[Paper Review] Probing the internal magnetism of stars using asymptotic magneto-asteroseismology

S. Mathis, L. Bugnet+4 more|arXiv (Cornell University)|Dec 20, 2020

Stellar, planetary, and galactic studiesPhysics and Astronomy90 references44 citations

TL;DR

This paper develops asymptotic magneto-asteroseismic diagnostics to probe the internal magnetic fields of stars using low-frequency gravity (g) and high-frequency acoustic (p) modes. By extending perturbative theory to magnetic effects, it shows that magnetic frequency splittings scale with the square of the Alfvén frequency relative to mode frequency, enabling detection of axisymmetric fossil or dynamo-generated fields via asymmetries in prograde/retrograde mode splittings when combined with rotational effects.

ABSTRACT

Our knowledge of the dynamics of stars has undergone a revolution thanks to the simultaneous large amount of high-quality photometric observations collected by space-based asteroseismology and ground-based high-precision spectropolarimetry. They allowed us to probe the internal rotation of stars and their surface magnetism in the whole Hertzsprung-Russell diagram. However, new methods should still be developed to probe the deep magnetic fields in those stars. Our goal is to provide seismic diagnoses that allow us to sound the internal magnetism of stars. Here, we focus on asymptotic low-frequency gravity modes and high-frequency acoustic modes. Using a first-order perturbative theory, we derive magnetic splittings of their frequencies as explicit functions of stellar parameters. As in the case of rotation, we show how asymptotic gravity and acoustic modes can allow us to probe the different components of the magnetic field in the cavities where they propagate. This demonstrates again the high potential of using mixed-modes when this is possible.

Motivation & Objective

• To develop seismic diagnostics for probing deep stellar magnetic fields, especially in evolved low- and intermediate-mass stars.
• To address the limitation of surface spectropolarimetry, which cannot access internal field distributions.
• To extend the success of asteroseismology in probing internal rotation to the case of internal magnetism.
• To enable detection of stable fossil or large-scale dynamo-generated magnetic fields through seismic signatures.
• To provide a framework for combining asteroseismology with spectropolarimetry to map magnetic fields from surface to core.

Proposed method

• Applies first-order perturbative theory to compute magnetic frequency splittings in asymptotic limits for low-frequency g (gi) and high-frequency p modes.
• Derives explicit expressions for magnetic splittings as functions of stellar parameters, integrating the squared ratio of Alfvén frequency to mode frequency along the mode propagation path.
• Uses the linearised Lorentz force term involving the cross product of displacement and magnetic field (ξ ∧ B) to model mode coupling with magnetic fields.
• Considers axisymmetric, large-scale dipolar magnetic configurations (poloidal + toroidal) representative of fossil or dynamo fields.
• Compares magnetic splittings with rotational splittings to identify asymmetries in total frequency splitting due to opposite signs for pro- and retrograde modes.
• Proposes a combined seismic-spectropolarimetric strategy to detect core magnetism in bright stars observed by TESS and PLATO.

Experimental results

Research questions

• RQ1 Can asymptotic magneto-asteroseismology detect internal magnetic fields in stars using low-frequency gravity and high-frequency acoustic modes?
• RQ2 How do magnetic splittings in asymptotic modes compare to rotational splittings in form and detectability?
• RQ3 Can the asymmetry between prograde and retrograde mode splittings reveal the presence of an axisymmetric magnetic field?
• RQ4 Do g-modes and p-modes probe different components of the magnetic field due to their distinct propagation geometries?
• RQ5 What is the detectability threshold for magnetic field signatures in high-precision asteroseismic data like those from TESS and PLATO?

Key findings

• Magnetic splittings for asymptotic g and p modes scale with the square of the local Alfvén frequency relative to the mode frequency, integrated along the mode path.
• For axisymmetric dipolar fields, magnetic splittings are identical for prograde and retrograde modes (m > 0 and m < 0), unlike rotational splittings which are opposite in sign.
• This leads to a detectable asymmetry in total frequency splitting when magnetic and rotational effects are combined, providing a unique seismic signature for internal magnetic fields.
• Low-frequency g (gi) modes, which propagate horizontally in central regions, primarily probe the radial component of the magnetic field.
• High-frequency p modes, which propagate vertically in outer layers, primarily probe the horizontal (latitudinal and azimuthal) components of the magnetic field.
• The method enables probing magnetic fields from the stellar core to the surface using mixed modes, analogous to how mixed modes have revealed core and envelope rotation.