Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Physics, 2007.Includes bibliographical references (p. 105-114).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). 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 zi measurements of this source into question), with typical upper limits of Jil < 2.5 x 10-14 Hz s-1 (2a). However, combining data from all the outbursts shows with high (6 a) significance that the pulsar is undergoing long-term spin down at a rate /i = (-5.6 ± 2.0) x 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 < 4.4 x 1036 g cm2 for the mass quadrupole moment. We also measured an orbital period derivative of Porb = (3.5 + 0.2) x 10-12 s s-1 We identify a strong anti-correlation between the fractional amplitude of the harmonic (r2) and the X-ray flux (fx) in the persistent pulsations of four sources: SAX J1808.4-3658, IGR J00291+5934, and XTE J1751-305, XTE J1807-294. These sources exhibit a powerlaw relationship r2 x( fx7 with slopes ranging from y = -0.47 to -0.70. The three other accreting millisecond pulsars that we analyzed, XTE J0929-314, XTE J1814-338, and HETE J1900.1-2455, do not as fully explore a wide range of fluxes, but they too seem to obey a similar relation. We argue that these trends may be evidence of the recession of the accretion disk as the outbursts dim. We examine the energy dependence of the persistent pulsations and thermonuclear burst oscillations from SAX J1808.4-3658.We confirm the soft phase lags previously discovered from this source, and we discover that these phase lags increase as the source flux decays slowly following its peak flux. When the source decay becomes rapid and the outburst enters its flaring tail stage, this relationship reverses, and the phase lags diminish as the flux dims further. This result, along with the pulse profile changes observed at the beginning of the flairing tail stage, suggests an abrupt change in the geometry of the accretion disk and column at this time in the outburst. In contrast, the thermonuclear burst oscillation timing does not show appreciable lags, and the burst oscillation phases and fractional amplitudes appear to be relatively independent of energy.by Jacob M. Hartman.Ph.D
