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The formation of close massive black-hole binaries is a challenge for binaryevolutionary models, especially the intriguing system M33 X-7 which harboursone of the most massive stellar-mass black holes (16 solar masses) orbiting a70 solar mass O-star every 3.5 days. In standard binary evolution theory anepisode of mass transfer or common envelope is inevitable in a binary with sucha small orbital period, which complicates the formation of a black hole withsuch a high mass.  To explain this system, we discuss a new binary evolution channel (De Mink etal. 2009), in which rotational mixing plays an important role. In very massiveclose binaries, tides force the rotation rate of the stars to be so high thatrotationally induced mixing becomes very efficient. Helium produced in thecenter is mixed throughout the envelope. Instead of expanding during theirmainsequence evolution (with the inevitable consequence of mass transfer),these stars stay compact, and avoid filling their Roche lobe. They graduallyevolve into massive helium stars. This scenario naturally leads to theformation of very massive black holes in a very close orbit with a less evolvedmassive companion such as M33 X-7.

A new evolutionary scenario for the formation of massive black-hole binaries such as M33 X-7 and IC 10 X-1