Finding the birthplace of HMXBs in the Galaxy using Gaia EDR3: Kinematical age determination through orbit integration

Context. High-mass X-ray binaries (HMXBs) are produced after the first supernova event in a massive binary. These objects are intrinsically young and can suffer from a significant natal kick. As such, the progenitors of HMXBs are likely to have formed away from the current location of the X-ray emitting systems. Aims. We aim to find the birthplace of the known HMXBs of our Milky Way. Specifically, we want to answer the question of whether the formation of HMXBs can be associated with open stellar clusters and/or Galactic spiral structures and, from that, infer the time elapsed since the first supernova event. Methods. We used astrometric data from Gaia Early Data Release 3 to initialise the position and velocity of each known HMXB from the Galaxy, and to integrate their motion back in time. In parallel, we performed the same calculations on a sample of 1381 open clusters detected by Gaia as well as for four Galactic spiral arms for which shape and motion have also been recently modelled using Gaia data. We report on all the encounter candidates between HMXBs and clusters or spiral arms in the past 100 Myr. Results. In our sample of 26 HMXBs, we infer that seven were born in clusters and eight were born near a Galactic spiral arm, and we conclude that seven others could have formed isolated from these Galactic structures. The birthplaces of the remaining four HMXBs are still inconclusive due to a combination of great distance, poor astrometric data, and a lack of a known open cluster in the vicinity. We provide the kinematical age since the supernova of 15 HMXBs. Conclusions. The astrometry from Gaia and the orbit integration we employed are effective at finding the birthplaces of HMXBs in the Milky Way. By considering the biases in our data and method, we find it is likely that the progenitors of HMXBs preferentially formed alongside other massive stars in open clusters.