On the nature of the X-ray emission from the accreting millisecond pulsar SAX J1808.4-3658

We study the pulse profiles of the accreting X-ray millisecond pulsar SAX J1808.4-3658 at different energies. The two main emission components, the blackbody and the Comptonized tail, which are clearly identified in the time-averaged spectrum, show strong variability with the first component lagging the second one. The observed variability can be explained if the emission is produced by Comptonization in a hot slab (radiative shock) of Thomson optical depth similar to0.3-1 at the neutron star surface. The blackbody radiation is strongly beamed along the normal to the slab (a 'knife'-like or 'pencil'-like emission pattern), while the Comptonized emission has a broader angular distribution peaking at about 50degrees-60degrees from the slab normal (a 'fan'-like pattern). We construct a detailed model of the X-ray production accounting for the Doppler boosting, relativistic aberration and gravitational light bending in the Schwarzschild space-time. We present also accurate analytical formulae for computations of the light curves from rapidly rotating neutron stars using the formalism recently developed by Beloborodov. Our model reproduces well the pulse profiles at different energies simultaneously, corresponding phase lags, as well as the time-averaged spectrum. We constrain the compact star mass to be bounded between 1.2 and 1.6 M-circle dot. By fitting the observed profiles, we determine the radius of the compact object to be R similar to 11 km if M = 1.6 M-circle dot, while for M = 1.2 M-circle dot the best-fitting radius is similar to6.5 km, indicating that the compact object in SAX J1808.4-3658 can be a strange star. We obtain a lower limit on the inclination of the system of 65degrees.