The Discrete X-Ray Source Population in M31

We report the results of the analysis of the entire set of Einstein imaging observations of M31. We detect 108 individual X-ray sources, with (0.2-1.0 keV) luminosities ranging from 5 X 10^36^ ergs s^-1^ to above 10^38^ ergs s^-1^ at the distance of M31 (690 kpc). Fourteen of these sources are luminous enough to perform a spectral fit of the X-ray data. Fourteen sources are found to vary between Einstein observations, in addition to the two sources already reported by Collura, Reale, and Peres. We do not find any substantial difference between the luminosity distributions of X-ray sources in the bulge and in the disk, contrary to earlier reports. The luminosity distribution of these X-ray sources is well represented by a power law with slopes between - 1 and -0.66(1 σ). About 20%-30% of the counts detected in the bulge region are not accounted for by the individual sources. This additional emission can be easily explained by the integrated contribution of sources below the detection threshold. Nevertheless, if we use this component to set a conservative upper limit on the emission of a putative gaseous component, we find that no more than ~2 x 10^6^ M_sun_ of hot gas can be present in the bulge. This limit is consistent with optical, H I, and IR estimates and implies the presence of galactic winds in M31. We present contour maps of the X-ray emission in the central region, and we compare the radial distribution of the surface brightness with the optical profiles. This comparison suggests that the disk is relatively underluminous in X-rays, relative to the stellar content. We compare the spatial distribution of bulge sources with that of optical novae and with emission-line images of the bulge. These comparisons constrain models of formation of low-mass X-ray binaries.