Why is it difficult to detect a millisecond pulsar in neutron star X-ray binaries?

We explain why it is possible to detect directly X-ray emission from near the surface of the neutron star (NS) in SAX J1808.4-3658 but not in most other low-mass X-ray binaries (LMXBs), with the exception that emission from the surface can be seen during burst events. We show that the X-ray emission from SAX J1808.4-3658 mostly originates in the Comptonization process in a relatively optically thin hot region (with an optical depth tau(0) around 4 and temperature around 20 keV). Such a transparent region does not prevent us from detecting coherent X-ray pulsation due to hot spots on the NS surface. We give a precise model for the loss of modulation: such suppression of the quasi-periodic oscillation (QPO) amplitude due to scattering can explain the disappearance of kilohertz QPOs with increasing QPO frequency. We also formulate general conditions under which the millisecond X-ray pulsation can be detected in LMXBs. We demonstrate that the observed soft phase lag of the pulsed emission is a result of the downscattering of the hard X-ray photons in the relatively cold material near the NS surface. In the framework of this downscattering model, we propose a method to determine the atmosphere density in that region from soft-lag measurements.