The Frequency Stability of Millisecond Oscillations in Thermonuclear   X-Ray Bursts
  We analyze the frequency evolution of millisecond oscillations observed during type I X-ray bursts with the Rossi X-ray Timing Explorer in order to establish the stability of the mechanism underlying the oscillations. Our sample contains 68 pulse trains detected in a search of 159 bursts from 8 accreting neutron stars. As a first step, we confirm that the oscillations usually drift upward in frequency by about 1% toward an apparent saturation frequency. Previously noted anomalies, such as drifts toward lower frequencies as the oscillations disappear (``spin-down'' episodes) and instances of two signals present simultaneously at frequencies separated by a few Hz, occur in 5% of oscillations. Having verified the generally accepted description of burst oscillations, we proceed to study the coherence of the oscillations during individual bursts, and the dispersion in the asymptotic frequencies in bursts observed over five years. On short time scales, we find that 30% of the oscillation trains do not appear to evolve smoothly in phase. This suggests either that two signals are present simultaneously with a frequency difference too small to resolve (< 1 Hz), that the frequency evolution is discontinuous, or that discrete phase jumps occur. On time scales of years, the maximum frequencies of the oscillations exhibit fractional dispersions of < 0.004. In the case of 4U 1636-536, this dispersion is uncorrelated with the known orbital phase, which indicates that a mechanism besides orbital Doppler shifts prevents the oscillations from appearing perfectly stable. We interpret these results under the assumption that the oscillations originate from anisotropies in the emission from the surfaces of these rotating neutron stars. (Abridged) 
Michael P. Muno, Deepto Chakrabarty, Duncan K. Galloway (MIT), and   Dimitrios Psaltis (IAS)