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 123 X-ray sources with detections in our Chandra X-ray Visionary Program (XVP), supplemented by 14 additional (likely and confirmed) HMXBs identified by Haberl & Sturm that fall within the XVP area, but are neither detected in our survey (nine sources) nor matched with any of the 127 sources identified in the XVP data (five sources). Specifically, we examine the number ratio of the HMXBs [N(HMXBs)] to (a) the number of OB stars, (b) the local star formation rate (SFR), and (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 ∼40-60 Myr, and then gradually decreases. The formation efficiency peaks at ∼30-40 Myr with average rates of {\text{}}{{N}}({HMXB})/{SFR}={339}_-83⁺⁷⁸ {({M}_⊙ /{yr})}^-1, and N(HMXB)/M \star =({8.74}_-0.92^+1.0)× {10}^-6 {M}_⊙ ^-1, in good agreement with previous estimates of the average formation efficiency in the broad ∼20-60 Myr age range.