The Direct Effect of Toroidal Magnetic Fields on Stellar Oscillations: An Analytical Expression for the General Matrix Element

Abstract

Where is the solar dynamo located and what is its modus operandi? These are still open questions in solar physics. Helio- and asteroseismology can help answer them by enabling us to study solar and stellar internal structures through global oscillations. The properties of solar and stellar acoustic modes are changing with the level of magnetic activity. However, until now, the inference on subsurface magnetic fields with seismic measures has been very limited. The aim of this paper is to develop a formalism to calculate the effect of large-scale toroidal magnetic fields on solar and stellar global oscillation eigenfunctions and eigenfrequencies. If the Lorentz force is added to the equilibrium equation of motion, stellar eigenmodes can couple. In quasi-degenerate perturbation theory, this coupling, also known as the direct effect, can be quantified by the general matrix element. We present the analytical expression of the matrix element for a superposition of subsurface zonal toroidal magnetic field configurations. The matrix element is important for forward calculations of perturbed solar and stellar eigenfunctions and frequency perturbations. The results presented here will help to ascertain solar and stellar large-scale subsurface magnetic fields, and their geometric configuration, strength, and their change over the course of activity cycles.

arXiv comment20 pages, accepted for publication in The Astrophysical Journal

References in corpus (16)

• Fast core rotation in red-giant stars revealed by gravity-dominated mixed modes
• Solar Interior Rotation and its Variation
• Detection of Equatorward Meridional Flow and Evidence of Double-Cell Meridional Circulation inside the Sun
• CoRoT reveals a magnetic activity cycle in a Sun-like star
• Giant star seismology
• Transport and mixing in the radiation zones of rotating stars II. Axisymmetric magnetic field
• Global helioseismic evidence for a deeply penetrating Solar meridional flow consisting of multiple flow cells
• Stellar magnetic activity and variability of oscillation parameters - An investigation of 24 solar-like stars observed by Kepler
• Magnetic variability in the young solar analog KIC 10644253: Observations from the Kepler satellite and the HERMES spectrograph
• Meridional Circulation and Global Solar Oscillations
• Effect of a fossil magnetic field on the structure of a young Sun
• A Three-Dimensional Babcock-Leighton Solar Dynamo Model: Initial Results with Axisymmetric Flows
• Constraining differential rotation of Sun-like stars from asteroseismic and starspot rotation periods
• Solar Magnetic Field Signatures in Helioseismic Splitting Coefficients
• A Helioseismic Perspective on the Depth of the Minimum Between Solar Cycles 23 and 24
• Seismic sensitivity of Normal-mode Coupling to Lorentz stresses in the Sun

Cited by in corpus (9)

• Modeling of Magneto-Rotational Stellar Evolution I. Method and first applications
• Core magnetic field imprint in the non-radial oscillations of red giant stars
• The Effect of Toroidal Magnetic Fields on Solar Oscillation Frequencies
• Signature of solar g modes in first-order p-mode frequency shifts
• Sensitivity kernels for inferring Lorentz stresses from normal-mode frequency splittings in the Sun
• Recipe for inferring sub-surface solar magnetism via local mode-coupling using Slepian basis functions
• The impact of rotation on the stochastic excitation of stellar acoustic modes in solar-like pulsators
• Empirical Relations for the Sensitivities of Solar-like Oscillations to Magnetic Perturbations
• Effects of Dynamo-Generated Large-Scale Magnetic Fields on the Surface Gravity ($f$) Mode