  Following the recent abundance measurements of Mg, Al, Ca, Fe, and Ni in the
black hole X-ray binary XTE J1118+480 using medium-resolution Keck II/ESI
spectra of the secondary star (Gonz\'alez Hern\'andez et al. 2006), we perform
a detailed abundance analysis including the abundances of Si and Ti. These
element abundances, higher than solar, indicate that the black hole in this
system formed in a supernova event, whose nucleosynthetic products could
pollute the atmosphere of the secondary star, providing clues on the possible
formation region of the system, either Galactic halo, thick disk, or thin disk.
We explore a grid of explosion models with different He core masses,
metallicities, and geometries. Metal-poor models associated with a formation
scenario in the Galactic halo provide unacceptable fits to the observed
abundances, allowing us to reject a halo origin for this X-ray binary. The
thick-disk scenario produces better fits, although they require substantial
fallback and very efficient mixing processes between the inner layers of the
explosion and the ejecta, making quite unlikely an origin in the thick disk.
The best agreement between the model predictions and the observed abundances is
obtained for metal-rich progenitor models. In particular, non-spherically
symmetric models are able to explain, without strong assumptions of extensive
fallback and mixing, the observed abundances. Moreover, asymmetric mass
ejection in a supernova explosion could account for the required impulse
necessary to launch the system from its formation region in the Galactic thin
disk to its current halo orbit.
