Black hole spin of Cygnus X-1 determined from the softest state ever observed.

We show the softest ever spectrum from Cyg X-1, detected in 2013 with Suzaku. This has the weakest high-energy Compton tail ever seen from this object, so should give the cleanest view of the underlying disk spectrum, and hence the best determination of black hole spin from disk continuum fitting. Using the standard model of a disk with simple non-thermal Comptonization to produce the weak high-energy tail gives a high-spin black hole. However, we get a significantly better fit by including an additional, low-temperature thermal Comptonization component, which allows a much lower black hole spin. Corroboration of the existence of an additional Compton component comes from the frequency-dependent hard lags seen in the rapid variability in archival high/soft state data. These cannot be explained if the continuum is a single non-thermal Comptonization component, but are instead consistent with a radially stratified, multi-zone Comptonization spectrum, where the spectrum is softer further from the black hole. A complex multi-zone Comptonization continuum is required to explain both spectra and timing together, and this has an impact on the derived black hole spin