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 undergravity towards the magnetic equator, burying the polar magnetic field andcompressing it into a narrow equatorial belt. Steady-state, Grad-Shafranovcalculations with a self-consistent mass-flux distribution (and asemi-quantitative treatment of Ohmic diffusion) show that, for $\Ma \gtrsim10^{-5}\Msun$, the maximum field strength and latitudinal half-width of theequatorial magnetic belt are $B_{\rm max} = 5.6\times 10^{15}(\Ma/10^{-4}\Msun)^{0.32}$ G and $\Delta\theta = \max[3^{\circ}(\Ma/10^{-4}\Msun)^{-1.5},3^{\circ} (\Ma/10^{-4}\Msun)^{0.5}(\dot{M}_{\rma}/10^{-8}\Msun {\rm yr}^{-1})^{-0.5}]$ respectively, where $\Ma$ is the totalaccreted mass and $\dot{M}_{\rm a}$ is the accretion rate. It is shown that thebelt prevents north-south heat transport by conduction, convection, radiation,and ageostrophic shear. This may explain why millisecond oscillations observedin the tails of thermonuclear (type I) X-ray bursts in low-mass X-ray binariesare highly sinusoidal: the thermonuclear flame is sequestered in the magnetichemisphere which ignites first. The model is also consistent with theoccasional occurrence of closely spaced pairs of bursts. Time-dependent,ideal-magnetohydrodynamic simulations confirm that the equatorial belt is notdisrupted by Parker and interchange instabilities.Comment: 8 pages, 3 figures, accepted for publication in The Astrophysical Journa