How lumpy is the Milky Way's dark matter halo?

Cold dark matter (CDM) simulations predict that there are hundreds of lumps with masses greater than 10(7) M-circle dot in the Milky Way halo. However, we know of only a dozen dwarf satellites close to this mass. Are these lumps simply lacking in stars, or is there a fundamental flaw in our most popular cosmology? By studying the tidal debris of known satellites, we can potentially address this question. In this paper, we quantify the effects of the dark matter lumps on tidal tails. The lumps scatter stars in the tidal tails from their original orbits, producing a distinctive signature. We simulate debris evolution in smooth and lumpy halo potentials, and use our simulations to motivate and test a statistical measure of the degree of scattering apparent in the angular position and radial velocity measurement of debris stars the scattering index. We find that the scattering index can in general distinguish between the levels of substructure predicted by CDM cosmologies and smooth Milky Way models, but the sensitivity of the debris depends on the orientation of the parent satellite's orbit relative to the largest lumps orbits. We apply our results to the carbon star stream associated with the Sagittarius dwarf galaxy (Sgr), and find that these stars appear to be more scattered than we expect for debris orbiting in a smooth halo. However, the degree of scattering is entirely consistent with that expected because of the influence of the Large Magellanic Cloud, which is on an orbit that intersects Sgr's own. We conclude that the current data are unable to constrain CDM models. Nevertheless, our study suggests that future data sets of debris stars associated with other Milky Way satellites could provide strong constraints on CDM models.