We have used the Wisconsin H-Alpha Mapper (WHAM) to observe the spatially extended distribution of ionized hydrogen in M31 beyond the stellar disk. We obtained five sets of observations, centered near the photometric major axis of M31, that extend from the center of the galaxy to just off the edge of the southwestern HI disk. Beyond the bright stellar disk, but within the HI disk, weak H-alpha is detected with an intensity I(H-alpha) = 0.05 (+0.01 / -0.02) Rayleighs. Since M31 is inclined 77 degrees with respect to the line of sight, this implies that the ambient intergalactic ionizing flux onto each side of M31 is Phi_0 <= 1.6 x 10^4 photons cm^-2 s^-1. Just beyond the outer boundary of the HI disk we find no significant detection of H-alpha and place an upper limit I(H-alpha) <= 0.019 Rayleighs.

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