arXiv subjects

Vincent Prat

Publications and source records attributed to Vincent Prat.

At least 19 recordsLinked to original sources

arXiv2021

The traditional approximation of rotation for rapidly rotating stars and planets. II. Deformation and differential rotation

We examine the dynamics of low-frequency gravito-inertial waves (GIWs) in differentially rotating deformed radiation zones in stars and planets by generalising the traditional approximation of rotation (TAR). The TAR treatment was built on the assumptions that the star is spherical and uniformly rotating. However, it has been generalised in our previous work by including the effects of the centrifugal deformation using a non-perturbative approach in the uniformly rotating case. We aim to carry out a new generalisation of the TAR treatment to account for the differential rotation and the strong centrifugal deformation simultaneously. We generalise our previous work by taking into account the differential rotation in the derivation of our complete analytical formalism that allows the study of the dynamics of GIWs in differentially and rapidly rotating stars. We derived the complete set of equations that generalises the TAR, simultaneously taking the full centrifugal acceleration and the differential rotation into account. Within the validity domain of the TAR, we derived a generalised Laplace tidal equation for the horizontal eigenfunctions and asymptotic wave periods of the GIWs, which can be used to probe the structure and dynamics of differentially rotating deformed stars with asteroseismology. A new generalisation of the TAR, which simultaneously takes into account the differential rotation and the centrifugal acceleration in a non-perturbative way, was derived. This generalisation allowed us to study the detectability and the signature of the differential rotation on GIWs in rapidly rotating deformed stars and planets. We found that the effects of the differential rotation in early-type deformed stars on GIWs is theoretically largely detectable in modern space photometry using observations from $\textit{Kepler}$ and TESS.

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arXiv2021

The traditional approximation of rotation for rapidly rotating stars and planets. I. The impact of strong deformation

The Traditional Approximation of Rotation (TAR) is a treatment of the hydrodynamic equations of rotating and stably stratified fluids in which the action of the Coriolis acceleration along the direction of the entropy and chemical stratifications is neglected because it is weak in comparison with the buoyancy force. The dependent variables in the equations for the dynamics of gravito-inertial waves (GIWs) then become separable into radial and horizontal parts as in the non-rotating case. The TAR is built on the assumptions that the star is spherical (i.e. its centrifugal deformation is neglected) and uniformly rotating. We study the feasibility of carrying out a generalisation of the TAR to account for the centrifugal acceleration in the case of strongly deformed uniformly and rapidly rotating stars (and planets), and to identify the validity domain of this approximation. We built analytically a complete formalism that allows the study of the dynamics of GIWs in spheroidal coordinates which take into account the flattening of rapidly rotating stars by assuming the hierarchies of frequencies adopted within the TAR in the spherical case and by deriving a generalised Laplace tidal equation for the horizontal eigenfunctions of the GIWs and their asymptotic wave periods, which can be used to probe the structure and dynamics of rotating deformed stars with asteroseismology. Using 2D ESTER stellar models, we determine the validity domain of the generalised TAR as a function of the rotation rate of the star normalised by its critical angular velocity and its pseudo-radius. This generalisation allows us to study the signature of the centrifugal effects on GIWs in rapidly rotating deformed stars. We found that the effects of the centrifugal acceleration in rapidly rotating early-type stars on GIWs are theoretically detectable in modern space photometry using observations from Kepler.

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arXiv2021

Anisotropic turbulent transport with horizontal shear in stellar radiative zones

Context. Turbulent transport in stellar radiative zones is a key ingredient of stellar evolution theory, but the anisotropy of the transport due to the stable stratification and the rotation of these regions is poorly understood. The assumption of shellular rotation, which is a cornerstone of the so-called rotational mixing, relies on an efficient horizontal transport. However, this transport is included in many stellar evolution codes through phenomenological models that have never been tested. Aims. We investigate the impact of horizontal shear on the anisotropy of turbulent transport. Methods. We used a relaxation approximation (also known as τ approximation) to describe the anisotropising effect of stratification, rotation, and shear on a background turbulent flow by computing velocity correlations. Results. We obtain new theoretical scalings for velocity correlations that include the effect of horizontal shear. These scalings show an enhancement of turbulent motions, which would lead to a more efficient transport of chemicals and angular momentum, in better agreement with helio- and asteroseismic observations of rotation in the whole Hertzsprung-Russell diagram. Moreover, we propose a new choice for the non-linear time used in the relaxation approximation, which characterises the source of the turbulence. Conclusions. For the first time, we describe the effect of stratification, rotation, and vertical and horizontal shear on the anisotropy of turbulent transport in stellar radiative zones. The new prescriptions need to be implemented in stellar evolution calculations. To do so, it may be necessary to implement non-diffusive transport.

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arXiv2021

The effect of the centrifugal acceleration on period spacings of gravito-inertial modes in intermediate-mass stars

The Kepler and TESS missions delivered high-precision, long-duration photometric time series for hundreds of main-sequence stars with gravito-inertial (g) pulsation modes. This high precision allows us to evaluate increasingly detailed theoretical stellar models. Recent theoretical work extended the traditional approximation of rotation (TAR), a framework to evaluate the effect of the Coriolis acceleration on g-modes, to include the effects of the centrifugal acceleration in the approximation of slightly deformed stars, which so far had mostly been neglected in asteroseismology. This extension of the TAR was conceived by rederiving the TAR in a centrifugally deformed, spheroidal coordinate system. We explore the effect of the centrifugal acceleration on g modes and assess its detectability in space-based photometry. We implement the new framework to calculate the centrifugal deformation of precomputed 1D spherical stellar structure models and compute the corresponding g-mode frequencies, assuming uniform rotation. The framework is evaluated for a grid of stellar structure models covering a relevant parameter space for observed g-mode pulsators. The centrifugal acceleration modifies the effect of the Coriolis acceleration on g modes, narrowing the equatorial band in which they are trapped. Furthermore, the centrifugal acceleration causes the pulsation periods and period spacings of the most common g modes (prograde dipole modes and r modes) to increase with values similar to the observational uncertainties in Kepler and TESS data. The effect of the centrifugal acceleration on g~modes is formally detectable in modern space photometry. Implementation of the new theoretical framework in stellar structure and pulsation codes will allow for more precise asteroseismic modelling of centrifugally deformed stars, to assess its effect on mode excitation, -trapping and -damping.

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arXiv2020

Probing the internal magnetism of stars using asymptotic magneto-asteroseismology

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.

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arXiv2020

Horizontal shear instabilities in rotating stellar radiation zones: II. Effects of the full Coriolis acceleration

Stellar interiors are the seat of efficient transport of angular momentum all along their evolution. Understanding the dependence of the turbulent transport triggered by the shear instabilities due to the differential rotation in stellar radiation zones is mandatory. Indeed, it constitutes one of the cornerstones of the rotational transport and mixing theory which is implemented in stellar evolution codes to predict the rotational and chemical evolutions of stars. We investigate horizontal shear instabilities in stellar radiation zones by considering the full Coriolis acceleration with both the dimensionless horizontal component $\tilde{f}$ and the vertical component $f$. We performed a linear stability analysis for a horizontal shear flow with a hyperbolic tangent profile, both numerically and asymptotically using the WKBJ approximation. As in the traditional approximation, we identified the inflectional and inertial instabilities. The inflectional instability is destabilized as $\tilde{f}$ increases and its maximum growth rate increases significantly, while the thermal diffusivity stabilizes the inflectional instability similarly to the traditional case. The inertial instability is also strongly affected; for instance, the inertially unstable regime is extended in the non-diffusive limit as $0<f<1+\tilde{f}^{2}/N^{2}$, where $N$ is the dimensionless Brunt-Väisälä frequency. More strikingly, in the high-thermal-diffusivity limit, it is always inertially unstable at any colatitude $θ$ except at the poles (i.e., $0^{\circ}<θ<180^{\circ}$). Using the asymptotic and numerical results, we propose a prescription for the effective turbulent viscosities induced by the instabilities to be possibly used in stellar evolution models. The characteristic time of this turbulence is short enough to redistribute efficiently angular momentum and mix chemicals in the radiation zones.

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arXiv2020

Detecting axisymmetric magnetic fields using gravity modes in intermediate-mass stars

Context: Angular momentum (AM) transport models of stellar interiors require improvements to explain the strong extraction of AM from stellar cores that is observed with asteroseismology. One of the often invoked mediators of AM transport are internal magnetic fields, even though their properties, observational signatures and influence on stellar evolution are largely unknown. Aims: We study how a fossil, axisymmetric internal magnetic field affects period spacing patterns of dipolar gravity mode oscillations in main-sequence stars with masses of 1.3, 2.0 and 3.0 M$_\odot$. We assess the influence of fundamental stellar parameters on the magnitude of pulsation mode frequency shifts. Methods: We compute dipolar gravity mode frequency shifts due to a fossil, axisymmetric poloidal-toroidal internal magnetic field for a grid of stellar evolution models, varying stellar fundamental parameters. Rigid rotation is taken into account using the traditional approximation of rotation and the influence of the magnetic field is computed using a perturbative approach. Results: We find magnetic signatures for dipolar gravity mode oscillations in terminal-age main-sequence stars that are measurable for a near-core field strength larger than $10^{5}$ G. The predicted signatures differ appreciably from those due to rotation. Conclusions: Our formalism demonstrates the potential for the future detection and characterization of strong fossil, axisymmetric internal magnetic fields in gravity-mode pulsators near the end of core-hydrogen burning from Kepler photometry, if such fields exist.

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arXiv2020

Period spacings of gravity modes in rapidly rotating magnetic stars II. The case of an oblique dipolar fossil magnetic field

Context. Stellar internal magnetic fields have recently been shown to leave a detectable signature on period spacing patterns of gravity modes. Aims. We investigate the effect of the obliquity of a mixed (poloidal and toroidal) dipolar internal fossil magnetic field with respect to the rotation axis on the frequency of gravity modes in rapidly rotating stars. Methods. We use the traditional approximation of rotation to compute non-magnetic modes, and a perturbative treatment of the magnetic field to compute the corresponding frequency shifts. We apply the new formalism to HD 43317, a magnetic, rapidly rotating, slowly pulsating B-type star, whose field has an obliquity angle of about 80°. Results. We find that frequency shifts induced by the magnetic field on high-radial-order gravity modes are larger with increasing obliquity angle, when the magnetic axis is closer to the equatorial region, where these modes are trapped. The maximum value is reached for an obliquity angle of 90°. This trend is observed for all mode geometries. Conclusions. Our results predict that the signature of an internal oblique dipolar magnetic field is detectable using asteroseismology of gravity modes.

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arXiv2020

Horizontal shear instabilities in rotating stellar radiation zones: I. Inflectional and inertial instabilities and the effects of thermal diffusion

Rotational mixing, the key process in stellar evolution, transports angular momentum and chemical elements in stellar radiative zones. In the past two decades, an emphasis has been placed on the turbulent transport induced by the vertical shear instability. However, instabilities arising from horizontal shear and the strength of the anisotropic turbulent transport that they may trigger remain relatively unexplored. This paper investigates the combined effects of stable stratification, rotation, and thermal diffusion on the horizontal shear instabilities in the context of stellar radiative zones. The eigenvalue problem describing linear instabilities of a flow with a hyperbolic-tangent horizontal shear profile was solved numerically for a wide range of parameters. As a first step, we consider a polar $f$-plane where the gravity and rotation vector are aligned. Two types of instabilities are identified: the inflectional and inertial instabilities. The inflectional instability that arises from the inflection point is the most unstable when at a zero vertical wavenumber and a finite wavenumber in the streamwise direction along the imposed-flow direction. The three-dimensional inflectional instability is destabilized by stratification, while it is stabilized by thermal diffusion. The inertial instability is rotationally driven, and a WKBJ analysis reveals that its growth rate reaches the maximum $\sqrt{f(1-f)}$ in the inviscid limit as the vertical wavenumber goes to infinity, where $f$ is the dimensionless Coriolis parameter. The inertial instability for a finite vertical wavenumber is stabilized as the stratification increases, whereas it is destabilized by the thermal diffusion. Furthermore, we found a self-similarity in both the inflectional and inertial instabilities based on the rescaled parameter $PeN^2$ with the Péclet number $Pe$ and the Brunt-Väisälä frequency $N$.

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arXiv2019

The Traditional Approximation of Rotation including the centrifugal acceleration for slightly deformed stars

The Traditional Approximation of Rotation (TAR) is a treatment of the dynamical equations of rotating stably stratified fluids where the action of the Coriolis acceleration along the direction of the entropy (and chemicals) stratification is neglected while assuming that the fluid motions are mostly horizontal because of their inhibition in the vertical direction by the buoyancy force. This leads to neglect the horizontal projection of the rotation vector in the equations for the dynamics of gravito-inertial waves (GIWs) that become separable as in the non-rotating case while they are not in the case with the full Coriolis acceleration. This approximation has been broadly applied in stellar (and planetary) astrophysics to study low-frequency GIWs. TAR is built on the assumptions that the star is spherical (i.e. its centrifugal deformation is neglected) and uniformly rotating while an adiabatic treatment of the dynamics of the waves is adopted. However, it has been recently generalised with including the effects of a differential rotation. We aim to do a new generalisation that takes into account the centrifugal acceleration in the case of moderately uniformly rotating deformed stars. As in the case of a differentially rotating spherical star, the problem becomes 2D but can be treated analytically if assuming the Cowling, anelastic and JWKB approximations, which are relevant for low-frequency GIWs. It allows us to derive a generalised Laplace tidal equation for the horizontal eigenfunctions and asymptotic wave periods that can be used to probe the structure and dynamics of rotating deformed stars thanks to asteroseismology. A first numerical exploration of its eigenvalues and horizontal eigenfunctions shows their variation as a function of the pseudo-radius for different rotation rates and frequencies and the development of avoided crossings.

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arXiv2018

Impact of general differential rotation on gravity waves in rapidly rotating stars

Differential rotation plays a key role in stellar evolution by triggering hydrodynamical instabilities and large-scale motions that induce transport of chemicals and angular momentum and by modifying the propagation and the frequency spectrum of gravito-inertial waves. It is thus crucial to investigate its effect on the propagation of gravity waves to build reliable seismic diagnostic tools, especially for fast rotating stars, where perturbative treatments of rotation fail. Generalising a previous work done in the case of uniform rotation, we derived a local dispersion relation for gravity waves in a differentially rotating star, taking the full effect of rotation (both Coriolis and centrifugal accelerations) into account. Then we modelled the propagation of axisymmetric waves as the propagation of rays. This allowed us to efficiently probe the properties of the waves in various regimes of differential rotation.

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arXiv2018

Waves in the radiative zones of rotating, magnetized stars

Asteroseismology has reached a level of accuracy that may allow us to detect the effect of a deep magnetic field on oscillation modes. We thus aim to develop an asymptotic theory for short-wavelength waves in radiative zones of rotating stars with a general magnetic field topology (toroidal and poloidal). A dispersion relation is derived for a uniformly rotating star with a low-amplitude, axisymmetric magnetic field. The parameter space of this model is explored with a Hamiltonian ray-tracing method. The features of the gravito-inertial waves modified by the magnetic field are studied with different magnetic topologies.

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arXiv2018

Anisotropic turbulent transport in stably stratified rotating stellar radiation zones

Rotation is one of the key physical mechanisms that deeply impact the evolution of stars. Helio- and asteroseismology reveal a strong extraction of angular momentum from stellar radiation zones over the whole Hertzsprung-Russell diagram. Turbulent transport in differentially rotating stably stratified stellar radiation zones should be carefully modeled and its strength evaluated. Stratification and rotation imply that this turbulent transport is anisotropic. Only phenomenological prescriptions have been proposed for the transport in the horizontal direction, which however constitutes a cornerstone in current theoretical formalisms for stellar hydrodynamics in evolution codes. We derive a new theoretical prescription for the anisotropy of the turbulent transport in radiation zones using a spectral formalism for turbulence that takes simultaneously stable stratification, rotation, and a radial shear into account. Then, the horizontal turbulent transport resulting from 3D turbulent motions sustained by the instability of the radial differential rotation is derived. We implement this framework in the stellar evolution code STAREVOL and quantify its impact on the rotational and structural evolution of low-mass stars from the pre-main-sequence to the red giant branch. The anisotropy of the turbulent transport scales as $N^4τ^2/\left(2Ω^2\right)$, $N$ and $Ω$ being the buoyancy and rotation frequencies respectively and $τ$ a time characterizing the source of turbulence. This leads to a horizontal turbulent transport of similar strength in average that those obtained with previously proposed prescriptions even if it can be locally larger below the convective envelope. As a consequence, a complementary transport mechanism like internal gravity waves or magnetic fields is still needed to explain the observed strong transport of angular momentum along stellar evolution.

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arXiv2018

Asymptotic theory of gravity modes in rotating stars II. Impact of general differential rotation

Context. Differential rotation has a strong influence on stellar internal dynamics and evolution, notably by triggering hydrodynamical instabilities, by interacting with the magnetic field, and more generally by inducing transport of angular momentum and chemical elements. Moreover, it modifies the way waves propagate in stellar interiors and thus the frequency spectrum of these waves, the regions they probe, and the transport they generate. Aims. We investigate the impact of a general differential rotation (both in radius and latitude) on the propagation of axisymmetric gravito-inertial waves. Methods. We use a small-wavelength approximation to obtain a local dispersion relation for these waves. We then describe the propagation of waves thanks to a ray model that follows a Hamiltonian formalism. Finally, we numerically probe the properties of these gravito-inertial rays for different regimes of radial and latitudinal differential rotation. Results. We derive a local dispersion relation that includes the effect of a general differential rotation. Subsequently, considering a polytropic stellar model, we observe that differential rotation allows for a large variety of resonant cavities that can be probed by gravito-inertial waves. We identify that for some regimes of frequency and differential rotation, the properties of gravito-inertial rays are similar to those found in the uniformly rotating case. Furthermore, we also find new regimes specific to differential rotation, where the dynamics of rays is chaotic. Conclusions. As a consequence, we expect modes to follow the same trend. Some parts of oscillation spectra corresponding to regimes similar to those of the uniformly rotating case would exhibit regular patterns, while parts corresponding to the new regimes would be mostly constituted of chaotic modes with a spectrum rather characterised by a generic statistical distribution.

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arXiv2016

Period spacing of gravity modes strongly affected by rotation. Going beyond the traditional approximation

Context. As of today, asteroseismology mainly allows us to probe the internal rotation of stars when modes are only weakly affected by rotation using perturbative methods. Such methods cannot be applied to rapidly rotating stars, which exhibit complex oscillation spectra. In this context, the so-called traditional approximation, which neglects the terms associated with the latitudinal component of the rotation vector, describes modes that are strongly affected by rotation. This approximation is sometimes used for interpreting asteroseismic data, however, its domain of validity is not established yet. Aims. We aim at deriving analytical prescriptions for period spacings of low-frequency gravity modes strongly affected by rotation through the full Coriolis acceleration, which can be used to probe stellar internal structure and rotation. Methods. We approximated the asymptotic theory of gravito-inertial waves in uniformly rotating stars using ray theory described in a previous paper in the low-frequency regime, where waves are trapped near the equatorial plane. We put the equations of ray dynamics into a separable form and used the EBK quantisation method to compute modes frequencies from rays. Results. Two spectral patterns that depend on stratification and rotation are predicted within this new approximation: one for axisymmetric modes and one for non-axisymmetric modes. Conclusions. The detection of the predicted patterns in observed oscillation spectra would give constraints on internal rotation and chemical stratification of rapidly rotating stars exhibiting gravity modes, such as $γ$ Doradus, SPB, or Be stars. The obtained results have a mathematical form that is similar to that of the traditional approximation, but the new approximation takes the full Coriolis, which allows for propagation near the centre, and centrifugal accelerations into account.

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arXiv2016

Seismic diagnosis from gravity modes strongly affected by rotation

Most of the information we have about the internal rotation of stars comes from modes that are weakly affected by rotation, for example by using rotational splittings. In contrast, we present here a method, based on the asymptotic theory of Prat et al. (2016), which allows us to analyse the signature of rotation where its effect is the most important, that is in low-frequency gravity modes that are strongly affected by rotation. For such modes, we predict two spectral patterns that could be confronted to observed spectra and those computed using fully two-dimensional oscillation codes.

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arXiv2016

Shear mixing in stellar radiative zones - II. Robustness of numerical simulations

Recent numerical simulations suggest that the model by Zahn (1992, A&A, 265, 115) for the turbulent mixing of chemical elements due to differential rotation in stellar radiative zones is valid. We investigate the robustness of this result with respect to the numerical configuration and Reynolds number of the flow. We compare results from simulations performed with two different numerical codes, including one that uses the shearing-box formalism. We also extensively study the dependence of the turbulent diffusion coefficient on the turbulent Reynolds number. The two numerical codes used in this study give consistent results. The turbulent diffusion coefficient is independent of the size of the numerical domain if at least three large turbulent structures fit in the box. Generally, the turbulent diffusion coefficient depends on the turbulent Reynolds number. However, our simulations suggest that an asymptotic regime is obtained when the turbulent Reynolds number is larger than $10^3$. Shear mixing in the regime of small Péclet numbers can be investigated numerically both with shearing-box simulations and simulations using explicit forcing. Our results suggest that Zahn's model is valid at large turbulent Reynolds numbers.

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arXiv2016

On the relevance of bubbles and potential flows for stellar convection

Recently Pasetto et al. have proposed a new method to derive a convection theory appropriate for the implementation in stellar evolution codes. Their approach is based on the simple physical picture of spherical bubbles moving within a potential flow in dynamically unstable regions, and a detailed computation of the bubble dynamics. Based on this approach the authors derive a new theory of convection which is claimed to be parameter free, non-local and time-dependent. This is a very strong claim, as such a theory is the holy grail of stellar physics. Unfortunately we have identified several distinct problems in the derivation which ultimately render their theory inapplicable to any physical regime. In addition we show that the framework of spherical bubbles in potential flows is unable to capture the essence of stellar convection, even when equations are derived correctly.

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