Constraining the size of the Comptonizing medium by modelling the energy-dependent time lags of kHz QPOs of neutron star system

Abstract

We study the dependence of the estimated size and geometry of the medium on the timeaveraged spectral model assumed and on the frequency of the kHz quasi-periodic oscillation (QPO) in the framework of a thermal Comptonization model.We use the high-quality time lag and rms obtained during 1996 March 3 observation of 4U 1608-52 by RXTE as well as other observations of the source at different QPO frequencies where a single time lag between two broad energy bands has been reported. We compare the results obtained when assuming that the time-averaged spectra are represented by the spectrally degenerate 'hot (kTb ≥ 1 keV)' and 'cold (kTb ≤ 0.5 keV)' seed spectral models where Tb is seed source temperature.We find that for the 'hot-seed' model the medium size is in the range of 0.3-2.0 km and the size decreases with increasing QPO frequency. On the other hand, for the 'cold-seed' model, the range for the sizes is much larger 0.5-20 km and hence perhaps show no variation with QPO frequency. Our results emphasize the need for broad-band spectral information combined with high-frequency timing to lift this degeneracy.We further compare the rms as a function of energy for the upper kHz QPO, and indeed we find that the driver for this QPO should be temperature variations of the corona identical to the lower kHz QPO. However, the time lag reported for the upper kHz QPO is hard, which if confirmed would challenge the simple Comptonization model presented here.