Magnetic burial and the harmonic content of millisecond oscillations in thermonuclear X-ray bursts

Matter accreting onto the magnetic poles of a neutron star spreads under gravity toward the magnetic equator, burying the polar magnetic field and compressing it into a narrow equatorial belt. Steady state, Grad-Shafranov calculations with a self-consistent mass-flux distribution (and a semiquantitative treatment of Ohmic diffusion) show that, for Ma greater than or similar to 10(-5) M-circle dot, the maximum field strength and latitudinal half-width of the equatorial magnetic belt are B-max = 5.6 x 10(15)(M-a/10(-4) M-circle dot)(0.32) G and Delta theta = max [3 degrees(M-a/10(-4) M-circle dot)(-1.5), 3 degrees(M-a/10(-4) M-circle dot)(0.5)(M-a/10(-8) M-circle dot yr(-1))(-0.5)], respectively, where M-a is the total accreted mass and M-a is the accretion rate. It is shown that the belt prevents north-south heat transport by conduction, convection, radiation, and ageostrophic shear. This may explain why millisecond oscillations observed in the tails of thermonuclear (type I) X-ray bursts in low-mass X-ray binaries are highly sinusoidal; the thermonuclear flame is sequestered in the magnetic hemisphere that ignites first. The model is also consistent with the occasional occurrence of closely spaced pairs of bursts. Time-dependent, ideal-magnetohydrodynamic simulations confirm that the equatorial belt is not disrupted by Parker and interchange instabilities.