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In Gou et al. (2011), we reported that the black hole primary in the X-raybinary Cygnus X-1 is a near-extreme Kerr black hole with a spin parametera*>0.95(3{\sigma}). We confirm this result while setting a new and morestringent limit: a*>0.983 at the 3{\sigma}(99.7%) level of confidence. Theearlier work, which was based on an analysis of all three useful spectra thatwere then available, was possibly biased by the presence in these spectra of arelatively strong Compton power-law component: The fraction of the thermal seedphotons scattered into the power law was f_s=23-31%, while the upper limit forreliable application of the continuum-fitting method is f_s<25%. We havesubsequently obtained six additional spectra of Cygnus X-1 suitable for themeasurement of spin. Five of these spectra are of high quality with f_s in therange 10% to 19%, a regime where the continuum-fitting method has been shown todeliver reliable results. Individually, the six spectra give lower limits onthe spin parameter that range from a*>0.95 to a*>0.98, allowing us toconservatively conclude that the spin of the black hole is a*>0.983(3{\sigma}).

Confirmation Via the Continuum-Fitting Method that the Spin of the Black Hole in Cygnus X-1 is Extreme