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During accretion a neutron star (NS) is spun up as angular momentum istransported through its surface layers. We study the resulting differentiallyrotating profile, focusing on the impact this has for type I X-ray bursts. Thepredominant viscosity is likely provided by the Tayler-Spruit dynamo. Theradial and azimuthal magnetic field components have strengths of ~10^5 G and~10^10 G, respectively. This leads to nearly uniform rotation at the depths ofinterest for X-ray bursts. A remaining small shear transmits the accretedangular momentum inward to the NS interior. Though this shear gives littleviscous heating, it can trigger turbulent mixing. Detailed simulations will berequired to fully understand the consequences of mixing, but our modelsillustrate some general features. Mixing has the greatest impact when thebuoyancy at the compositional discontinuity between accreted matter and ashesis overcome. This occurs at high accretion rates, at low spin frequencies, ormay depend on the ashes from the previous burst. We then find two new regimesof burning. The first is ignition in a layer containing a mixture of heavierelements from the ashes. If ignition occurs at the base of the mixed layer,recurrence times as short as ~5-30 minutes are possible. This may explain theshort recurrence time of some bursts, but incomplete burning is still needed toexplain these bursts' energetics. When mixing is sufficiently strong, a secondregime is found where accreted helium mixes deep enough to burn stably,quenching X-ray bursts. We speculate that the observed change in X-ray burstproperties near one-tenth the Eddington accretion rate is from this mechanism.The carbon-rich material produced by stable helium burning would be importantfor triggering and fueling superbursts. (abridged)

Turbulent Mixing in the Surface Layers of Accreting Neutron Stars