Millisecond Oscillations During Thermonuclear X-ray Bursts
  I review the basic phenomenology and theory of the millisecond brightness oscillations observed during thermonuclear X-ray bursts from 13 of approximately 70 accreting neutron stars in low-mass X-ray binaries. Compelling observations indicate that the oscillations are produced by surface brightness patterns on the rapidly rotating neutron stars. However, it remains to be understood (1) why the brightness patterns producing them persist for up to 15 s during an X-ray burst, whereas the burning should cover the entire surface in less than 1 s, and (2) why the frequencies drift upward by about 5 Hz during the course of the burst. These peculiarities can probably be explained by taking into account the expansion of the surface layers caused by the burning, zonal flows that form due to pressure gradients between the equator and poles, and Rossby-Alfven modes that are excited in the surface ocean. Further progress toward understanding how burning progresses on the surface of the neutron star can be made with a next-generation X-ray timing mission, which would provide a larger sample of sources with oscillations, detect sideband signals produced by the spectrum of modes that should be excited in the neutron star ocean, and measure harmonic structure in the profiles of the oscillations. These observations would be crucial for measuring the distribution of the rotation rates of neutron stars, the progression of unstable nuclear burning in the accreted ocean, and the curvature of the space-time around the neutron star. 
Michael P. Muno