Star-formation history and X-ray binary populations: the case of the
  Large Magellanic Cloud
  In the present work we investigate the link between high-mass X-ray binaries
(HMXBs) and star formation in the Large Magellanic Cloud (LMC), our nearest
star-forming galaxy. Using optical photometric data, we identify the most
likely counterpart of 44 X-ray sources. Among the 40 HMXBs classified in this
work, we find 33 Be/X-ray binaries, and 4 supergiant XRBs. Using this census
and the published spatially resolved star-formation history map of the LMC, we
find that the HMXBs (and as expected the X-ray pulsars) are present in regions
with star-formation bursts $\sim$6-25 Myr ago, in contrast to the Small
Magellanic Cloud (SMC), for which this population peaks at later ages
($\sim$25-60 Myr ago). We also estimate the HMXB production rate to be equal to
1 system per $\sim43.5\times10^{-3}$ Mo/yr, or 1 system per $\sim$143 Mo of
stars formed during the associated star-formation episode. Therefore, the
formation efficiency of HMXBs in the LMC is $\sim$17 times lower than that in
the SMC. We attribute this difference primarily in the different ages and
metallicity of the HMXB populations in the two galaxies. We also set limits on
the kicks imparted on the neutron star during the supernova explosion. We find
that the time elapsed since the supernova kick is $\sim$3 times shorter in the
LMC than the SMC. This in combination with the average offsets of the HMXBs
from their nearest star clusters results in $\sim$4 times faster transverse
velocities for HMXBs in the LMC than in the SMC.
