How to calculate dark matter direct detection exclusion limits that are consistent with gamma rays from annihilation in the Milky Way halo

Abstract: When comparing constraints on the Weakly Interacting Massive Particle (WIMP) properties from direct and indirect detection experiments it is crucial that the assumptions made about the dark matter (DM) distribution are realistic and consistent. For instance, if the Fermi-LAT Galactic centre GeV gamma-ray excess was due to WIMP annihilation, its morphology would be incompatible with the Standard Halo Model that is usually used to interpret data from direct detection experiments. In this article, we calculate exclusion limits from direct detection experiments using self-consistent velocity distributions, derived from mass models of the Milky Way where the DM halo has a generalized NFW profile. We use two different methods to make the mass model compatible with a DM interpretation of the Galactic centre gamma-ray excess. Firstly, we fix the inner slope of the DM density profile to the value that best fits the morphology of the excess. Secondly, we allow the inner slope to vary and include the morphology of the excess in the data sets used to constrain the gravitational potential of the Milky Way. The resulting direct detection limits differ significantly from those derived using the Standard Halo Model, in particular for light WIMPs, due to the differences in both the local DM density and velocity distribution.