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Stéphane Mathis

Publications and source records attributed to Stéphane Mathis.

At least 37 records · Page 2Linked to original sources
arXiv2024

Nonlinear internal waves breaking in stellar radiation zones. Parametrisation for the transport of angular momentum: bridging geophysical to stellar fluid dynamics

Internal gravity waves (hereafter IGWs) are one of the mechanisms that can play a key role to redistribute efficiently angular momentum in stars along their evolution. The study of IGWs is thus of major importance since space-based asteroseismology reveals a transport of angular momentum in stars, which is stronger by two orders of magnitude than the one predicted by stellar models ignoring their action or those of magnetic fields. IGWs trigger angular momentum transport when they are damped by heat or viscous diffusion, when they meet a critical layer or when they break. Theoretical prescriptions have been derived for the transport of angular momentum induced by IGWs because of their radiative and viscous dampings and of the critical layers they encounter along their propagation. However, none has been proposed for the transport triggered by their nonlinear breaking. In this work, we aim to derive such a physical and robust prescription, which can be implemented in stellar structure and evolution codes. We adapt an analytical saturation model, which has been developed for IGWs nonlinear convective breaking in the Earth atmosphere and has been successfully compared to in-situ measurements in the stratosphere, to the case of deep spherical stellar interiors. In a first step, we neglect the modification of IGWs by the Coriolis acceleration and the Lorentz force, which are discussed and taken into account in a second step. We derive a complete semi-analytical prescription for the transport of angular momentum by IGWs, which takes into account both their radiative damping and their potential nonlinear breaking because of their convective and vertical shear instabilities. This allows us to bring the physical prescription for the interactions between IGWs and the differential rotation to the same level of realism that the one used in global circulation models for the atmosphere.

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arXiv2024

Improving the parametrization of transport and mixing processes in planetary atmospheres: the importance of implementing the full Coriolis acceleration

With the ongoing characterisation of the atmospheres of exoplanets by the JWST, we are unveiling a large diversity of planetary atmospheres, both in terms of composition and dynamics. As such, it is necessary to build coherent atmospheric models for exoplanetary atmospheres to study their dynamics in any regime of thickness, stratification and rotation. However, many models only partially include the Coriolis acceleration with only taking into account the local projection of the rotation vector along the vertical direction (this is the so-called "Traditional Approximation of Rotation") and do not accurately model the effects of the rotation when it dominates the stratification. In this contribution, we report the ongoing efforts to take the full Coriolis acceleration into account for the transport of momentum and the mixing of chemicals. First, we show how the horizontal local component of the rotation vector can deeply modifies the instabilities of horizontal sheared flows and the turbulence they can trigger. Next, we show how the interaction between waves and zonal winds can be drastically modified because of the modification of the wave damping or breaking when taking into account the full Coriolis acceleration. These works are devoted to improve the parameterization of waves and turbulent processes in global atmospheric models.

astro-ph.EP↗
arXiv2024

The impact of differential rotation on the stochastic excitation of acoustic modes in solar-like stars

We model the stochastic excitation of acoustic modes in solar-like pulsators taking into account the action of differential rotation. We derive the theoretical formalism for the stochastic excitation with differential rotation and make use of rotating convection Mixing-Length Theory to assess how the convective velocity is modified by rotation. Finally, we use the stellar structure and evolution code MESA combined with the stellar pulsation code GYRE to compute acoustic modes amplitudes.

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arXiv2024

Impact of uniform rotation on the stochastic excitation of acoustic modes in solar-like oscillators

We evaluate the impact of the rotation on the stochastic excitation of acoustic (p) modes in solar-like pulsators. First, we derive the forced wave equation taking rotation into account and we compute the source terms, which inject energy into the oscillations. We make use of the Rotating Mixing Length Theory (R-MLT) to assess how the convective root mean square velocities are modified by the Coriolis acceleration. Finally, we use the stellar structure and evolution code MESA combined with the stellar pulsation code GYRE to show that the resulting modes amplitudes are inhibited by rotation.

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arXiv2024

Constraining core-to-envelope differential rotation in gamma-doradus stars from inertial dips properties

The presence of dips in the gravito-inertial modes period-spacing pattern of gamma-Dor stars is now well established by recent asteroseismic studies. Such Lorentzian-shaped inertial dips arise from the interaction of gravito-inertial modes propagating in the radiative envelope of intermediate-mass main sequence stars with pure inertial modes that propagate in their convective core. We aim to investigate the signature of a differential rotation between the convective core and the near-core region inside gamma-Dor stars from the inertial dip properties. We first describe the bi-layer rotation profile we use and the approximations we adopt to maintain the analyticity of our study. We then describe our results on the inertial dip formation, location, and shape. We derive a modified Lorentzian profile and we compare it to the previously obtained results in the solid-body rotation case. This work highlights the inertial dips' probing power of the convective core rotation, an important observable in the context of the understanding of the angular momentum transport and chemicals mixing inside stars.

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arXiv2024

Stochastic excitation of waves in magnetic stars -- I. Scaling laws for the modes amplitudes

Stellar oscillations are key to unravelling stars' properties, such as their mass, radius and age. Amplitudes of acoustic modes in solar-like stars are intrinsically linked to their convective turbulent excitation source, which in turn is influenced by magnetism. In the observations of the Sun and stars, the amplitude of the modes is modulated following their magnetic activity cycles: the higher the magnetic field, the lower the modes' amplitudes. When the magnetic field is strong, it can even inhibit the acoustic modes, which are not detected in a majority of solar-like stars presenting a strong magnetic activity. Magnetic fields are known to freeze convection when stronger than a critical value: an "on-off" approach is used in the literature. In this work, we investigate the impact of magnetic fields on the stochastic excitation of acoustic modes. First, we generalise the forced wave equation formalism, including the effects of magnetic fields. Second, we assess how convection is affected by magnetic fields using results from Magnetic Mixing-Length Theory. We provide the source terms of stochastic excitation, including a new magnetic source term and the Reynolds stresses. We provide scaling laws for the amplitudes of the modes, taking into account both the driving and the damping. Those scalings are based on the inverse Alfvén dimensionless parameter: the damping increases with the magnetic field and reaches a saturation threshold when the magnetic field is strong. The driving of the modes diminishes when the magnetic field becomes stronger, the turbulent convection being weaker. As expected from the observations, we find that a higher magnetic field diminishes the resulting modes amplitudes. Evaluating the inverse Alfvén number in stellar models provides a means to estimate the expected amplitudes of acoustic modes in magnetic active solar-type stars.

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arXiv2023

Asteroseismic g-mode period spacings in strongly magnetic rotating stars

Strong magnetic fields are expected to significantly modify the pulsation frequencies of waves propagating in the cores of red giants or in the radiative envelopes of intermediate- and high-mass main-sequence stars. We calculate the g-mode frequencies of stars with magnetic dipole fields which are aligned with their rotational axes, treating both the Lorentz and Coriolis forces non-perturbatively. We provide a compact asymptotic formula for the g-mode period spacing, and universally find that strong magnetism decreases this period spacing substantially more than is predicted by perturbation theory. These results are validated with explicit numerical mode calculations for realistic stellar models. The approach we present is highly versatile: once the eigenvalues $λ$ of a certain differential operator are precomputed as a function of the magnetogravity and rotational frequencies (in units of the mode frequency), the non-perturbative impact of the Coriolis and Lorentz forces is understood under a broad domain of validity, and is readily incorporated into asteroseismic modeling.

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arXiv2023

Hydrodynamic modelling of dynamical tides dissipation in Jupiter's interior as revealed by Juno

The Juno spacecraft has acquired exceptionally precise data on Jupiter's gravity field, offering invaluable insights into Jupiter's tidal response, interior structure, and dynamics, establishing crucial constraints. We develop a new model for calculating Jupiter's tidal response based on its latest interior model, while also examining the significance of different dissipation processes for the evolution of its system. We study the dissipation of dynamical tides in Jupiter by thermal, viscous and molecular diffusivities acting on gravito-inertial waves in stably stratified zones and inertial waves in convection ones. We solve the linearised equations for the equilibrium tide. Next, we compute the dynamical tides using linear hydrodynamical simulations based on a spectral method. The Coriolis force is fully taken into account, but the centrifugal effect is neglected. We study the dynamical tides occurring in Jupiter using internal structure models that respect Juno's constraints. We study specifically the dominant quadrupolar tidal components and our focus is on the frequency range that corresponds to the tidal frequencies associated with Jupiter's Galilean satellites. By incorporating the different dissipation mechanisms, we calculate the total dissipation and determine the imaginary part of the tidal Love number. We find a significant frequency dependence in dissipation spectra, indicating a strong relationship between dissipation and forcing frequency. Furthermore, our analysis reveals that, in the chosen parameter regime in which kinematic viscosity, thermal and molecular diffusivities are equal, the dominant mechanism contributing to dissipation is viscosity, exceeding in magnitude both thermal and chemical dissipation. We find that the presence of stably stratified zones plays an important role in explaining the high dissipation observed in Jupiter.

astro-ph.EP↗
arXiv2023

Hydrodynamical modelling of tidal dissipation in gas giant planets at the time of space missions

Gas giant planets are differentially rotating magnetic objects that have strong and complex interactions with their environment. In our Solar system, they interact with their numerous moons while exoplanets with very short orbital periods (hot Jupiters), interact with their host star. The dissipation of waves excited by tidal forces in their interiors shapes the orbital architecture and the rotational dynamics of these systems. Recently, astrometric observations of Jupiter and Saturn systems have challenged our understanding of their formation and evolution, with stronger tidal dissipation in these planets than previously predicted, in contrast to what appears to be weaker in gas giant exoplanets. These new constraints are motivating the development of realistic models of tidal dissipation inside these planets. At the same time, the Juno and Cassini space missions have revolutionised our knowledge of the interiors of Jupiter and Saturn, whose structure is a combination of stably stratified zones and convective regions. In this work, we present results of hydrodynamical calculations modelling tidal waves and their dissipation in Jupiter, taking for the first time the latest, state-of-the-art interior model of the planet. We performed 2D numerical simulations of linear tidal gravito-inertial waves that propagate and dissipate within Jupiter interior by taking into account viscous, thermal and chemical diffusions. This new model allows us to explore the properties of the dissipation and the associated tidal torque as a function of all the key hydrodynamical and structural parameters.

astro-ph.EP↗
arXiv2023

In search of gravity mode signatures in main sequence solar-type stars observed by Kepler

Gravity modes (g modes), mixed gravito-acoustic modes (mixed modes), and gravito-inertial modes (gi modes) possess unmatched properties as probes for stars with radiative interiors. The structural and dynamical constraints that they are able to provide cannot be accessed by other means. While they provide precious insights into the internal dynamics of evolved stars as well as massive and intermediate-mass stars, their non-detection in main sequence (MS) solar-type stars make them a crucial missing piece in our understanding of angular momentum transport in radiative zones and stellar rotational evolution. In this work, we aim to apply certain analysis tools originally developed for helioseismology in order to look for g-mode signatures in MS solar-type stars. We select a sample of the 34 most promising MS solar-type stars with Kepler four-year long photometric time series. All these stars are well-characterised late F-type stars with thin convective envelopes, fast convective flows, and stochastically excited acoustic modes (p modes). For each star, we compute the background noise level of the Fourier power spectrum to identify significant peaks at low frequency. After successfully detecting individual peaks in 12 targets, we further analyse four of them and observe distinct patterns of surrounding peaks with a low probability of being noise artifacts. Comparisons with the predictions from reference models suggest that these patterns are compatible with the presence of non-asymptotic low-order pure g modes, pure p modes, and mixed modes. Given their sensitivity to both the convective core interface stratification and the coupling between p- and g-mode resonant cavities, such modes are able to provide strong constraints on the structure and evolutionary states of the related targets. [abridged]

astro-ph.SR↗
arXiv2023

Mode coupling coefficients between the convective core and radiative envelope of $γ\,$Doradus and slowly pulsating B stars

Signatures of coupling between an inertial mode in the convective core and a gravito-inertial mode in the envelope have been found in four-year Kepler light curves of 16 rapidly rotating $γ\,$Doradus ($γ\,$Dor) stars. This makes it possible to obtain a measurement of the rotation frequency in their convective core. Despite their similar internal structure and available data, inertial modes have not yet been reported for slowly pulsating B (SPB) stars. We aim to provide a numerical counterpart of the recently published theoretical expressions for the mode-coupling coefficients, $\varepsilon$ and $\tilde{\varepsilon}$. These coefficients represent the two cases of a continuous and a discontinuous Brunt-Väisälä frequency profile at the core-envelope interface, respectively. We used asteroseismic forward models of two samples consisting of 26 SPB stars and 37 $γ\,$Dor stars to infer their numerical values of $\varepsilon$. The asteroseismically inferred values of $\varepsilon$ for the two samples are between 0.0 and 0.34. While $\varepsilon$ is most strongly correlated with the near-core rotation frequency for $γ\,$Dor stars, the fractional radius of the convective core instead provides the tightest correlation for SPB stars. We find $\varepsilon$ to decrease mildly as the stars evolve. Our asteroseismic results for the mode coupling support the theoretical interpretation and reveal that young, fast-rotating $γ\,$Dor stars are most suitable for undergoing couplings between inertial modes in the rotating convective core and gravito-inertial modes in the radiative envelope. The phenomenon has been found in 2.4\% of such pulsators with detected period spacing patterns, whereas it has not been seen in any of the SPB stars so far. (shortened abstract to meet the arXiv limits)

astro-ph.SR↗
arXiv2023

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

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.

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arXiv2023

Secular dipole-dipole stability of magnetic binaries

The presence of strong large-scale stable magnetic fields in a significant portion of early-type stars, white dwarfs, and neutron stars is well established. Despite this, the origins of these fields remain unresolved, with leading propositions advocating fossil fields, mergers, and shear-driven dynamos as the main mechanism. A potential key for further insight could lie in the connection with binarity: notably, magnetism can play a role in the long-term orbital and rotational dynamics of binaries. In gravitational wave astronomy, the advanced sensitivity of upcoming detectors such as LISA and the Einstein Telescope will enable the characterisation of the orbital inspirals of compact systems, including their magnetic properties. A comprehensive understanding of the dynamics of magnetism in these systems is required for the interpretation of the gravitational wave signals and to avoid calibration biases. Furthermore, this knowledge can be used to create new magnetic population models and to provide insight into the nature of their internal fields. The aim of this study is to investigate the secular spin precession dynamics of binary systems under pure magnetic dipole interactions, focusing on stars with strong, stable, dipolar fields. We employ an orbit-averaging procedure for the spin equations and obtain an effective secular description. By minimising the magnetic energy, we derive the configurations of equilibrium. We show that among the four states, only one is stable, consisting of the spin and magnetic axes of one star reversed with respect to the companions', and orthogonal to the orbital plane. Our long-term stability results disagree with usual methods, which tend to neglect orbital motion. Finally, we provide analytical solutions for the system out of equilibrium, which can be used to derive secular orbital evolution in the context of gravitational wave astronomy.

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arXiv2023

Spin evolution of Venus-like planets subjected to gravitational and thermal tides

The arrival of powerful instruments will provide valuable data for the characterization of rocky exoplanets. It is then crucial to accurately model the dynamical state of exoplanets. Rocky planets with sufficiently large orbits should have non-zero eccentricities and/or obliquities. Realistic models of tides for rocky planets can allow for higher spin states than the synchronization state in the presence of eccentricities or obliquities. This work explores the secular evolution of a star-planet system under tidal interactions, both gravitational and thermal, induced respectively by the quadrupolar component of the gravitational potential and the irradiation of the planet's surface. We use the formalism of Kaula associated with an Andrade rheology to model a relevant response of a rocky planet to gravitational tides and a prescription of thermal tides fitted for Venus to model the response of the atmosphere to the thermal tides. We implemented the general secular evolution equations of tidal interactions in the secular code ESPEM (French acronym for Evolution of Planetary System and Magnetism). We show the possible spin-orbit evolution and resonances for eccentric orbits and explore the possible spin orbit resonances raised by the obliquity of the planet. Our simulations have shown that the secular evolution of the spin and obliquity can lead to the retrograde spin of the Venus-like planet if the system starts from a high spin obliquity, in agreement to previous studies. Taking into account the luminosity evolution of the Sun changes the picture. We find that the planet never reaches the equilibrium: the timescale of rotation evolution is longer than the luminosity variation timescale, which suggests that Venus may never reach a spin equilibrium state but may still evolve.

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arXiv2023

How do tidal waves interact with convective vortices in rapidly-rotating planets and stars?

The dissipation of tidal inertial waves in planetary and stellar convective regions is one of the key mechanisms that drive the evolution of star-planet/planet-moon systems. In this context, the interaction between tidal inertial waves and turbulent convective flows must be modelled in a realistic and robust way. In the state-of-the-art simulations, the friction applied by convection on tidal waves is modelled most of the time by an effective eddy-viscosity. This approach may be valid when the characteristic length scales of convective eddies are smaller than those of tidal waves. However, it becomes highly questionable in the case where tidal waves interact with potentially stable large-scale vortices, as those observed at the pole of Jupiter and Saturn. They are potentially triggered by convection in rapidly-rotating bodies in which the Coriolis acceleration forms the flow in columnar vortical structures along the direction of the rotation axis. In this paper, we investigate the complex interactions between a tidal inertial wave and a columnar convective vortex. We use a quasi-geostrophic semi-analytical model of a convective columnar vortex. We perform linear stability analysis to identify the unstable regime and conduct linear numerical simulations for the interactions between the convective vortex and an incoming tidal inertial wave. We verify that in the unstable regime, an incoming tidal inertial wave triggers the most unstable mode of the vortex leading to turbulent dissipation. For stable vortices, the wave-vortex interaction leads to the momentum mixing while it creates a low-velocity region around the vortex core and a new wave-like perturbation in the form of a progressive wave radiating in the far field. The emission of this secondary wave is the strongest when the wavelength of the incoming wave is close to the characteristic size of the vortex.

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arXiv2022

Gravitational waves radiated by magnetic galactic binaries and detection by LISA

In the context of the future Laser Interferometer Space Antenna (LISA) mission, galactic binary systems of white dwarfs and neutron stars will represent the dominant source of Gravitational Waves (GWs) within the $10^{-4}-10^{-1}\,\mathrm{Hz}$ frequency band. It is expected that LISA will measure simultaneously, the GWs from more than ten thousands of these compact galactic binaries. The analysis of such a superposition of signals will represent one of the greatest challenge for the mission. Currently, in the LISA Datacode Challenge, each galactic binary is modeled as a quasi-monochromatic source of GWs. This corresponds to the circular motion of two point-masses at the 2.5 post-Newtonian approximation. If this picture is expected to be an accurate description for most of the galactic binaries that LSIA will detect, we nevertheless expect to observe eccentric systems with complex physical properties beyond the point-mass approximation. In this work, we investigate how a binary system of highly magnetic objects in quasi-circular orbit could affect the quasi-monochromatic picture of the GW signal detected by LISA. We demonstrate that the eccentricity generates additional frequency peaks at harmonics of the mean motion and that magnetism is responsible for shifting each frequency peak with respect to the case without magnetism. We provide analytical estimates and argue that LISA will be able to detect magnetism if it can measure the main peaks at two and three times the mean motion with a sufficient accuracy.

gr-qc↗
arXiv2022

Impact of magnetism on gravitational waves emitted by compact galactic binaries in quasi-circular orbits

The LISA (Laser Interferometer Space Antenna) mission will observe in the low frequency band from 0.1 mHz to 1 Hz. In this regime, we expect the galactic binaries to be the dominant (by number) sources of gravitational waves signal. Considering that galactic binaries are composed of the most magnetized astrophysical objects in the universe (i.e., the white dwarfs and the neutron stars), LISA is expected to bring new informations about the origin and the nature of magnetism inside degenerated stars. Currently, the data processing assumes that the galactic binary systems are non-magnetic and in circular orbits which can potentially biased the determination of the parameters of the sources and also the calibration of the detector. In this work, we investigate the impact of magnetism on gravitational waves emitted by compact galactic binaries assuming quasi-circular orbits.

gr-qc↗
arXiv2022

Can we detect deep axisymmetric toroidal magnetic fields in stars?

One of the major discoveries of asteroseismology is the signature of a strong extraction of angular momentum (AM) in the radiative zones of stars across the entire Hertzsprung-Russell diagram, resulting in weak core-to-surface rotation contrasts. Despite all efforts, a consistent AM transport theory, which reproduces both the internal rotation and mixing probed thanks to the seismology of stars, remains one of the major open problems in modern stellar astrophysics. A possible key ingredient to figure out this puzzle is magnetic field with its various possible topologies. Among them, strong axisymmetric toroidal fields, which are subject to the so-called Tayler MHD instability, could play a major role. They could trigger a dynamo action in radiative layers while the resulting magnetic torque allows an efficient transport of AM. But is it possible to detect signatures of these deep toroidal magnetic fields? The only way to answer this question is asteroseismology and the best laboratories of study are intermediate-mass and massive stars because of their external radiative envelope. Since most of these are rapid rotators during their main-sequence, we have to study stellar pulsations propagating in stably stratified, rotating, and potentially strongly magnetised radiative zones. For that, we generalise the traditional approximation of rotation, which provides in its classic version a flexible treatment of the adiabatic propagation of gravito-inertial modes, by taking simultaneously general axisymmetric differential rotation and toroidal magnetic fields into account. Using this new non-perturbative formalism, we derive the asymptotic properties of magneto-gravito-inertial modes and we explore the different possible field configurations. We found that the magnetic effects should be detectable for equatorial fields using high-precision asteroseismic data.

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