The Long-Term Evolution of the Spin, Pulse Shape, and Orbit of the Accretion-powered Millisecond Pulsar SAX J1808.4-3658

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 dot nu measurements of this source into question), with typical upper limits of |dot nu| <~ 2.5 × 10^-14 Hz s^-1 (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 dot nu = (-5.6 +/- 2.0) × 10^-16 Hz s^-1, 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 < 1.5 × 10⁸ G for the pulsar's surface dipole magnetic field and Q/I < 5 × 10^-9 for the fractional mass quadrupole moment. We also measured an orbital period derivative of dot P_orb = (3.5 +/- 0.2) × 10^-12 s s^-1. This surprisingly large dot P_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.