Asymmetries of frequency splittings of dipolar mixed modes: a window on the topology of deep magnetic fields

Abstract

Space asteroseismology is revolutionizing our knowledge of the internal structure and dynamics of stars. A breakthrough is ongoing with the recent discoveries of signatures of strong magnetic fields in the core of red giant stars. The key signature for such a detection is the asymmetry these fields induce in the frequency splittings of observed dipolar mixed gravito-acoustic modes. We investigate the ability of the observed asymmetries of the frequency splittings of dipolar mixed modes to constrain the geometrical properties of deep magnetic fields. We use the powerful analytical Racah-Wigner algebra used in Quantum Mechanics to characterize the geometrical couplings of dipolar mixed oscillation modes with various possible realistic fossil magnetic fields' topologies and compute the induced perturbation of their frequencies. First, in the case of an oblique magnetic dipole, we provide the exact analytical expression of the asymmetry as a function of the angle between the rotation and magnetic axes. Its value provides a direct measure of this angle. Second, considering a combination of axisymmetric dipolar and quadrupolar fields, we show how the asymmetry is blind to unravel the relative strength and sign of each component. Finally, in the case of a given multipole, we show that a negative asymmetry is a signature of non-axisymmetric topologies. Therefore, asymmetries of dipolar mixed modes provide key but only partial information on the geometrical topology of deep fossil magnetic fields. Asteroseismic constraints should therefore be combined with spectropolarimetric observations and numerical simulations, which aim to predict the more probable stable large-scale geometries.

arXiv comment10 pages, 3 figures, Letter accepted for publication in Astronomy & Astrophysics

References in corpus (31)

• Modules for Experiments in Stellar Astrophysics (MESA)
• Dynamo action by differential rotation in a stably stratified stellar interior
• Gravity modes as a way to distinguish between hydrogen- and helium-burning red giant stars
• A fossil origin for the magnetic fields of A-stars and white dwarfs
• Spin down of the core rotation in red giants
• Stable magnetic fields in stellar interiors
• Slowing the Spins of Stellar Cores
• Seismic constraints on the radial dependence of the internal rotation profiles of six Kepler subgiants and young red giants
• Probing the interior physics of stars through asteroseismology
• Angular Momentum Transport in Stellar Interiors
• The MiMeS Survey of Magnetism in Massive Stars: Introduction and overview
• Giant star seismology
• Core rotation braking on the red giant branch for various mass ranges
• Surface rotation and photometric activity for Kepler targets. II. G and F main-sequence stars, and cool subgiant stars
• On non-axisymmetric magnetic equilibria in stars
• Transport and mixing in the radiation zones of rotating stars II. Axisymmetric magnetic field
• Seismic diagnostics for transport of angular momentum in stars 2. Interpreting observed rotational splittings of slowly-rotating red giant stars
• Solar structure and evolution
• Stable magnetic equilibria and their evolution in the upper main sequence, white dwarfs, and neutron stars
• 30 to 100-kG magnetic fields in the cores of red giant stars
• Strong magnetic fields detected in the cores of 11 red giant stars using gravity-mode period spacings
• Magnetic signatures on mixed-mode frequencies. I. An axisymmetric fossil field inside the core of red giants
• Effect of a fossil magnetic field on the structure of a young Sun
• Rotation in stellar interiors: General formulation and an asteroseismic-calibrated transport by the Tayler instability
• Probing the internal magnetic field of slowly pulsating B-stars through g modes
• Origin and evolution of magnetic fields in PMS stars : influence of rotation and structural changes
• Period spacings of gravity modes in rapidly rotating magnetic stars II. The case of an oblique dipolar fossil magnetic field
• Spin-down by dynamo action in simulated radiative stellar layers
• Magnetic signatures on mixed-mode frequencies. II. Period spacings as a probe of the internal magnetism of red giants
• Magnetic energy cascade in spherical geometry: I. The stellar convective dynamo case
• Linking the Interiors and Surfaces of Magnetic Stars

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• Mode identification and ensemble asteroseismology of 119 $\beta$ Cep stars detected by Gaia light curves and monitored by TESS
• Unveiling complex magnetic field configurations in red giant stars
• Tidal Dissipation in Evolved Low and Intermediate Mass Stars
• Detectability of axisymmetric magnetic fields from the core to the surface of oscillating post-main sequence stars
• Interior rotation modelling of the $\beta$ Cep pulsator HD 192575 including multiplet asymmetries
• Discovery of new magnetic δ Scuti stars and impact of magnetism on pulsation excitation
• Conversion and Damping of Nonaxisymmetric Internal Gravity Waves in Magnetized Stellar Cores
• Asteroseismic detection of an internal magnetic field in the B0.5V pulsator HD 192575
• Exploring the probing power of gamma-Dor's inertial dip for core magnetism: case of a toroidal field
• Near-critical magnetic fields in Kepler red giants
• Magneto-Archeology of White Dwarfs. Revisiting the fossil field scenario with observational constraints during the red giant branch
• Co-existence of Internal Gravity Waves and Tayler-Spruit Magnetic Fields in the Radiative Core of Low-mass Stars
• Near-degeneracy effects in Quadrupolar Mixed Modes. From an Asymptotic Description to Data Fitting