Time domain analysis of variability in Cygnus X-1: Constraints on the emission models

We use time domain analysis techniques to investigate the rapid variability of Cygnus X-1. We show that the cross-correlation functions between hard and soft energy bands reach values very close to unity and peak at a lag of less than 2 ms for energies separated by a factor of 10. This confirms that the process that produces X-ray photons at different energies is extremely coherent on short timescales and strongly constrains emission models proposed to explain Fourier-frequency - dependent time lags. We present autocorrelation functions at different energies and note that their widths decrease with increasing energy. We show that the extended Compton corona model produces autocorrelation functions whose widths increase with increasing energy and that the model of cylindrical waves moving inward through a transition disk has too large a peak lag in the cross-correlation function. Models of magnetic flaring and of drifting blobs in a hot corona can qualitatively fit the observations.