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Through a suite of direct N-body simulations, we explore how the structuraland kinematic evolution of a star cluster located at the center of a dwarfgalaxy is affected by the shape of its host's dark matter density profile. Thestronger central tidal fields of cuspier halos minimize the cluster's abilityto expand in response to mass loss due to stellar evolution during its earlyevolutionary stages and during its subsequent long-term evolution driven bytwo-body relaxation. Hence clusters evolving in cuspier dark matter halos arecharacterized by more compact sizes, higher velocity dispersions and remainapproximately isotropic at all clustercentric distances. Conversely, clustersin cored halos can expand more and develop a velocity distribution profile thatbecomes increasingly radially anisotropic at larger clustercentric distances.Finally, the larger velocity dispersion of clusters evolving in cuspier darkmatter profiles results in them having longer relaxation times. Hence clustersin cuspy galaxies relax at a slower rate and, consequently, they are both lessmass segregated and farther from complete energy equipartition than cluster'sin cored galaxies. Application of this work to observations allows for starclusters to be used as tools to measure the distribution of dark matter indwarf galaxies and to distinguish isolated star clusters from ultra-faint dwarfgalaxies.

The Structural and Kinematic Evolution of Central Star Clusters in Dwarf Galaxies and Their Dependence on Dark Matter Halo Profiles