perturbed
  halo potential
  WLM is a dwarf irregular that is seen almost edge-on that has prompted a
number of kinematical studies investigating its rotation curve and its dark
matter content. In this paper, we investigate the origin of the strong
asymmetry of the rotation curve, which shows a significant discrepancy between
the approaching and the receding side. We first examine whether an $m = 1$
perturbation (lopsidedness) in the halo potential could be a mechanism creating
such kinematical asymmetry. To do so, we fit a theoretical rotational velocity
associated with an $m = 1$ perturbation in the halo potential model to the
observed data via a $\chi-$squared minimization method. We show that a lopsided
halo potential model can explain the asymmetry in the kinematic data reasonably
well. We then verify that the kinematical classification of WLM shows that its
velocity field is significantly perturbed due to both its asymmetrical rotation
curve and also its peculiar velocity dispersion map. In addition, based on a
kinemetry analysis, we find that it is possible for WLM to lie in the
transition region, where the disk and merger coexist. In conclusion, it appears
that the rotation curve of WLM diverges significantly from that of an ideal
rotating disk, which may significantly affect investigations of its dark matter
content.
