X-Ray Variability Coherence: How to Compute It, What It Means, and How It Constrains Models of GX 339-4 and Cygnus X-1

We describe how the coherence function—a Fourier frequency–dependent measure of the linear correlation between time series measured simultaneously in two energy channels—can be used in conjunction with energy spectra, power spectra, and time delays between energy channels to constrain models of the spectrum and variability of X-ray binaries. Here we present a procedure for estimating the coherence function in the presence of counting noise. We apply this method to the black hole candidates Cyg X-1 and GX 33924 and find that the near-perfect coherence between low- and high-energy X-ray photons rules out a wide range of models that postulate spatially extended fluctuating emission, thermal flares, and overlapping shot noise.