Surface Modes on Bursting Neutron Stars and X-ray Burst Oscillations

Accreting neutron stars (NSs) often show coherent modulations during type I X-ray bursts, called burst oscillations. We consider whether a nonradial mode can serve as an explanation for burst oscillations from those NSs which are not magnetic. We find that a surface wave in the shallow burning layer transitions into a crustal interface wave as the envelope cools, a new and previously uninvestigated phenomenon. The surface modulations decrease dramatically as the mode switches, explaining why burst oscillations often disappear before burst cooling ceases. When we include rotational modifications, we find mode frequencies and drifts consistent with those observed. The large NS spin ($\approx270-620 {\rm Hz}$) needed to make this match implies that accreting NSs are spinning at frequencies $\approx4 {\rm Hz}$ above the burst oscillation. Since the asymptotic frequency is set by the crustal interface wave, the observed late time frequency drifts are a probe of the composition and temperature of NS crusts. We compare our model with the observed drifts and persistent luminosities of X-ray burst sources, and find that NSs with a higher average accretion rate show smaller drifts, as we predict. Furthermore, the drift sizes are consistent with crusts composed of iron-like nuclei, as expected for the ashes of the He-rich bursts that are exhibited by these objects.