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 millisecond 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 time scales and strongly constrains emission models proposed to explain Fourier-frequency-dependent time lags. We present autocorrelation functions at different energies, and note their widths decrease with increasing energy. We show that the extended Compton corona model produces auto-correlation functions whose widths increase with increasing energy, 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.