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

Abstract

Matter accreting onto the magnetic poles of a neutron star spreads under gravity towards 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 semi-quantitative treatment of Ohmic diffusion) show that, for $\Ma \gtrsim 10^{-5}\Msun$, the maximum field strength and latitudinal half-width of the equatorial magnetic belt are $B_{\rm max} = 5.6\times 10^{15} (\Ma/10^{-4}\Msun)^{0.32}$ G and $\Delta\theta = \max[3^{\circ} (\Ma/10^{-4}\Msun)^{-1.5},3^{\circ} (\Ma/10^{-4}\Msun)^{0.5}(\dot{M}_{\rm a}/10^{-8}\Msun {\rm yr}^{-1})^{-0.5}]$ respectively, where $\Ma$ is the total accreted mass and $\dot{M}_{\rm a}$ 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 which 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.