We develop a technique to investigate the possibility that some of the recently discovered ultra-faint dwarf satellites of the Milky Way might be cusp caustics rather than gravitationally self-bound systems .
Such cusps can form when a stream of stars folds , creating a region where the projected 2-D surface density is enhanced .
In this work , we construct a Poisson maximum likelihood test to compare the cusp and exponential models of any substructure on an equal footing .
We apply the test to the Hercules dwarf ( d \sim 113 kpc , M _ { V } \sim - 6.2 , e \sim 0.67 ) .
The flattened exponential model is strongly favored over the cusp model in the case of Hercules , ruling out at high confidence that Hercules is a cusp catastrophe .
This test can be applied to any of the Milky Way dwarfs , and more generally to the entire stellar halo population , to search for the cusp catastrophes that might be expected in an accreted stellar halo .