  We report the detection of diffuse hot gas in M31, using archival Chandra
observations which allow us to map out a 30' by 30' field (covering a
galactocentric radius up to 4.5 kpc) and to detect sources in the galaxy down
to a 0.5-8 keV luminosity limit of ~10^35 ergs/s. We estimate the remaining
stellar contribution from fainter X-ray sources (primarily cataclysmic
variables and coronally active binaries), assuming that they spatially follow
the stellar distribution. Indeed, the near-IR K-band light of the galaxy
closely traces the 2-8 keV unresolved X-rays, indicating a collective stellar
X-ray emissivity consistent with those determined for the Galactic ridge and
M32, whereas the amount of the 0.5-2 keV unresolved emission is significantly
greater than the expected stellar contribution, especially within a
galactocentric radius of ~2 kpc. Morphologically, this soft X-ray excess
appears substantially rounder than the bulge as seen in K-band and is elongated
approximately along the minor-axis at large radii. The excess thus most likely
represents the emission of diffuse hot gas in and around the galactic bulge.
Furthermore, the near side of the M31 disk casts an apparent shadow against the
soft X-ray excess, indicating that the hot gas extends to at least 2.5 kpc from
the galactic plane. We briefly discuss the implications of these results on the
energy balance in the M31 bulge and on understanding the large-scale soft X-ray
enhancement observed toward the inner region of our own Galaxy.
