Do assumptions about the central density of subhaloes affect dark matter annihilation and lensing calculations?

Subhalo models play a critical role in dark matter annihilation predictions and galaxy-galaxy lensing studies; however, the internal structure of subhaloes remains highly uncertain. In particular, a growing body of evidence suggests that the central density of cuspy dark matter subhaloes is conserved in minor mergers, whereas empirical models of subhalo evolution -- calibrated using limited-resolution simulations -- often assume a drop in the central density. To assess the impact of these assumptions, we systematically explore how a wide range of initial mass profiles and tidal evolution prescriptions influence annihilation and lensing calculations, including the physically motivated Energy Truncation model, which explicitly preserves the central density of subhaloes. We find that annihilation calculations are very sensitive to the assumed inner density profile, and different models can produce more than an order of magnitude difference in the annihilation rate of individual subhaloes, and a factor of $\sim5$ in the total annihilation rate expected in the Milky Way. Since the innermost parts of haloes will always be difficult to resolve in simulations, we conclude that developing a theoretical understanding of subhalo evolution is crucial to be able to make accurate predictions of the dark matter annihilation signal. On the other hand, while the shear and convergence profiles used in galaxy-galaxy lensing are sensitive to the initial profile assumed (e.g., NFW versus Einasto), they are otherwise well-approximated by a simple stripping model in which the original profile is sharply truncated at a tidal radius.