over the line-of-sight. $dN_{\gamma}/dE_{\gamma}$ is the gamma ray spectrum generated per WIMP annihilation.

Averaging over a solid angle centered around a direction, $\psi$, we arrive at $$\Phi_{\gamma}(E_{\gamma}) \approx 2.8 \times 10^{-12} \, \rm{cm}^{-2} \, \rm{s}^{-1} \, \frac{dN_{\gamma}}{dE_{\gamma}} \bigg(\frac{\sigv}{3 \times 10^{-26} \,\rm{cm}^3/\rm{s}}\bigg)  \bigg(\frac{1 \, \rm{TeV}}{m_{\rm{X}}}\bigg)^2 J(\Delta \Omega, \psi) \Delta \Omega,
\label{flux2}$$ where $\Delta \Omega$ is the solid angle observed. The quantity $J(\Delta \Omega, \psi)$ depends only on the dark matter distribution, and is the average over the solid angle of the quantity: $$J(\psi) = \frac{1}{8.5 \, \rm{kpc}} \bigg(\frac{1}{0.3 \, \rm{GeV}/\rm{cm}^3}\bigg)^2 \, \int_{\rm{los}} \rho^2(r(l,\psi)) dl.$$ $J(\psi)$ is normalized such that a completely flat halo profile, with a density equal to the value at the solar circle, integrated along the line-of-sight to the Galactic Center would yield a value of one. In dark matter distributions favored by N-body simulations, however, this value can be much larger. The Narvarro-Frenk-White profile [@nfw], which is a commonly used benchmark halo model, leads to values of $J(\Delta \Omega=10^{-5} \, {\rm sr}, \psi=0) \sim 10^5$. The effects adiabatic contraction due to the cooling of baryons is further expected to increase this quantity [@ac].

The recent discovery of a bright, very high-energy gamma ray source in the galactic center 