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The recent detection of two faint and extended star clusters in the centralregions of two Local Group dwarf galaxies, Eridanus II and Andromeda XXV,raises the question of whether clusters with such low densities can survive thetidal field of cold dark matter haloes with central density cusps. Using bothanalytic arguments and a suite of collisionless N-body simulations, I show thatthese clusters are extremely fragile and quickly disrupted in the presence ofcentral cusps $\rho\sim r^{-\alpha}$ with $\alpha\gtrsim 0.2$. Furthermore, thescenario in which the clusters where originally more massive and sank to thecenter of the halo requires extreme fine tuning and does not naturallyreproduce the observed systems. In turn, these clusters are long lived in coredhaloes, whose central regions are safe shelters for $\alpha\lesssim 0.2$. Theonly viable scenario for hosts that have preserved their primoridal cusp to thepresent time is that the clusters formed at rest at the bottom of thepotential, which is easily tested by measurement of the clusters propervelocity within the host. This offers means to readily probe the centraldensity profile of two dwarf galaxies as faint as $L_V\sim5\times 10^5 L_\odot$and $L_V\sim6\times10^4 L_\odot$, in which stellar feedback is unlikely to beeffective.

Deadly dark matter cusps vs faint and extended star clusters: Eridanus II and Andromeda XXV