Energy Dependent Time Delays of kHz Oscillations due to Thermal Comptonization

TL;DR

This paper models energy-dependent time delays in kHz oscillations caused by thermal Comptonization, revealing how different oscillation sources affect observed variability and constraining the size of the plasma region.

Contribution

It introduces a self-consistent model for energy-dependent variability in Comptonizing plasmas, considering oscillations in soft photon sources and heating rates, and compares predictions with observations.

Findings

Time lags depend on the oscillation source and photon back-impingement.

The model explains observed soft time-lags and r.m.s energy dependence.

Constraints on plasma size (~1 km) are derived from the model.

Abstract

We study the energy dependent photon variability from a thermal Comptonizing plasma that is oscillating at kHz frequencies. In particular, we solve the linearised 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 (r.m.s) 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 r.m.s increases with energy and the time lags are soft. As an example, we compare the results with the $\sim 850$ Hz oscillation observed on March 3, 1996 for 4U 1608-52 and show that both the observed soft time-lags as well as the r.m.s versus energy can be well described by such a model where the size of the Comptonizing plasma is $\sim 1$ 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.