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) proportional to SFRsimilar to 1.7 , and becomes linear only for a sufficiently high star formation rate, SFR greater than or similar to 4.5 M-circle dot yr(-1) (for M (*) > 8 M-circle dot). 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 similar to1.6, a cut-off at L (X) similar to few x 10(40) erg s(-1) and a normalization proportional to the star formation rate. We apply our results to (spatially unresolved) starburst galaxies observed by Chandra at redshifts up to z similar to 1.2 in the Hubble Deep Field North and show that the calibration of the collective luminosity of HMXBs as an SFR indicator based on the local sample agrees well with the SFR estimates obtained for these distant galaxies with conventional methods.