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The need for hypercritical accretion in massive black-hole binaries with large Kerr parameters

Recent measurements of the Kerr parameters of the black holes in M33 X-7 and LMC X-1 yield a*=0.84\pm0.05 and a*=0.90^{+.04}_{-.09} respectively. We study massive binary evolution scenarios that can reproduce such high values for the Kerr parameters. We first discuss a model with Case C mass transfer leading to a common envelope and tidal synchronization of the primary before it collapses into a black hole. We also study a Case M evolution model (which involves tidally-locked, rotationally-mixed, chemically-homogeneous stars in a close binary). Our analysis suggests that, regardless of the specific scenario, the observed Kerr parameters for the black holes in M33 X-7 and LMC X-1 had to be obtained through hypercritical mass accretion.