Understanding compact object formation and natal kicks. IV. the case of IC 10 X-1

The extragalactic X-ray binary IC 10 X-1 has attracted attention as it is possibly the host of the most massive stellar-mass black-hole (BH) known to date. Here we consider all available observational constraints and construct its evolutionary history up to the instant just before the formation of the BH. Our analysis accounts for the simplest possible history, which includes three evolutionary phases: binary orbital dynamics at core collapse, common envelope (CE) evolution, and evolution of the BH-helium star binary progenitor of the observed system. We derive the complete set of constraints on the progenitor system at various evolutionary stages. Specifically, right before the core collapse event, we find the mass of the BH immediate progenitor to be ≳ 31 M_̇ (at 95% of confidence, same hereafter). The magnitude of the natal kick imparted to the BH is constrained to be ≲ 130 km s^-1. Furthermore, we find that the "enthalpy" formalism recently suggested by Ivanova & Chaichenets is able to explain the existence of IC 10 X-1 without the need to invoke unreasonably high CE efficiencies. With this physically motivated formalism, we find that the CE efficiency required to explain the system is in the range of ≃ 0.6-1.