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 4 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 ν̇ measurements of this source into question), with typical upper limits of |ν̇| . 2.5 × 10 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 ν̇ = (−5.6± 2.0)× 10 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 < 1.5 × 10 G for the pulsar’s surface dipole magnetic field and Q/I < 5 × 10 for the fractional mass quadrupole moment. We also measured an orbital period derivative of Ṗorb = (3.5 ± 0.2) × 10 s s. This surprising large Ṗorb is reminiscent of the large and quasi-cyclic orbital period variation observed in the so-called “black widow” millisecond radio pulsars. This 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 arcsec) source position from optical data. Subject headings: stars: individual (SAX J1808.4−3658) — stars: neutron — X-rays: stars