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Fig. 4.

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Narrow window in the parameter space for the SMT channel converging to a well-defined narrow range of final orbits regardless of uncertainties in binary physics. We plot the orbital periods of BBH merger progenitors from before the mass transfer (BH+O-star stage, left) and after the SMT phase has taken place (BH+He-star stage, right). The figure is based on grids of detailed binary models with MBH; 1 = 10 M and varying assumptions on the orbital shrinkage during mass transfer (i.e., γ values, shown in different colors). Changing the assumption on γ significantly shifts the pre-SMT periods of BBH merger progenitors, but has little effect on the post-interaction orbits at the BH+He-star stage (or the properties of BBH mergers). The dashed red line shows the lower limit on the period of a BH+He-star systems, such that the naked helium star does not overflow its Roche lobe. We mark the periods and mass ratios of the known BH+OB-star systems (left panel, including supergiant high mass X-ray binaries) and of BH+Wolf-Rayet X-ray binaries (right). Cyg X-3 cannot be reproduced by SMT in our models, suggesting its origin in CE evolution.

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