Turbulent Mixing in the Surface Layers of Accreting Neutron Stars

During accretion a neutron star (NS) is spun up as angular momentum is transported through its surface layers. We study the resulting differentially rotating profile, focusing on the impact this has for type I X-ray bursts. The predominant viscosity is likely provided by the Tayler-Spruit dynamo, where toroidal magnetic field growth and Tayler instabilities balance to support a steady-state magnetic field. The radial and azimuthal components have strengths of ∼ 105 G and ∼ 1010 G, respectively. This field provides a Maxwell stress on the shearing surface layers, which leads to nearly uniform rotation at the depths of interest for X-ray bursts (near densities of ≈ 106 g cm−3). A remaining small shear transmits the accreted angular momentum inward to the NS interior. Though this shear gives little viscous heating, it can trigger turbulent mixing. Detailed simulations will be required to fully understand the consequences of mixing, but our models illustrate some general features. Mixing has the greatest impact when the buoyancy at the compositional discontinuity between accreted matter and ashes is overcome. This occurs at high accretion rates, at low spin frequencies (when the spin is small, the relative speed of the accreted material is larger), or may depend on the ashes from the previous burst. We then find two new regimes of burning. The first is ignition in a layer containing a mixture of heavier elements 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 the short recurrence time of some bursts, but incomplete burning is still needed to explain these bursts’ energetics. When mixing is sufficiently strong, a second regime is found where accreted helium mixes deep enough to burn stably, quenching X-ray bursts. We speculate that the observed change in X-ray burst properties near one-tenth the Eddington accretion rate is from this mechanism. The carbon-rich material produced by stable helium burning would be important for triggering and fueling superbursts. Subject headings: accretion, accretion disks — stars: magnetic fields — stars: neutron — X-rays: bursts — X-rays: stars