Relativistic effects in the pulse profile of the 2.5 millisecond X-ray pulsar SAX J1808.4-3658

I analyze the properties of the pulsed emission from the accreting millisecond pulsar SAX J1808.4-3658 in observations of its 1998 April outburst by the Rossi X-Ray Timing Explorer. Pulse phase spectroscopy shows that the emission evolves from a hard spectrum (power law with photon index of 2.39 +/- 0.06) to a soft spectrum (index of 3.39 +/- 0.24). This softening is also observable as a phase lag in the fundamental of low-energy photons with respect to high-energy photons. I show that this lag is roughly constant over 10 days of the outburst. I fit these data with a model in which the pulse emission is from a hot spot on the rotating neutron star and the flux as a function of phase is determined in a calculation which includes the effects of general relativity. The energy-dependent lags are very well described by this model. The harder spectra at earlier phases (i.e., as the spot approaches) are the result of larger Doppler-boosting factors that are important for this fast pulsar. Since this model is sensitive to the equatorial speed as an independent parameter and since the spin frequency is known, this offers us a new means of measuring the neutron star radius, which is notoriously difficult to determine.