The recent detection of two faint and extended star clusters in the central regions of two Local Group dwarf galaxies , Eridanus II and Andromeda XXV , raises the question of whether clusters with such low densities can survive the tidal field of cold dark matter haloes with central density cusps .
Using both analytic arguments and a suite of collisionless N-body simulations , I show that these clusters are extremely fragile and quickly disrupted in the presence of central cusps \rho \sim r ^ { - \alpha } with \alpha \gtrsim 0.2 .
Furthermore , the scenario in which the clusters were originally more massive and sank to the center of the halo requires extreme fine tuning and does not naturally reproduce the observed systems .
In turn , these clusters are long lived in cored haloes , whose central regions are safe shelters for \alpha \lesssim 0.2 .
The only viable scenario for hosts that have preserved their primoridal cusp to the present time is that the clusters formed at rest at the bottom of the potential , which is easily tested by measurement of the clusters proper velocity within the host .
This offers means to readily probe the central density profile of two dwarf galaxies as faint as L _ { V } \sim 5 \times 10 ^ { 5 } L _ { \odot } and L _ { V } \sim 6 \times 10 ^ { 4 } L _ { \odot } , in which stellar feedback is unlikely to be effective .