Soft Phase Lags of Pulsed Emission from the Millisecond X-Ray Pulsar SAX J1808.4–3658

We report the discovery of phase shifts between X-ray pulses at different energies in the newly discovered millisecond X-ray pulsar SAX J1808.4-3658. The results show that low-energy pulses lag high-energy pulses by as much as ~0.2 ms (or ~8% of the pulse period). The measurements were made in two different ways: (1) computing cross-power spectra between different energy bands, and (2) cross-correlating the folded pulse profiles in different energy bands; consistent results were obtained. We speculate that the observed soft lags might be related to the lateral expansion and subsequent cooling of a "hot spot" on the neutron star surface in which the pulsed X-ray emission originates. Also presented is the possibility of producing soft lags via Compton downscattering of hard X-ray photons from the hot spot in the cool surrounding atmosphere. We will discuss possible X-ray production mechanisms for SAX J1808.4-3658 and constraints on the emission environment, based on the observed soft lags, pulse profiles, and energy spectrum.