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Soft phase lags, in which X-ray pulses in lower energy bands arrive laterthan pulses in higher energy bands, have been observed in nearly allaccretion-powered millisecond pulsars, but their origin remains an openquestion. In a study of the 2.5 ms accretion-powered pulsar SAX J1808.4-3658,we report that the magnitude of these lags is strongly dependent on theaccretion rate. During the brightest stage of the outbursts from this source,the lags increase in magnitude as the accretion rate drops; when the outburstsenter their dimmer flaring-tail stage, the relationship reverses. We evaluatethis complex dependence in the context of two theoretical models for the lags,one relying on the scattering of photons by the accretion disk and the otherinvoking a two-component model for the photon emission. In both cases, theturnover suggests that we are observing the source transitioning into the"propeller" accretion regime.

The Luminosity and Energy Dependence of Pulse Phase Lags in the Accretion-powered Millisecond Pulsar SAX J1808.4-3658