The X-ray source M33 X-7 in the nearby galaxy Messier 33 is among the most massive X-ray binary stellar systems known, hosting a rapidly spinning, 15.65M ™ black hole orbiting an underluminous, 70M ™ main-sequence companion in a slightly eccentric 3.45-day orbit (M ™, solar mass). Although post-main-sequence mass transfer explains the masses and tight orbit, it leaves unexplained the observed X-ray luminosity, the star's underluminosity, the black hole's spin and the orbital eccentricity. A common envelope phase, or rotational mixing, could explain the orbit, but the former would lead to a merger and the latter to an overluminous companion. A merger would also ensue if mass transfer to the black hole were invoked for its spin-up. Here we report simulations of evolutionary tracks which reveal that if M33 X-7 started as a primary body of 85M ™ 99M ™ and a secondary body of 28M ™ 32M ™, in a 2.8 3.1-d orbit, its observed properties can be consistently explained. In this model, the main-sequence primary transfers part of its envelope to the secondary and loses the rest in a wind; it ends its life as a 1/416M ™ helium star with an irong-nickel core that collapses to a black hole (with or without an accompanying supernova). The release of binding energy, and possibly collapse asymmetries, kickg ™ the nascent black hole into an eccentric orbit. Wind accretion explains the X-ray luminosity, and the black-hole spin can be natal.
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