  Diffuse gamma-ray radiation in galaxies is produced by cosmic ray
interactions with the interstellar medium. With the completion of EGRET
observations, the only extragalactic object from which there has been a
positive detection of diffuse gamma-ray emission is the Large Magellanic Cloud.
We systematically estimate the expected diffuse gamma-ray flux from Local Group
galaxies, and determine their detectability by new generation gamma-ray
observatories such as GLAST. For each galaxy, the expected gamma-ray flux
depends only on its total gas content and its cosmic ray flux. We present a
method for calculating cosmic ray flux in these galaxies in terms of the
observed rate of supernova explosions, where cosmic ray acceleration is
believed to take place. The difficulty in deriving accurate supernova rates
from observational data is a dominant uncertainty in our calculations. We
estimate the gamma-ray flux for Local Group galaxies and find that our
predictions are consistent with the observations for the LMC and with the
observational upper limits for the Small Magellanic Cloud and M31. Both the
Andromeda galaxy, with a flux of $\sim 1.0 \times 10^{-8}$ photons sec$^{-1}$
cm$^{-2}$ above 100 MeV, and the SMC, with a flux of $\sim 1.7 \times 10^{-8}$
photons sec$^{-1}$ cm$^{-2}$ above 100 MeV, are expected to be observable by
GLAST. M33 is at the limit of detectability with a flux of $\sim 0.11 \times
10^{-8}$ sec$^{-1}$ cm$^{-2}$. Other Local Group galaxies are at least two
orders of magnitude below GLAST sensitivity.

Astrophysics