Baryonic Dark Matter and the Diffuse Gamma Ray Background

We show that the baryonic gas content of the halo of our galaxy can be probed by performing a multipole expansion on the distribution of diffuse background gamma-ray emission. While the monopole moment (isotropic background) can be used to constrain the baryonic fraction of the halo gas, the quadrupole to monopole ratio is a sensitive probe of the distribution of gas in the halo, {\it i.e.} the degree of flattening of the gas distribution. The predicted diffuse gamma ray flux is found to be very sensitive to the adopted cosmic ray density distribution throughout the halo. If the cosmic rays are uniform, then the upper bound on the gas fraction is $16.6\%$ regardless of the flattening of the halo gas distribution. However, this bound can be weakened by taking into account the removal of flux in and close to the galactic plane, especially for a oblate ($e <1$) gas distribution. On the other hand, in the more realistic situation that the cosmic rays linearly trace the smoothed halo mass (and halo gas) distribution, then a stringent bound on the baryonic gas fraction in the halo $\eta$, $\eta \ltwid 3\%$, can be placed with existing data, regardless of halo flattening.