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

In earlier works, we had shown that the observed soft lags and r.m.s versus energy of the lower kHz QPO of neutron star binaries can be explained in the framework of a thermal Comptonization model. It was also shown that such an interpretation can provide estimates of the size and geometry of the Comptonizing medium. Here we study the dependence of these estimates on the time-averaged spectral model assumed and on the frequency of the QPO. We use the high quality time lag and r.m.s obtained during March 3rd 1996 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 have been reported. We compare the results obtained when assuming that the time-averaged spectra are represented by the spectrally degenerate "hot" and "cold" seed photon spectral models. We find that for the "hot" seed photon model the medium size is in the range of 0.3-2.0 kms and the size decreases with increasing QPO frequency. On the other hand for the "cold" seed photon model the range for the sizes are much larger 0.5-20 kms and hence perhaps show no variation with QPO frequency. Our results emphasis the need for broad band spectral information combined with high frequency timing to lift this degeneracy. We further show that the r.m.s as a function of energy for the upper kHz QPO is similar to the lower one 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. It would perhaps imply that reverberation lags are also important and/or the dominate spectral component is not a single temperature medium but a multi-temperature complex one.