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We present a coherent timing analysis of the 2003 outburst of the accreting millisecond pulsar (AMXP) XTE J1807-294. We find a 95% confidence interval for the pulse frequency derivative of (+0.7, + 4.7) x 10-14 Hz s-1 and (-0.6, + 3.8) x 10-14 Hz s-1 for the fundamental and second harmonics, respectively. The sinusoidal fractional amplitudes of the pulsations are the highest observed among AMXPs and can reach values of up to 27% (2.5-30 keV). The pulse arrival time residuals of the fundamental frequency follow a linear anti-correlation with the fractional amplitudes that suggests hot spot motion both in longitude and latitude over the surface of the neutron star. An anti-correlation between residuals and X-ray flux suggests an influence of the accretion rate on pulse phase and casts doubts on the interpretation of pulse frequency derivatives in terms of changes of spin rates and torques on the neutron star.

The Rossi X-ray Timing Explorer has observed five outbursts from the transient 2.5 ms accretion-powered pulsar SAX J1808.4-3658 during 1998-2008. We present a pulse timing study of the most recent outburst and compare it with the previous timing solutions. The spin frequency of the source continues to decrease at a rate of (-5.5 +- 1.2) x 10-18 Hz s-1, which is consistent with the previously determined spin derivative. The spin down occurs mostly during quiescence, and is most likely due to the magnetic dipole torque from a B = 1.5 x 108 G dipolar field at the neutron star surface. We also find that the 2 hr binary orbital period is increasing at a rate of (3.80 +- 0.06) x 10-12 s s-1, also consistent with previous measurements. It remains uncertain whether this orbital change reflects secular evolution or short-term variability.

Soft phase lags, in which X-ray pulses in lower energy bands arrive later than pulses in higher energy bands, have been observed in nearly all accretion-powered millisecond pulsars, but their origin remains an open question. 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 the accretion rate. During the brightest stage of the outbursts from this source, the lags increase in magnitude as the accretion rate drops; when the outbursts enter their dimmer flaring-tail stage, the relationship reverses. We evaluate this 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 other invoking a two-component model for the photon emission. In both cases, the turnover suggests that we are observing the source transitioning into the "propeller" accretion regime.

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 n $˙{ν }$ measurements of this source into question), with typical upper limits of |n| [?] 2.5 x 10[?]14 $&vert; ˙{ν }&vert; &lesssim; 2.5 × 10⁻¹⁴$ Hz s[?]1 (2 s). However, combining data from all the outbursts shows with high (6 s) significance that the pulsar is undergoing long-term spin down at a rate n = ([?]5.6 +- 2.0) x 10[?]16 $˙{ν } = (− 5.6 ± 2.0) × 10⁻¹⁶$ 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 x 108 G for the pulsar's surface dipole magnetic field and Q/I < 5 x 10[?]9 for the fractional mass quadrupole moment. We also measured an orbital period derivative of Porb = (3.5 +- 0.2) x 10[?]12 $˙{P}_orb = (3.5 ± 0.2) × 10⁻¹²$ s s[?]1. This surprisingly large Porb $˙{P}_orb$ 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.

The accretion-powered millisecond pulsar IGR J00291+5934 underwent two [?]10 day long outbursts during 2008, separated by 30 days in quiescence. Such a short quiescent period between outbursts has never been seen before from a neutron star X-ray transient. X-ray pulsations at the 599 Hz spin frequency are detected throughout both outbursts. For the first time, we derive a pulse phase model that connects two outbursts, providing a long baseline for spin frequency measurement. Comparison with the frequency measured during the 2004 outburst of this source gives a spin-down during quiescence of -(4 +- 1) x 10-15 Hz s-1, approximately an order of magnitude larger than the long-term spin-down observed in the 401 Hz accretion-powered pulsar SAX J1808.4-3658. If this spin-down is due to magnetic dipole radiation, it requires a 2 x 108 G field strength, and its high spin-down luminosity may be detectable with the Fermi Large Area Telescope. Alternatively, this large spin-down could be produced by gravitational wave emission from a fractional mass quadrupole moment of Q/I = 1 x 10-9. The rapid succession of the outbursts also provides a unique test of models for accretion in low-mass X-ray binaries. Disk instability models generally predict that an outburst will leave the accretion disk too depleted to fuel a second outburst after such a brief quiescence. We suggest a modification in which the outburst is shut off by the onset of a propeller effect before the disk is depleted. This model can explain the short quiescence and the unusually slow rise of the light curve of the second 2008 outburst.