High Mass X-ray Binaries as a Star Formation Rate Indicator in Distant Galaxies

Based on CHANDRA 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 the star formation rate exists. The relation between SFR and collective luminosity of HMXBs is non-linear in the low SFR regime, $L_X\propto \SFR^{\approx 1.7}$, and becomes linear only for sufficiently high star formation rate, when the total number of HMXB sources becomes sufficiently large. Such behaviour is caused by the fact, that we measure collective luminosity of a population of the discrete sources. Although more subtle SFR dependent effects are likely to exist, the data 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 $\sim 1.6$, a cutoff at $L_X \sim few \times 10^{40}$ erg/sec and a normalisation proportional to the star formation rate. We apply our results to (spatially unresolved) starburst galaxies observed by CHANDRA at redshifts up to $z\sim 1$ in the Hubble Deep Field North and show that the calibration of the collective luminosity of HMXBs as a SFR indicator based on the local sample agrees well with the SFR estimates obtained for these distant galaxies with conventional methods.