  We study the morphology of the 511 keV signal that could be produced by
exciting dark matter (XDM) in the Milky Way. In this model, collisions between
dark matter particles excite the dark matter to a state that can then decay
back to the ground state, releasing an electron-positron pair. These electrons
and positrons would then annihilate, producing 511 keV photons that could
explain the 511 keV signal seen by INTEGRAL at the Galactic Center. We compare
the resulting flux with the most recent INTEGRAL data, performing the first
full statistical analysis of the exciting dark matter model. We focus on
exciting dark matter in the mass and cross section ranges 100 GeV $\lesssim
m_{\chi} \lesssim$ 3 TeV and $10^{-19}$ cm$^3$ s$^{-1} \lesssim \langle \sigma
v \rangle \lesssim 10^{-16}$ cm$^3$ s$^{-1}$. We show that exciting dark matter
can provide a significantly better fit than the simpler case of annihilating
dark matter, with $\Delta\chi^2 > 16$ for all but one of the density profiles
we consider.
