The Milky Way in X-rays for an outside observer: Log(N)-Log(S) and Luminosity Function of X-ray binaries from RXTE/ASM data

We study the Log(N)-Log(S) and X-ray luminosity function in the 2-10 keV energy band, and the spatial (3-D) distribution of bright, log(L_X) > 34-35 erg/s, X-ray binaries in the Milky Way. In agreement with theoretical expectations and earlier results we found significant differences between the spatial distributions of low (LMXB) and high (HMXB) mass X-ray binaries. The volume density of LMXB sources peaks strongly at the Galactic Bulge. HMXBs tend to avoid the inner 3-4 kpc of the Galaxy, HMXBs are more concentrated towards the Galactic Plane and show clear signatures of the spiral structure in their spatial distribution. LMXB sources have a flatter Log(N)-Log(S) distribution and luminosity function than HMXBs. The integrated 2-10 keV luminosities of X-ray binaries, averaged over 1996--2000, are 2-3 * 10^39 (LMXB) and 2-3 * 10^38 (HMXB) erg/s. Normalised to the stellar mass and the star formation rate, respectively, these correspond to 5 * 10^28 erg/s/M_sol for LMXBs and 5 * 10^37 erg/s/(M_sol/yr) for HMXBs. Due to the shallow slopes of the luminosity functions the integrated emission of X-ray binaries is dominated by the 5-10 most luminous sources which determine the appearance of the Milky Way in the standard X-ray band for an outside observer. In particular variability of individual sources or an outburst of a bright transient source can increase the integrated luminosity of the Milky Way by as much as a factor of ~2. Although the average LMXB luminosity function shows a break near the Eddington luminosity for a 1.4 M_sol neutron star, at least 11 sources showed episodes of super-Eddington luminosity during ASM observations. We provide the maps of distribution of X-ray binaries in the Milky Way in various projections, which can be compared to images of nearby galaxies taken by CHANDRA and XMM-Newton.