  Globular clusters have long been known for presenting (at times) significant
deviations from spherical symmetry. While rotation has been the main proposed
explanation, other complicating factors such as their constant interaction with
the strong gravitational potential of their host galaxy have made it difficult
for a consensus to be reached. To address this question we have obtained
high-resolution spectra of WLM-1, the lone globular cluster associated with the
isolated, low-mass dwarf irregular galaxy WLM. Using archival HST WFPC2 data,
we measure the radial ellipticity profile of WLM-1, finding it to be highly
elliptical, with a mean value of 0.17 in the region 0.5-5" -- which is
comparable to what is found in our Galaxy for the most elliptical globular
clusters. There is no evidence of isophote twisting, except for the innermost
regions of the cluster (r < 0.5"). To investigate whether the observed
flattening can be ascribed to rotation, we have obtained long-slit
high-resolution VLT/UVES spectra of this cluster along and perpendicular to the
axis of flattening. Using cross-correlation we find that the velocity profile
of the cluster is consistent with zero rotation along either axis. Thus neither
cluster rotation nor galactic tides can be responsible for the flattened
morphology of WLM-1. We argue that the required velocity dispersion anisotropy
between the semi-major and semi-minor axes that would be required to account
for the observed flattening is relatively small, of order 1 km/s. Even though
our errors preclude us from conclusively establishing that such a difference
indeed exists, velocity anisotropy remains at present the most plausible
explanation for the shape of this cluster.
