The atmospheres of weakly-magnetized neutron stars expand hydrostatically and
rotate differentially during thermonuclear X-ray bursts. Differential rotation
is probably related to the frequency drifts of millisecond burst oscillations
exhibited by about a dozen nuclear-powered X-ray pulsars. Here, we analyze the
linear stability of this differential rotation with respect to local,
axisymmetric, multi-diffusive MHD perturbations, at various heights in the
neutron star atmosphere. Unstable magneto-rotational modes are identified from
within to well above the burning layers. Properties of the fastest growing
modes depend sensitively on the local magnetic field geometry. Linear estimates
suggest that momentum transport due to magneto-rotational instabilities can
affect atmospheric rotation profiles on time-scales relevant to burst
oscillations. This transport would likely strengthen the coherence of burst
oscillations and contribute to their drifts.Comment: 11 pages, 6 figures, 2 tables, accepted for publication in MNRA