Understanding compact object formation and natal kicks. II. the case of XTEJ1118 + 480

In recent years, an increasing number of proper motions have been measured for Galactic X-ray binaries. When supplemented with accurate determinations of the component masses, orbital period, and donor effective temperature, these kinematical constraints harbor a wealth of information on the system's past evolution. Here, we consider all this available information to reconstruct the full evolutionary history of the black hole X-ray binary XTEJ1118 + 480, assuming that the system originated in the Galactic disk and the donor has solar metallicity. This analysis accounts for four evolutionary phases: mass transfer through the ongoing X-ray phase, tidal evolution before the onset of Roche lobe overflow, motion through the Galactic potential after the formation of the black hole, and binary orbital dynamics due to explosive mass loss and possibly a black hole natal kick at the time of core collapse. We find that right after black hole formation, the system consists of a ≃6.0-10.0 M black hole and a ≃1.0-1.6 M main-sequence star. We also find that that an asymmetric natal kick is not only plausible but required for the formation of this system, and derive a lower and upper limit on the black hole natal kick velocity magnitude of and , respectively.