# 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 change over the course of activity cycles.

- Authors:

- Kiepenheuer-Institut für Sonnenphysik, Schöneckstraße 6, D-79104 Freiburg (Germany)

- Publication Date:

- OSTI Identifier:
- 22679850

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Astrophysical Journal; Journal Volume: 846; Journal Issue: 2; Other Information: Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 79 ASTROPHYSICS, COSMOLOGY AND ASTRONOMY; DISTURBANCES; EIGENFREQUENCY; EIGENFUNCTIONS; EQUATIONS OF MOTION; EQUILIBRIUM; LORENTZ FORCE; MAGNETIC FIELD CONFIGURATIONS; MAGNETIC FIELDS; MATRIX ELEMENTS; OSCILLATIONS; PERTURBATION THEORY; SIMULATION; STARS; TOROIDAL CONFIGURATION

### Citation Formats

```
Kiefer, René, Schad, Ariane, and Roth, Markus.
```*The Direct Effect of Toroidal Magnetic Fields on Stellar Oscillations: An Analytical Expression for the General Matrix Element*. United States: N. p., 2017.
Web. doi:10.3847/1538-4357/AA8634.

```
Kiefer, René, Schad, Ariane, & Roth, Markus.
```*The Direct Effect of Toroidal Magnetic Fields on Stellar Oscillations: An Analytical Expression for the General Matrix Element*. United States. doi:10.3847/1538-4357/AA8634.

```
Kiefer, René, Schad, Ariane, and Roth, Markus. Sun .
"The Direct Effect of Toroidal Magnetic Fields on Stellar Oscillations: An Analytical Expression for the General Matrix Element". United States.
doi:10.3847/1538-4357/AA8634.
```

```
@article{osti_22679850,
```

title = {The Direct Effect of Toroidal Magnetic Fields on Stellar Oscillations: An Analytical Expression for the General Matrix Element},

author = {Kiefer, René and Schad, Ariane and Roth, Markus},

abstractNote = {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 change over the course of activity cycles.},

doi = {10.3847/1538-4357/AA8634},

journal = {Astrophysical Journal},

number = 2,

volume = 846,

place = {United States},

year = {Sun Sep 10 00:00:00 EDT 2017},

month = {Sun Sep 10 00:00:00 EDT 2017}

}