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Gou et al., "The Extreme Spin of the Black Hole in Cygnus X-1," http://arxiv.org/abs/1106.3690
Pretty cool. I'd been under the mistaken impression that real black holes were unlikely to be near the limiting spin.
The compact primary in the X-ray binary Cygnus X-1 was the first black hole to be established via dynamical observations. We have recently determined accurate values for its mass and distance, and for the orbital inclination angle of the binary. Building on these results, which are based on our favored (asynchronous) dynamical model, we have measured the radius of the inner edge of the black hole's accretion disk by fitting its thermal continuum spectrum to a fully relativistic model of a thin accretion disk. Assuming that the spin axis of the black hole is aligned with the orbital angular momentum vector, we have determined that Cygnus X-1 contains a near-extreme Kerr black hole with a spin parameter a/M>0.97 (3 \sigma). For a less probable (synchronous) dynamical model, we find a/M>0.91 (3 \sigma). Our results take into account all significant sources of observational and model-parameter uncertainties, which are dominated by the uncertainties in black hole mass, orbital inclination angle and distance. The uncertainties introduced by the thin-disk model we employ are particularly small in this case, given the disk's low luminosity (L/L_{Edd} \approx 0.02).
Pretty cool. I'd been under the mistaken impression that real black holes were unlikely to be near the limiting spin.