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Energy dependent ~100 μs time lags as observational evidence of Comptonization effects in the neutron star plasma environment

We present a Comptonization model for the observed properties of the energy-dependent soft/hard time lags and pulsed fraction (amplitude) associated with the pulsed emission of a neutron star (NS). We account for the soft lags by downscattering of hard X-ray photons in the relatively cold plasma of the disk or NS surface. A fraction of the soft X-ray photons coming from the disk or NS surface upscatter off hot electrons in the accretion column. This effect leads to hard lags as a result of thermal Comptonization of the soft photons. This model reproduces the observed soft and hard lags due to the down- and upscattered radiation as a function of the electron number densities of the reflector, n_{e}^{ref}, and the accretion column, n_{e}^{hot}. In the case of the accretion-powered millisecond pulsars IGR J00291+5934, XTE J1751-305, and SAX J1808.4-3658, the observed time lags agree well with the model. Soft lags are observed only if n_e^{ref} << n_e^{hot}. Scattering of the pulsed emission in the NS environment may account for the observed time lags as a non-monotonic function of energy. The time lag measurements can be used as a probe of the innermost parts of the NS and accretion disk. We determine the upper and lower limits of the density variation in this region using the observed time lags. The observed energy-dependent pulsed amplitude allows us to infer a variation of the Thomson optical depth of the Compton cloud in which the accretion column is embedded.