  If the supermassive black hole Sgr A* at the center of the Milky Way grew
adiabatically from an initial seed embedded in an NFW dark matter (DM) halo,
then the DM profile near the hole has steepened into a spike. We calculate the
dramatic enhancement to the gamma ray flux from the Galactic center (GC) from
such a spike if the 1-3 GeV excess observed in Fermi data is due to DM
annihilations. We find that for the parameter values favored in recent fits,
the point source-like flux from the spike is 35 times greater than the flux
from the inner $1^\circ$ of the halo, far exceeding all Fermi point source
detections near the GC. We consider the dependence of the spike signal on
astrophysical and particle parameters and conclude that if the GC excess is due
to DM, then a canonical adiabatic spike is disfavored by the data. We discuss
alternative Galactic histories that predict different spike signals, including:
(i) the nonadiabatic growth of the black hole, possibly associated with halo
and/or black hole mergers, (ii) gravitational interaction of DM with baryons in
the dense core, such as heating by stars, or (iii) DM self-interactions. We
emphasize that the spike signal is sensitive to a different combination of
particle parameters than the halo signal, and that the inclusion of a spike
component to any DM signal in future analyses would provide novel information
about both the history of the GC and the particle physics of DM annihilations.
