A Monte Carlo estimate for the fraction of thermal Comptonized photons that impinge back on the soft source in neutron star LMXBs

Abstract

In earlier works, it was shown that the energy dependent soft time lags observed in kHz QPOs of neutron star low mass X-ray binaries (LMXBs) can be explained as being due to Comptonization lags provided a significant fraction ($η\sim 0.2$ - $0.8$) of the Comptonized photons impinge back into the soft photon source. Here we use a Monte Carlo scheme to verify if such a fraction is viable or not. In particular we consider three different Comptonizing medium geometries: (i) a spherical shell, (ii) a boundary layer like torus and (iii) a corona on top of an accretion disk. Two set of spectral parameters corresponding to the 'hot' and 'cold' seed photon models were explored. The general result of the study is that for a wide range of sizes, the fraction lies within $η\sim 0.3$ - $0.7$, and hence compatible with the range required to explain the soft time lags. Since there is a large uncertainty in the range, we cannot concretely rule out any of the geometries or spectral models, but the analysis suggests that a boundary layer type geometry with a 'cold' seed spectral model is favoured over an accretion corona model. Better quality data will allow one to constrain the geometry more rigorously. Our results emphasise that there is significant heating of the soft photon source by the Comptonized photons and hence this effect needs to be taken into account for any detailed study of these sources.