  A thermal relic WIMP remains a prime candidate for the nature of Dark Matter,
particularly for the more poorly constrained case of a heavy ($\gtrsim$ 1 TeV)
WIMP. The highest fluxes from WIMP annihilations are expected in the region of
the Galactic Centre (GC) where current and near future gamma-ray observatories
can be exploited to place tight limits on the WIMP paradigm. It is regularly
noted that the annihilation flux of gammas will be accompanied by charged
secondary particles which can produce 'delayed' inverse Compton (IC) gamma-ray
emission, but this component is often neglected in indirect Dark Matter
searches. In this work the inverse Compton emission is studied for the specific
conditions of heavy WIMP annihilation in the GC. Using models for the magnetic
and radiation fields of the region, and taking into consideration the transport
of secondary particles, we find that for TeV WIMPs the IC component cannot be
neglected in the GC, with the particles produced cooling within the region
rather than propagating out in to the Galaxy. This effect changes the predicted
spectral shape substantially and thus boosts the detection prospects for heavy
WIMPs.
