Correlated spectral and recurrence variations of Cygnus X-1

We present results of recurrence analysis of the black hole X-ray binary Cygnus X-1 using combined observations from the Rossi X-ray Timing Explorer All-sky Monitor and the Japanese Monitor of All-sky X-ray Image aboard the International Space Station. From the time-dependent windowed recurrence plot (RP), we compute 10 recurrence quantities that describe the dynamical behaviour of the source and compare them to the spectral state at each point in time. We identify epochs of state changes corresponding to transitions into highly deterministic or highly stochastic dynamical regimes and their correlation to specific spectral states. We compare k-Nearest Neighbors and Random Forest models for various sizes of the time-dependent RP. The spectral state in Cygnus X-1 can be predicted with greater than 95 per cent accuracy for both types of models explored across a range of RP sizes based solely on the recurrence properties. The primary features from the RP that distinguish between spectral states are the determinism, Shannon entropy, and average line length, all of which are systematically higher in the hard state compared to the soft state. Our results suggest that the hard and soft states of Cygnus X-1 exhibit distinct dynamical variability and the time domain alone can be used for spectral state classification.