  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.
