The Formation of Rapidly Rotating Black Holes in High Mass X-ray Binaries

High mass X-ray binaries (HMXRBs) like Cygnus X-1, host some of the most rapidly spinning black holes (BHs) known to date, reaching spin parameters $a \gtrsim 0.84$. However, there are several effects that can severely limit the maximum BH spin parameter that could be obtained from direct collapse, such as tidal synchronization, magnetic core-envelope coupling and mass loss. Here we propose an alternative scenario where the BH is produced by a {\it failed} supernova (SN) explosion that is unable to unbind the stellar progenitor. A large amount of fallback material ensues, whose interaction with the secondary naturally increases its overall angular momentum content, and therefore, the spin of the BH when accreted. Through SPH hydrodynamic simulations, we studied the unsuccessful explosion of a $8M_{\odot }$ pre-SN star in a close binary with a $12M_{\odot}$ companion with an orbital period of $\approx1.2$ days, finding that it is possible to obtain a BH with a high spin parameter $a\gtrsim0.8$ even when the expected spin parameter from direct collapse is $a \lesssim 0.3$. This scenario also naturally explains the atmospheric metal pollution observed in HMXRB stellar companions.