  Through a suite of direct N-body simulations, we explore how the structural
and kinematic evolution of a star cluster located at the center of a dwarf
galaxy is affected by the shape of its host's dark matter density profile. The
stronger central tidal fields of cuspier halos minimize the cluster's ability
to expand in response to mass loss due to stellar evolution during its early
evolutionary stages and during its subsequent long-term evolution driven by
two-body relaxation. Hence clusters evolving in cuspier dark matter halos are
characterized by more compact sizes, higher velocity dispersions and remain
approximately isotropic at all clustercentric distances. Conversely, clusters
in cored halos can expand more and develop a velocity distribution profile that
becomes increasingly radially anisotropic at larger clustercentric distances.
Finally, the larger velocity dispersion of clusters evolving in cuspier dark
matter profiles results in them having longer relaxation times. Hence clusters
in cuspy galaxies relax at a slower rate and, consequently, they are both less
mass segregated and farther from complete energy equipartition than cluster's
in cored galaxies. Application of this work to observations allows for star
clusters to be used as tools to measure the distribution of dark matter in
dwarf galaxies and to distinguish isolated star clusters from ultra-faint dwarf
galaxies.
