The effect of rotation and a buried magnetic field on stellar oscillations

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Abstract
Rotation, a magnetic field and any other symmetry-breaking agent raise the degeneracy of the resonant frequencies of stellar oscillations. Here a perturbation method is presented for calculating the resultant frequency modification caused by rotation and an internal magnetic field. The shift in the average multiplet frequency is also addressed. Only axisymmetric magnetic fields are considered explicitly, though the axis of symmetry is not constrained to coincide with the rotation axis. A short-wavelength asymptotic analysis derived from ray theory is also presented. The effects on high-order solar acoustic modes of various hypothetical angular velocity and magnetic field configurations are investigated using both methods of calculation. The asymptotic formulae provide a good estimate for the frequency splitting of five-minute modes when the field and the rotation vary sufficiently smoothly. On the other hand, a localized magnetic field, for example at the base of the convection zone, produces a characteristic oscillatory perturbation to the eigenfrequencies. We present our results in a form that we hope will be useful for comparison with future observations, and discuss them in the light of currently available splitting data.

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