High-mass X-ray binaries and recent star formation history of the Small Magellanic Cloud

We study the relation between high-mass X-ray binary (HMXB) population and recent star formation history (SFH) for the Small Magellanic Cloud (SMC). Using archival optical SMC observations, we have approximated the color-magnitude diagrams of the stellar population by model stellar populations and, in this way, reconstructed the spatially resolved SFH of the galaxy over the past 100 Myr. We analyze the errors and stability of this method for determining the recent SFH and show that uncertainties in the models of massive stars at late evolutionary stages are the main factor that limits its accuracy. By combining the SFH with the spatial distribution of HMXBs obtained from XMM-Newton observations, we have derived the dependence of the HMXB number on the time elapsed since the star formation event. The number of young systems with ages less than or similar to 10 Myr is shown to be smaller than the prediction based on the type-II supernova rate. The HMXB number reaches its maximum similar to 20-50 Myr after the star formation event. This may be attributable, at least partly, to a low luminosity threshold in the population of X-ray sources studied, L-min similar to 10(34) erg s(-1). Be/X systems make a dominant contribution to this population, while the contribution from HMXBs with black holes is relatively small.