HMXB, ULX and star formation

Based on recent X-ray observations of the Milky Way, Magellanic Clouds and nearby starburst galaxies we study the population of high-mass X-ray binaries (HMXBs), their connection with ultra-luminous X-ray sources (ULXs) and the relation to the star formation rate (SFR). Although more subtle SFR-dependent effects are likely to exist, the data in the log(L-X) similar to 36 - 40.5 luminosity range are broadly consistent with the existence of a universal luminosity function of HMXBs, which can be roughly described as a power law with a differential slope of similar to 1.6 and a cutoff at log(L-X) similar to 40.5. The ULX sources found in many starburst galaxies occupy the high-luminosity end of this single-slope power-law distribution, whereas its low-luminosity part is composed of ordinary high-mass X-ray binaries, observed, e.g. in the Milky Way and Magellanic Clouds. As the normalization of the universal luminosity function is proportional to the star formation rate, the number and/or the collective X-ray luminosity of HMXBs can be used to measure the current value of the SFR in the host galaxy. Distant (unresolved) starburst galaxies observed by Chandra at redshifts of z similar to 0.2 - 1.3 obey the same L-X-SFR relation as local galaxies, indicating that the ULXs at these redshifts were not significantly more luminous than those found in nearby galaxies.