In γ Doradus stars, gravito-inertial modes in the radiative zone and inertial modes in the convective core can interact resonantly, which translates into the appearance of dip structures in the period spacing of modes. Those dips are information-rich, as they are related to the star core characteristics. Our aim is to characterise these dips according to stellar properties and thus to develop new seismic diagnostic tools to constrain the internal structure of γ Doradus stars, especially their cores. We used the two-dimensional oscillation code TOP to compute sectoral prograde and axisymmetric dipolar modes in γ Doradus stars at different rotation rates and evolutionary stages. We then characterised the dips we obtained by their width and location on the period spacing diagram. We found that the width and the location of the dips depend quasi-linearly on the ratio of the rotation rate and the Brunt-Väisälä frequency at the core interface. This allowed us to determine empirical relations between the width and location of dips as well as the resonant inertial mode frequency in the core and the Brunt-Väisälä frequency at the interface between the convective core and the radiative zone. We propose an approximate theoretical model to support and discuss these empirical relations. The empirical relations we established could be applied to dips observed in data, which would allow for the estimation of frequencies of resonant inertial modes in the core and of the Brunt-Väisälä jump at the interface between the core and the radiative zone. As those two parameters are both related to the evolutionary stage of the star, their determination could lead to more accurate estimations of stellar ages.
Gamma Doradus stars present an incredibly rich pulsation spectra, with gravito-inertial modes, in some cases supplemented with delta Scuti-like pressure modes and in numerous cases with Rossby modes. The present paper aims at showing that, in addition to these modes established in the radiative envelope, pure inertial modes, trapped in the convective core, can be detected in Kepler observations of gamma Doradus stars, thanks to their resonance with the gravito-inertial modes. We start by using a simplified model of perturbations in a full sphere of uniform density. Under these conditions, the …
The asteroseismic modelling of period spacing patterns from gravito-inertial modes in stars with a convective core is a high-dimensional problem. We utilise the measured period spacing pattern of prograde dipole gravity modes (acquiring $Π_0$), in combination with the effective temperature ($T_{\rm eff}$) and surface gravity ($\log g$) derived from spectroscopy, to estimate the fundamental stellar parameters and core properties of 37 $γ~$Doradus ($γ~$Dor) stars whose rotation frequency has been derived from $\textit{Kepler}$ photometry. We make use of two 6D grids of stellar models, one with s…
Recent asteroseismic observations by the $\it Kepler$ space mission have revealed the dip fine structure in the period-spacing versus period diagram of rapidly rotating $γ$ Doradus stars. Following the successful reproduction of the dip structure by numerical calculations in previous studies, we present in this paper the physical mechanism of how the dip is formed as a result of the interaction between the gravito-inertial waves in the radiative envelope and the pure inertial waves in the convective core. We analytically describe the wave solutions in both of the radiative envelope and the con…
$γ$ Doradus is the prototype star for the eponymous class of pulsating stars that consists of late A-early F main-sequence stars oscillating in low-frequency gravito-inertial modes. Being among the brightest stars of its kind (V = 4.2), $γ$ Dor benefits from a large set of observational data that has been recently completed by high-quality space photometry from the TESS mission. With these new data, we propose to study $γ$ Dor as an example of possibilities offered by synergies between multi-technical ground and space-based observations. Here, we present the preliminary results of our investig…
CONTEXT. Gamma Doradus stars (hereafter gamma Dor stars) are known to exhibit gravity- and/or gravito-intertial modes that probe the inner stellar region near the convective core boundary. The non-equidistant spacing of the pulsation periods is an observational signature of the stars' evolution and current internal structure and is heavily influenced by rotation. AIMS. We aim to constrain the near-core rotation rates for a sample of gamma Dor stars, for which we have detected period spacing patterns. METHODS. We combined the asymptotic period spacing with the traditional approximation of stell…
Aims: We investigate the thermal and chemical structure in the near-core region of stars with a convective core by means of gravito-inertial modes. We do so by determining the probing power of different asteroseismic observables and fitting methodologies. We focus on the case of the B-type star KIC$\,$7760680, rotating at a quarter of its critical rotation velocity. Methods: We compute grids of 1D stellar structure and evolution models for two different prescriptions of the temperature gradient and mixing profile in the near-core region. We determine which of these prescriptions is preferred a…
The gravito-inertial waves propagating over a shellular baroclinic flow inside a rotating spherical shell are analysed using the Boussinesq approximation. The wave properties are examined by computing paths of characteristics in the non-dissipative limit, and by solving the full dissipative eigenvalue problem using a high-resolution spectral method. Gravito-inertial waves are found to obey a mixed-type second-order operator and to be often focused around short-period attractors of characteristics or trapped in a wedge formed by turning surfaces and boundaries. We also find eigenmodes that show…
While many intermediate- and high-mass main sequence stars are rapidly and differentially rotating, the effects of rotation on oscillation modes are poorly known. In this communication we present a first study of axisymmetric gravito-inertial modes in the radiative zone of a differentially rotating star. We consider a simplified model where the radiative zone of the star is a linearly stratified rotating fluid within a spherical shell, with differential rotation due to baroclinic effects. We solve the eigenvalue problem with high-resolution spectral computations and determine the propagation d…
Core-envelope coupling of gravito-inertial waves in pre-main-sequence solar-type stars
INAF – Osservatorio Astrofisico di Catania（意大利国家天体物理研究所卡塔尼亚天文台）；STAR Institute, Université de Liège（列日大学STAR研究所）；Université Paris-Saclay, Université Paris Cité, CEA, CNRS, AIM（巴黎萨克雷大学、巴黎西岱大学、法国原子能和替代能源委员会、法国国家科学研究中心、天体物理学和分子生物学研究所）；Institute of Science and Technology Austria (ISTA)（奥地利科学与技术研究所）；INAF – IAPS, Istituto di Astrofisica e Planetologia Spaziali（意大利国家天体物理研究所空间天体物理学和行星学研究所）；Universität Innsbruck, Institut für Astro- und Teilchenphysik（因斯布鲁克大学天体与粒子物理研究所）
Gravity waves (or their signatures) are detected in stars thanks to helio- and asteroseismology and they may play an important role in the evolution of stellar angular momentum. Moreover, the observational study of the CoRoT target HD51452 by Neiner and collaborators demonstrated the potential strong impact of rotation on the stochastic excitation of gravito-inertial waves in stellar interiors. Our goal is to explore the action of rotation on the stochastic excitation of gravity and gravito-inertial waves in stars. The dynamics of gravito-inertial waves in stellar interiors, both in radiation …
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…
Context. OB stars are important building blocks of the Universe, but we have only a limited sample of them well understood enough from an asteroseismological point of view to provide feedback on the current evolutionary models. Our study adds one special case to this sample, with more observational constraints than for most of these stars. Aims. Our goal is to analyse and interpret the pulsational behaviour of the B3 IV star HD 43317 using the CoRoT light curve along with the ground-based spectroscopy gathered by the Harps instrument. This way we continue our efforts to map the Beta Cep and SP…
Context. The seismology of early-type stars is limited by our incomplete understanding of gravito-inertial modes. Aims. We develop a short-wavelength asymptotic analysis for gravito-inertial modes in rotating stars. Methods. The Wentzel-Kramers-Brillouin approximation was applied to the equations governing adiabatic small perturbations about a model of a uniformly rotating barotropic star. Results. A general eikonal equation, including the effect of the centrifugal deformation, is derived. The dynamics of axisymmetric gravito-inertial rays is solved numerically for polytropic stellar models of…
Gravito-inertial waves can be excited at the interface of convective and radiative regions and by the Reynolds stresses in the bulk of the convection zone. The magnitude of their energy flux will therefore vary with the properties of the convection. To assess how convection changes with rotation, a simplified local monomodal model for rotating convection is presented that provides the magnitude of the rms velocity, degree of superadiabaticity, and characteristic length scale as a function of the convective Rossby number as well as with thermal and viscous diffusivities. In the context of this …
Oscillations have been detected in a variety of stars, including intermediate- and high-mass main sequence stars. While many of these stars are rapidly and differentially rotating, the effects of rotation on oscillation modes are poorly known. In this communication we present a first study on axisymmetric gravito-inertial modes in the radiative zone of a differentially rotating star. These modes probe the deep layers of the star around its convective core. We consider a simplified model where the radiative zone of a star is a linearly stratified rotating fluid within a spherical shell, with di…
Non-linear saturation of gravito-inertial modes excited by tidal resonances in binary neutron stars
Max Planck Institute for Gravitational Physics (Albert Einstein Institute)（马克斯·普朗克引力物理研究所（爱因斯坦研究所））；University of Leeds（利兹大学）；Universitat d’Alacant（阿利坎特大学）；University of Tübingen（蒂宾根大学）
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…
Gravito-inertial waves are excited at the interface of convective and radiative regions and by the Reynolds stresses in the bulk of the convection zones of rotating stars and planets. Such waves have notable asteroseismic signatures in the frequency spectra of rotating stars, particularly among rapidly rotating early-type stars, which provides a means of probing their internal structure and dynamics. They can also transport angular momentum, chemical species, and energy from the excitation region to where they dissipate in radiative regions. To estimate the excitation and convective parameter …
Context. While rotation has a major impact on stellar structure and evolution, its effects are not well understood. Thanks to high- quality and long timebase photometric observations obtained with recent space missions, we are now able to study stellar rotation more precisely. Aims. We aim to constrain radial differential rotation profiles in gamma Doradus (gamma Dor) stars, and to develop new theoretical seismic diagnosis for such stars with rapid and potentially non-uniform rotation. Methods. We derive a new asymptotic description which accounts for the impact of weak differential near-core …
Stochastic gravity waves have been recently detected and characterised in stars thanks to space asteroseismology and they may play an important role in the evolution of stellar angular momentum. In this context, the observational study of the CoRoT hot Be star HD 51452 suggests a potentially strong impact of rotation on stochastic excitation of gravito-inertial waves in rapidly rotating stars. In this work, we present our results on the action of the Coriolis acceleration on stochastic wave excitation by turbulent convection. We study the change of efficiency of this mechanism as a function of…
Context: Rapid rotation is a common feature of early-type stars but which remains a challenge for the models. The understanding of its effect on stellar evolution is however imperative to interpret the observed properties of numerous stars. Aims: We wish to bring more observational constraints on the properties of fast rotating stars, especially on their oscillation modes. Methods: We focus on the nearby star Altair which is known as a very rapidly rotating star with an equatorial velocity estimated recently at 313 km/s. We observed this star with the high-resolution spectropolarimeter Neo-Nar…
A compact binary system implicating at least one rotating neutron star undergoes gravitomagnetic tidal resonances as it inspirals toward its final merger. These have a dynamical impact on the phasing of the emitted gravitational waves. The resonances are produced by the inertial modes of vibration of the rotating star. Four distinct modes are involved, and the resonances occur within the frequency band of interferometric gravitational-wave detectors when the star spins at a frequency that lies within this band. The resonances are driven by the gravitomagnetic tidal field created by the compani…
Very high precision seismic space missions such as CoRoT and Kepler provide the means for testing the modelling of transport processes in stellar interiors. For some stars, such as $δ$ Scuti $γ$ Doradus and Be stars, for instance, the observed pulsation spectra are modified by rotation to such an extent that it prevents any fruitful interpretation. Our aim is to characterise acoustic pulsation spectra of realistic stellar models in order to be able to interpret asteroseismic data from such stars. The 2-dimensional oscillation code ACOR, which treats rotation in a non-perturbative manner, is us…
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 dif…
Multi-dimensional (magneto-)hydrodynamical simulations of physical processes in stellar interiors depend on a multitude of uncalibrated free parameters, which set the spatial and time scales of their computations. We aim to provide an asteroseismic calibration of the wave and convective Rossby numbers, and of the stiffness at the interface between the convective core and radiative envelope of intermediate-mass stars. We deduce these quantities for rotating dwarfs from the observed properties of their identified gravity and gravito-inertial modes. We rely on near-core rotation rates and asteros…
HD49330 is a Be star that underwent an outburst during its five-month observation with the CoRoT satellite. An analysis of its light curve revealed several independent p and g pulsation modes, in addition to showing that the amplitude of the modes is directly correlated with the outburst. We modelled the results obtained with CoRoT. We modelled the flattening of the structure of the star due to rapid rotation in two ways: Chandrasekhar-Milne's expansion and 2D structure computed with ROTORC. We then modelled kappa-driven pulsations. We also adapted the formalism of the excitation and amplitude…
Inferring main-sequence stage and buoyancy-glitch amplitudes from Fourier spectra of gravity-mode period spacings: Ensemble Analysis of 26 Slowly Pulsating B Stars
The Be phenomenon, that is the ejection of matter from Be stars into a circumstellar disk, has been a long lasting mystery. In the last few years, the CoRoT (Convection, Rotation and planetary Transits) satellite brought clear evidence that Be outbursts are directly correlated with pulsations. We found that it may be the transport of angular momentum by waves or pulsation modes that brings the already rapid stellar rotation to its critical value at the surface, and allows the star to eject material. The recent discovery of stochastically excited gravito-inertial modes by CoRoT in a hot Be star…
A major uncertainty in the theory of stellar evolution is the angular momentum distribution inside stars and its change during stellar life. We compose a sample of 67 stars in the core-hydrogen burning phase with a $\log\,g$ value from high-resolution spectroscopy, as well as an asteroseismic estimate of the near-core rotation rate derived from gravity-mode oscillations detected in space photometry. This assembly includes 8 B-type stars and 59 AF-type stars, covering a mass range from 1.4 to 5\,M$_\odot$, i.e., it concerns intermediate-mass stars born with a well-developed convective core. The…
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 establish…
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 axi…
We present the CoRoT light curve of the bright B2.5V star HD 48977 observed during a short run of the mission in 2008, as well as a high-resolution spectrum gathered with the HERMES spectrograph at the Mercator telescope. We use several time series analysis tools to explore the nature of the variations present in the light curve. We perform a detailed analysis of the spectrum of the star to determine its fundamental parameters and its element abundances. We find a large number of high-order g-modes, and one rotationally induced frequency. We find stable low-amplitude frequencies in the p-mode …
We study low frequency waves that propagate in a region of layered semi-convection. Layered semi-convection is predicted to be present in stellar and planetary interiors and can significantly modify the rate of thermal and compositional mixing. We derive a series of analytical dispersion relations for plane-parallel layered semi-convection in the Boussinesq approximation using a matrix transfer formalism. We find that like a continuously stratified medium, a semi-convective staircase -- in which small convective regions are separated by sharp density jumps -- supports internal gravity waves (g…
