Patterns of energy-dependent variability from Comptonization

We study fractional variability as a function of energy from black hole X-ray binaries on time-scales from milliseconds to hundreds of seconds. We build a theoretical model of energy-dependent variability in which the X-ray energy spectrum varies in response to a changing physical parameter. We compare these models to rms spectra obtained from RXTE Proportional Counter Array (PCA) observations of black hole binaries XTE J1550-564 and XTE J1650-500. We show that two main variability models are consistent with the data: variable seed photon input in the hard state and variable power in the Comptonized component in the soft and very high states. The lack of clear reflection features in the rms spectra implies that the reflection and the X-ray continuum, when integrated over Fourier frequencies, are correlated and vary with similar fractional amplitudes. Our models predict two important features of rms spectra, not possible to be clearly seen by the PCA due sensitivity limits. At soft X-rays, less than or similar to 3 keV, we predict the presence of a break in the rms spectrum at energy directly related to the seed photon temperature. At higher energies, similar to 20-30 keV, we predict a peak in the rms spectrum originating from the variability of the spectrum produced by a hybrid thermal/non-thermal electron distribution. If these features are confirmed by broad-band observations, they will impose important constraints on the origin of the seed photons for Comptonization and the electron distribution in the hot plasma.