Energy dependent time delays of kHz oscillations due to thermal Comptonization

Abstract

We study the energy dependent photon variability from a thermal Comptonizing plasma that is oscillating at kHz frequencies. In particular, we solve the linearized time-dependent Kompaneets equation and consider the oscillatory perturbation to be either in the soft photon source or in the heating rate of the plasma. For each case, we self consistently consider the energy balance of the plasma and the soft photon source. The model incorporates the possibility of a fraction of the Comptonized photons impinging back into the soft photon source. We find that when the oscillation is due to the soft photon source, the variation of the fractional root mean sqaure (rms) is nearly constant with energy and the time-lags are hard. However, for the case when the oscillation is due to variation in the heating rate of the corona, and when a significant fraction of the photons impinge back into the soft photon source, the rms increases with energy and the time-lags are soft. As an example, we compare the results with the ∼850 Hz oscillation observed on 1996 March 3 for 4U 1608−52 and show that both the observed soft time-lags as well as the rms versus energy can be well described by such a model where the size of the Comptonizing plasma is ∼1 km. Thus, modelling of the time-lags as due to Comptonization delays, can provide tight constraints on the size and geometry of the system. Detailed analysis would require well-constrained spectral parameters.