2008ApJ...675.1468H

We present a 7 yr timing study of the 2.5 ms X-ray pulsar SAX J1808.4-3658, an X-ray transient with a recurrence time of ~2 yr, using data from the Rossi X-Ray Timing Explorer covering four transient outbursts (1998-2005). We verify that the 401 Hz pulsation traces the spin frequency fundamental and not a harmonic. Substantial pulse shape variability, both stochastic and systematic, was observed during each outburst. Analysis of the systematic pulse shape changes suggests that, as an outburst dims, the X-ray ``hot spot'' on the pulsar surface drifts longitudinally and a second hot spot may appear. The overall pulse shape variability limits the ability to measure spin frequency evolution within a given X-ray outburst (and calls previous ν{dot} measurements of this source into question), with typical upper limits of|ν{dot}|≲2.5x10^–14 Hz/s (2 σ). However, combining data from all the outbursts shows with high (6 σ) significance that the pulsar is undergoing long-term spin down at a rate ν{dot}=(-5.6±2.0)x10^–16 Hz/s, with most of the spin evolution occurring during X-ray quiescence. We discuss the possible contributions of magnetic propeller torques, magnetic dipole radiation, and gravitational radiation to the measured spin down, setting an upper limit of B<1.5x10⁸ G for the pulsar's surface dipole magnetic field and Q/I<5x10^–9 for the fractional mass quadrupole moment. We also measured an orbital period derivative of P{dot}_orb=(3.5±0.2)x10^–12 s/s. This surprisingly large P{dot}_orb is reminiscent of the large and quasi-cyclic orbital period variation observed in the so-called black widow millisecond radio pulsars, which further strengthens previous speculation that SAX J1808.4-3658 may turn on as a radio pulsar during quiescence. In an appendix we derive an improved (0.15") source position from optical data.