Latitudinal shear instabilities during type I X-ray bursts

Coherent oscillations have been observed during thermonuclear (type I) X-ray bursts from 14 accreting neutron stars in low-mass X-ray binaries, providing important information about their spin frequencies. However, the origin of the brightness asymmetry on the neutron star surface producing these oscillations is still not understood. We study the stability of a zonal shearing flow on the neutron star surface using a shallow-water model. We show that differential rotation of >= 2% between the pole and equator, with the equator spinning faster than the poles, is unstable to hydrodynamic shear instabilities. The unstable eigenmodes have a low azimuthal wavenumber m, wave speeds 1% or 2% below the equatorial spin rate, and e-folding times <= 1 s. Instability is related to low-frequency, buoyantly driven r-modes that have a mode frequency within the range of rotation frequencies in the differentially rotating shell. In addition, a modified Rayleigh's criterion based on potential vorticity rather than vorticity must be satisfied. The eigen-functions of the unstable modes have the largest amplitudes nearer to the rotational pole than the equator. We discuss the implications for burst oscillations. Growth of shear instabilities may explain the brightness asymmetry in the tails of X-ray bursts. However, some fine-tuning of the level of differential rotation and a spin frequency near 300 Hz are required in order for the fastest growing mode to have m = 1. If shear instabilities are to operate during a burst, temperature contrasts of >= 30% across the star must be created during ignition and spreading of the flash. The frequency drift may be related to the nonlinear development of the instability as well as the cooling of the burning layer. The properties and observability of the unstable modes vary strongly with neutron star rotation frequency.