Differential Rotation in Weakly-Magnetized Neutron Star Atmospheres

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.