The Physics of X-ray Emission from Accreting Millisecond Pulsars

By analyzing the Rossi X-ray Timing Explorer data on SAX J1808.4-3658 we show that the X-ray emission in accretion powered millisecond pulsars can be produced by Comptonization in a hot slab (radiative shock) of Thomson optical depth tau~1 at the neutron star surface. The escaping radiation consists of two components: a black body and a hard Comptonized tail. These components have very different angular distribution: the black body peaks along the slab normal (a ``pencil''--like emission pattern), while the tail has a broader angular distribution (a ``fan''--like pattern). This results in very different variability properties. We construct a detailed model of the X-ray production accounting for the Doppler boosting, relativistic aberration and gravitational light bending. We are able to reproduce the pulse profiles at different energies, corresponding phase lags, as well as the time-averaged spectrum. We obtain constraints on the neutron star radius: R~11 km if its mass M=1.6 Msun, and R~8.5 km if M=1.4 M_sun. We present simple analytical formulae for computing the light curves and oscillation amplitudes expected from hot spots in X-ray bursters and accretion powered millisecond pulsars. We also propose an analytical expression that can be used to determine the size of the black body emission region from the observed properties.