arXiv subjects

Armand Leclerc

Publications and source records attributed to Armand Leclerc.

13 recordsLinked to original sources

arXiv2026

On the feasibility of inverting the rotation of the solar core with mixed f/g modes

Context: Thanks to helioseismology, the rotation profile of the Sun has been measured with great precision down to 20% of its total radius. This rotation profile is used as a calibration to infer the rotation of other stars as well as a test of angular momentum transport theory in stellar interiors. However, the deepest 20% of the layers remain out of reach of current observations, preventing astronomers to discriminate between currently competing angular momentum transport mechanisms. Aims: The main obstacle is that no global oscillations modes sensitive to rotation (non-zero degree l) reaching the solar core have been detected yet, as nonradial p modes cannot reach it and g modes are evanescent at the surface and still elude detection. In this work, we propose and examine a new method to constrain the rotation of the core of the Sun, which does not require direct observation of solar g modes. Methods: It is based on a recent prediction that g modes in the radiative interior couple with f modes in the outer parts of the star. These mixed f /g are at the same time sensitive to the rotation of the core and able to reach the surface. These modes can be used together to build average inversion kernels and perform an inversion of the rotation of the solar core. Results: We find that the oscillations' spectrum of the Sun should present 6 mixed f /g modes that can be used to measure the rotation rate of the Sun at r = 0.07 and 0.2R. We estimate that the uncertainty on the measurements should be small enough to distinguish between competing scenarios of angular momentum transport in the Sun.

astro-ph.SR↗

arXiv2026

Asteroseismic imprints of strong non-axisymmetric fields in the cores of red giants

To date, magnetic fields have been asteroseismically measured in nearly one hundred red giant cores. However, most analyses assume weak magnetic fields and slow rotation so that perturbation theory can be applied. The "traditional approximation of rotation and magnetism" (TARM) method can predict gravity-mode frequencies under strong magnetic fields and rapid rotation rates. So far, this formalism requires the magnetic field to be symmetric about the rotation axis. We generalize the TARM formalism to apply to arbitrary magnetic field geometries, including cases where the magnetic and rotation axes are misaligned, as well as fields with no symmetry axis at all. The resulting gravity modes exhibit a rich diversity of wave behavior, including oblique pulsation and avoided crossings. We also clarify the domains of validity of perturbation theory and the TARM formalism.

astro-ph.SR↗

arXiv2026

Revealing mixed modes in compressible hydrodynamical simulations of red giant stars

Mixed modes are observed in many low-mass evolved stars. They provide information about core rotation rates of these stars, which are lower than predicted by stellar evolution models. The mixed modes themselves have been invoked as an angular momentum transport mechanism, but estimating their transport efficiency requires knowledge of their amplitudes. We constrain, for the first time, the mixed mode amplitudes in 2D hydrodynamical simulations of a $1.3M_\odot$ red giant using the code \textsc{music}. We perform two simulations with outer radial truncations at fractional radii $r_o/r_\star = 0.90$ and $r_o/r_\star = 0.98$. We compare the modes in the simulation with those found using both \textsc{gyre} and a \textsc{dedalus} eigenvalue solver. Excellent frequency agreement is found for all p-dominated modes, with minor discrepancies for g-dominated modes, especially in the frequency range $[60, \ 240]\ \mu\mathrm{Hz}$. We find excellent eigenfunction agreement for all modes except those in this frequency range. According to empirical predictions the largest kinetic energies are located around $\nu_{\mathrm{max}} = 312.8\ \mu\mathrm{Hz}$, but in both simulations the modes with frequencies $\nu <50\ \mu\mathrm{Hz}$ have the largest kinetic energies. In the simulation with $r/r_\star = 0.98$, the simulated modes have extrapolated surface velocities comparable to the empirical predictions, with highest surface velocities in a bell-shaped curve peaking around $\nu = 700 \ \mu\mathrm{Hz}$. The extrapolated surface velocities of the low frequency modes are small, and thus hard to observe, but their large kinetic energies deeper in the interior could significantly impact angular momentum transport, which has not yet been investigated.

astro-ph.SR↗

arXiv2026

Extending asteroseismic magnetometry across the diverse landscape of magnetic structures

Magnetic fields have now been asteroseismically measured in the cores of many red giants. However, most interpretations of these measurements assume that the magnetic field is far below the critical field strength known to be exceeded by red giants exhibiting gravity-mode suppression. A recent method based on the traditional approximation of rotation and magnetism accurately predicts mode frequencies under fields up to this critical value by modeling gravity waves as individual magnetogravity ``polarizations'' which propagate through a waveguide-like mode cavity. So far, this formalism has been limited to magnetic fields which are axisymmetric about the rotation axis. In this study, we extend this approach by calculating the polarizations of magnetogravity waves under arbitrarily shaped magnetic fields under potentially rapid rotation. We consider the special cases of a dipolar magnetic field misaligned with the rotation axis as well as a dipole-plus-quadrupole magnetic field with no rotational symmetry. We show that non-axisymmetric field configurations can induce avoided crossings between polarizations, and that waves in such systems can convert between magnetogravity polarizations as they propagate, especially when the magnetic field strength is locally below a stratification-dependent threshold value. This threshold is distinct from the critical field strength for gravity-mode suppression, and is instead similar to the magnetic field strength at which perturbation theory breaks down.

astro-ph.SR↗

arXiv2025

Radial modes of pressure bumps and dips in astrophysical discs

This study investigates the signatures of pressure extrema on global oscillations in discs. To this end, we use the framework of wave topology to establish a generalised local dispersion relation that includes pressure gradients. We highlight the influence of a previously unrecognized epicyclic-acoustic frequency and derive an analytical criterion for the existence of a branch of modes transiting between the inertial and the pressure bands. We find that pressure extrema consist of wave guides in which such topological modes propagate. The fundamental mode trapped at a pressure bump can propagate at all frequencies, allowing it to resonate with any temporal forcing, while the mode associated with a pressure gap propagates at a fixed frequency, propagates with arbitrary vertical phase velocity. These specific features make them attractive candidates for future discoseismology.

astro-ph.EP↗

arXiv2025

A core-sensitive mixed $f$/$g$ mode of the Sun predicted by wave topology and hydrodynamical simulation

Helioseismology has revolutionized our understanding of the Sun by analyzing its global oscillation modes. However, the solar core remains elusive, limiting a full understanding of its evolution. In this work, we study a previously unnoticed global oscillation mode of the Sun using a fully compressible, hydrodynamical simulation of the solar interior, and assess that it is a mixed $f$/$g$ mode with a period of about one hour. This is the first global stellar hydrodynamics simulation that successfuly couple compressible and gravity modes. To understand this coupling, we invoke a recent theory on the nature of $f$-modes seen through the prism of wave topology, characterizing their ability to propagate deep into stellar interiors. We demonstrate that the mixed $f$/$g$ mode is highly sensitive to the core's rotation rate, providing a new promising pathway to explore the Sun's core.

astro-ph.SR↗

arXiv2025

The importance of Berry phase in solar acoustic modes

An analytic expression for the frequencies of standing waves in stars, applicable to any radial order n, is derived from ray-tracing equations by the mean of Wigner-Weyl calculus. A correction to previous formulas currently employed in asteroseismology is identified as the Berry phase, which accounts for the vectorial nature of wave propagation in stars. Accounting for this quantity significantly improves upon previous laws for low n modes of the Sun, and we show that the Berry phase is indeed present in the available observational data of solar modes. This phase is due to inhomogeneities of the medium.

astro-ph.SR↗

arXiv2024

Wave topology of stellar inertial oscillations

Inertial waves in convective regions of stars exhibit topological properties linked to a Chern number of 1. The first of these is a unique, unidirectional, prograde oscillation mode within the cavity, which propagates at arbitrarily low frequencies for moderate azimuthal wavenumbers. The second one are phase singularities around which the phase winds in Fourier space, with winding numbers of $\pm 1$ depending on the hemisphere. Phase winding is a collective effect over waves propagating in all directions that is strongly robust to noise. This suggests a topology-based method for wave detection in noisy observational data.

astro-ph.SR↗

arXiv2024

PT and anti-PT symmetries for astrophysical waves

Context: Discrete symmetries have found numerous applications in photonics and quantum mechanics, but remain little studied in fluid mechanics, particularly in astrophysics. Aims: We aim to show how PT and anti-PT symmetries determine the behaviour of linear perturbations in a wide class of astrophysical problems. They set the location of Exceptional Points in the parameter space and the associated transitions to instability, and are associated to the conservation of quadratic quantities that can be determined explicitly. Methods: We study several classical local problems: the gravitational instability of isothermal spheres and thin discs, the Schwarzschild instability, the Rayleigh-B\'enard instability and acoustic waves in dust-gas mixtures. We calculate the locations and the order of the Exceptional Points with a method of resultant, as well as the conserved quantities in the different regions of the parameter space using Krein theory. Results: All problems studied here exhibit discrete symmetries, even though Hermiticity is broken by different physical processes (self-gravity, buoyancy, diffusion, drag). This analysis provides genuine explanations for certain instabilities, and for the existence of regions in the parameter space where waves do not propagate. Those correspond to breaking of PT and anti-PT symmetries respectively. Not all instabilities are associated to symmetry breaking (e.g. the Rayleigh-Benard instability).

astro-ph.SR↗

arXiv2024

Topology of shallow-water waves on the rotating sphere

Topological properties of the spectrum of shallow-water waves on a rotating spherical body are established. Particular attention is paid to its spectral flow, i.e. the modes whose frequencies transit between the Rossby and inertia-gravity wavebands as the zonal wave number is varied. Organising the modes according to the number of zeros of their meridional velocity, we conclude that the net number of modes transiting between the shallow-water wavebands on the sphere is null, in contrast with the Matsuno spectrum. This difference can be explained by a miscount of zeros under the $\beta$-plane approximation. We corroborate this result with the analysis of Delplace et al (2017) by showing that the curved metric discloses a pair of degeneracy points in the Weyl symbol of the wave operator, non-existent under the $\beta$-plane approximation, each of them bearing a Chern number $-1$.

physics.flu-dyn↗

arXiv2023

The Exceptional Ring of buoyancy instability in stars

We reveal properties of global modes of linear buoyancy instability in stars, characterised by the celebrated Schwarzschild criterion, using non-Hermitian topology. We identify a ring of Exceptional Points of order 4 that originates from the pseudo-Hermitian and pseudo-chiral symmetries of the system. The ring results from the merging of a dipole of degeneracy points in the Hermitian stablystratified counterpart of the problem. Its existence is related to spherically symmetric unstable modes. We obtain the conditions for which convection grows over such radial modes. Those are met at early stages of low-mass stars formation. We finally show that a topological wave is robust to the presence of convective regions by reporting the presence of a mode transiting between the wavebands in the non-Hermitian problem, strengthening their relevance for asteroseismology.

astro-ph.SR↗

arXiv2022

From ray tracing to waves of topological origin in continuous media

Inhomogeneous media commonly support a discrete number of wave modes that are trapped along interfaces defined by spatially varying parameters. When they are robust against continuous deformations of parameters, such waves are said to be of topological origin. It has been realized over the last decades that such waves of topological origin can be predicted by computing a single topological invariant, the first Chern number, in a dual bulk wave problem that is much simpler to solve than the original wave equation involving spatially varying coefficients. The correspondence between the simple bulk problem and the more complicated interface problem is usually justified by invoking an abstract index theorem. Here, by applying ray tracing machinery to the paradigmatic example of equatorial shallow water waves, we propose a physical interpretation of this correspondence. We first compute ray trajectories in a phase space given by position and wavenumber of the wave packet, using Wigner-Weyl transforms. We then apply a quantization condition to describe the spectral properties of the original wave operator. We show that the Chern number emerges naturally from this quantization relation.

physics.flu-dyn↗

arXiv2022

Topological modes in stellar oscillations

Stellar oscillations can be of topological origin. We reveal this deep and so-far hidden property of stars by establishing a novel parallel between stars and topological insulators. We construct an hermitian problem to derive the expression of the stellar $\mathrm{\textit{acoustic-buoyant}}$ frequency $S$ of non-radial adiabatic pulsations. A topological analysis then connects the changes of sign of the acoustic-buoyant frequency to the existence of Lamb-like waves within the star. These topological modes cross the frequency gap and behave as gravity modes at low harmonic degree $\ell$ and as pressure modes at high $\ell$. $S$ is found to change sign at least once in the bulk of most stellar objects, making topological modes ubiquitous across the Hertzsprung-Russel diagram. Some topological modes are also expected to be trapped in regions where the internal structure varies strongly locally.

astro-ph.SR↗