Fig. 9.

Relation between the tidal synchronization timescale in a BH-WR binary and the delay time (between the formation and the merger) of the corresponding BBH system plotted for several different mass ratios q = MWR/MBH, using Eq. (14) from Kushnir et al. (2016). Tidal interactions can efficiently spin-up the WR star only if the synchronization timescale is shorter than the BH-WR binary lifetime tBH-WR. The two dashed horizontal lines mark two different values of tBH-WR: roughly the maximum WR lifetime ∼ 3 × 105 yr, assumed by several authors (e.g., Kushnir et al. 2016; Hotokezaka & Piran 2017a; Piran & Hotokezaka 2018), and a significantly smaller value tBH-WR = 3 × 103 yr which is more realistic in the case of the CE channel at low metallicity.
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