HMXB, ULX and star formation

Based on recent X-ray observations of the Milky Way, Magellanic Clouds and nearby starburst galaxies we study population of high mass X-ray binaries, their connection with ultra-luminous X-ray sources and relation to the star formation. Although more subtle SFR dependent effects are likely to exist, the data in the lg(Lx)~36-40.5 luminosity range are broadly consistent with existence of a ``universal'' luminosity function of HMXBs, which can be roughly described as a power law with differential slope of ~1.6 and a cutoff at lg(Lx)~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 SFR in the host galaxy. Distant (unresolved) starburst galaxies observed by Chandra at redshifts of z~0.2-1.3 obey the same Lx-SFR relation as local galaxies, indicating that the ULXs at these redshifts were not significantly more luminous than those found in nearby galaxies.