High-mass X-ray binaries as a star formation rate indicator in distant galaxies

Based on Chandra and ASCA observations of nearby starburst galaxies and RXTE/ASM, ASCA and MIR-KVANT/TTM studies of high-mass X-ray binary (HMXB) populations in the Milky Way and Magellanic Clouds, we propose that the number and/or the collective X-ray luminosity of HMXBs can be used to measure the star formation rate (SFR) of a galaxy. We show that, within the accuracy of the presently available data, a linear relation between HMXB number and star formation rate exists. The relation between SFR and collective luminosity of HMXBs is non-linear in the low-SFR regime, L X SFR 1.7 , and becomes linear only for a sufficiently high star formation rate, SFR 4.5 M yr -1 (for M * > 8 M ). The non-linear L X -SFR dependence in the low-SFR limit is not related to non-linear SFR-dependent effects in the population of HMXB sources. It is rather caused by the fact that we measure the collective luminosity of a population of discrete sources, which might be dominated by the few brightest sources. Although more subtle SFR-dependent effects are likely to exist, over the entire range of SFRs the data are broadly consistent with the existence of a universal luminosity function of HMXBs that can be roughly described as a power law with a differential slope of 1.6, a cut-off at L X few 10 40 erg s -1 and a normalization proportional to the star formation rate.