Propagation of thermonuclear flames on rapidly rotating neutron stars: Extreme weather during type I X-ray bursts

We analyze the global hydrodynamic flow in the ocean of an accreting, rapidly rotating, nonmagnetic neutron star in a low-mass X-ray binary during a type I X-ray burst. We use both analytical arguments and numerical simulations of simplified models for ocean burning. Our analysis extends previous work by taking into account the rapid rotation of the star and the lift-up of the burning ocean during the burst. We find a new regime for the spreading of a nuclear burning front, where the flame is carried along a coherent shear flow across the front. If turbulent viscosity is weak, the speed of flame propagation is upsilon(flame) similar to (gh)(1/2)/ft(n) similar to 20 km s(-1), where h is the scale height of the burning ocean, g is the local gravitational acceleration, t(n) is the timescale for fast nuclear burning during the burst, and f is the Coriolis parameter, i.e., twice the local vertical component of the spin vector. If turbulent viscosity is dynamically important, the flame speed increases and reaches the maximum value, v(flame)(max) similar to (gh/ft(n))(1/2) similar to 300 km s(-1), when the eddy overturn frequency is comparable to the Coriolis parameter f. We show that, as a result of rotationally reduced gravity, the thermonuclear runaway which ignites the ocean is likely to begin on the equator. The equatorial belt is ignited at the beginning of the burst, and the flame then propagates from the equator to the poles. Inhomogeneous cooling (equator first, poles second) of the hot ashes drives strong zonal currents which may be unstable to the formation of Jupiter-type vortices; we conjecture that these vortices are responsible for coherent modulation of X-ray flux in the tails of some bursts. We consider the effect of strong zonal currents on the frequency of modulation of the X-ray flux and show that the large values of the frequency drifts observed in some bursts can be accounted for within our model combined with the model of homogeneous radial expansion. Additionally, if vortices or other inhomogeneities are trapped in the forward zonal flows around the propagating burning front, fast chirps with large frequency ranges (similar to25-500 Hz) may be detectable during the burst rise. Finally, we argue that an MHD dynamo within the burning front can generate a small-scale magnetic field, which may enforce vertically rigid flow in the front's wake and can explain the coherence of oscillations in the burst tail.