For a magnetar with a toroidal magnetic field confined to its crust, the paper derives the Zeeman-split magneto-elastic oscillation spectrum and gives simple formulas and fit constants for frequencies across stellar masses.
What Magnetar Seismology can Teach us about the Magnetic Fields
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abstract
The effect of magnetic fields on the frequencies of toroidal oscillations of neutron stars is derived to lowest order. Interpreting the fine structure in the QPO power spectrum of magnetars following giant flares reported by Strohmayer and Watts (2006) to be "Zeeman splitting" of degenerate toroidal modes, we estimate a crustal magnetic field of order 10^{15} Gauss or more. We suggest that residual m, -m symmetry following such splitting might allow beating of individual frequency components that is slow enough to be observed.
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Zeeman effect in oscillations of magnetars with toroidal magnetic fields
For a magnetar with a toroidal magnetic field confined to its crust, the paper derives the Zeeman-split magneto-elastic oscillation spectrum and gives simple formulas and fit constants for frequencies across stellar masses.