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Deep Chandra survey of the Small Magellanic Cloud. III. Formation efficiency of High-Mass X-ray binaries

We have compiled the most complete census of High-Mass X-ray Binaries (HMXBs) in the Small Magellanic Cloud with the aim to investigate the formation efficiency of young accreting binaries in its low metallicity environment. In total, we use 127 X-ray sources with detections in our \chandra X-ray Visionary Program (XVP), supplemented by 14 additional (likely and confirmed) HMXBs identified by \cite{2016A&A...586A..81H} that fall within the XVP area, but are not either detected in our survey (9 sources) or matched with any XVP source that has at least one OB counterpart in the OGLE-III catalog (5 sources). Specifically, we examine the number ratio of the HMXBs [N(HMXBs)] to {\it (a)} the number of OB stars, {\it (b)} the local star-formation rate (SFR), and {\it (c)} the stellar mass produced during the specific star-formation burst, all as a function of the age of their parent stellar populations. Each of these indicators serves a different role, but in all cases we find that the HMXB formation efficiency increases as a function of time (following a burst of star formation) up to $\sim$40--60\,Myr, and then gradually decreases. The peak formation efficiency N(HMXB)/SFR is (49 $\pm$ 14) $[10^{-5}~{\rm M_{\odot}/yr}]^{-1}$, in good agreement with previous estimates of the average formation efficiency in the broad $\sim$20--60\,Myr age range. The frequency of HMXBs is a factor of 8$\times$ higher than at $\sim$10\,Myr, and 4$\times$ higher than at $\sim$260\,Myr, i.e. at earlier and later epochs, respectively.