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Stars: dynamical Processes driving tidal Interactions, Rotation and Evolution

Periodic Reporting for period 3 - SPIRE (Stars: dynamical Processes driving tidal Interactions, Rotation and Evolution)

Reporting period: 2018-09-01 to 2020-02-29

Stars are dynamical objects: they are rotating, magnetic, turbulent, pulsating, and they strongly impact their environment because of their winds and tides. This dynamics drastically affects their evolution, the evolution of their surrounding planetary systems and the conditions for the emergence of life, and galactic evolution. In this context, our knowledge of stellar interiors, rotation, and magnetism has undergone a revolution thanks to helio- and astero-seismology (with SOHO, CoRoT and Kepler/K2) and ground-based spectropolarimetry (ESPaDOnS/CFHT, Narval/TBL, HARPSpol/ESO). For example, helio- and asteroseismology revealed, e.g. that the core of the Sun is close to a uniform rotation until 20% of its radius while those of subgiant and red giant stars slow down drastically during their evolution. These important results demonstrate that powerful dynamical mechanisms (internal waves, turbulence, magnetic fields) are in action to extract angular momentum all along the evolution of stars.

Simultaneously, since the discovery of the first extrasolar planetary system in 1995 by Mayor & Queloz, a large diversity of planetary systems orbiting various types of stars has been discovered both from the ground (e.g. HARPS and WASP surveys) and from space (CoRoT, Kepler/K2) bringing the problematic of star-planet interactions on the forefront of academic research. Simultaneously, a large population of multiple stars has been discovered that provide key constraints on the structure and the evolution of stars. These groundbreaking discoveries have opened a golden age for the integrated study of the dynamics of stars and their environment with the selected/forthcoming new space and ground-based facilities among which CHEOPS (ESA), TESS (NASA), SPIRou (CFHT), JWST (NASA), PLATO (ESA), ARIEL (ESA), and E-ELT (ESO). It put the urgency to progress on our understanding of star-planet and star-star interactions: highly complex dynamical processes leading to tidal dissipation in stars and planets play a key role to shape the orbital architecture of planetary and stellar systems and they may deeply modify their evolution.

To interpret these observational breakthroughs, it is necessary to develop now new frontier theoretical and numerical long-term evolution models of rotating magnetic stars and of their systems. The key questions to address are:
- For a given evolutionary stage, which dynamical processes drive the rotational evolution of stars?
- How does this dynamical evolution impact their chemical properties and magnetic activity?
- How does tidal interactions vary as a function of stellar mass and evolutionary stage?
- What is the respective strength and impact of tidal and magnetic interactions in stellar systems along the evolution of their host star(s)?
- How do the orbital architecture (and habitable zone) change along the host star’s evolution?
- How do the evolution of stars with companions differ from those of single stars?

To reach this ambitious objective, the SPIRE project develop new groundbreaking equations, prescriptions, and scaling laws that describe coherently all dynamical mechanisms that transport angular momentum (and chemicals) in stars and drive tidal dissipation in stellar and planetary interiors using advanced semi-analytical modeling and numerical simulations. They will be implemented in the new generation dynamical stellar evolution code STAREVOL and secular orbital/rotational evolution code ESPEM (Planetary System Evolution and Magnetism). This will allow us to provide state-of-the-art ab-initio integrated and coupled models for the long-term evolution of stars and of their systems, which cannot be directly simulated in 3D yet.
SPIRE will thus provide key inputs for the whole astrophysical community: understanding the dynamics of stars is a fundamental step to understand our Universe.
The SPIRE project aims to understand the dynamical processes driving the rotational evolution of stars and the dynamics of the orbital architecture of stellar/planetary systems along the evolution of the host star(s).
To reach these objectives, it is structured around two tasks:
- Task I (TI) devoted to the dynamical evolution of rotating magnetic stars;
- Task II (TII) devoted to the study of tides and integrated evolution of stellar systems.

TI: Dynamical evolution of rotating magnetic stars

We are studying in a systematic way the physical mechanisms able to transport angular momentum in convectively stable stellar radiation zones that drive the secular rotational and chemical evolutions of stars. These mechanisms strongly impact the magnetism of stars and their interactions with their environment studied in Task II.

First, we have built new 2D local and global models for the transport of angular momentum by waves driven by buoyancy and the rotation of the star through the Coriolis acceleration, the so-called gravito-inertial waves. We take into account simultaneously buoyancy, all the components of the Coriolis and centrifugal accelerations, and radial and latitudinal differential rotation. The models allow us for the first time to treat every possible hierarchy of these four different processes without any a-priori. We have computed the properties of the waves propagation and dissipation and related prescriptions for the transport of angular momentum, heat and chemicals they induce. In addition, these models also allow us to develop new seismic diagnosis for rapidly, potentially differentially, rotating stars to get important constrains on their rotation profile and chemical stratification.
We are now working on the effects of general axi- and non-axisymmetric magnetic fields on stellar waves propagation, dissipation, and induced transport of angular momentum. This constitutes one of the key objectives of the second period of the project.

To properly evaluate the amplitude of the transport of angular momentum by waves in stellar radiation zones, we have to compute the strength of their excitation by adjacent convective regions. To reach this goal, we are first developing new 3D nonlinear global numerical simulations of the stochastic excitation of gravito-inertial waves by turbulent convective cores. This will allow us to get mandatory information on their amplitude and on their frequency spectrum as a function of key stellar parameters such as rotation. In addition, we have developed a new mixing-length theory for turbulent convection in rotating stars where we have taken into account both viscous and heat diffusions. It allows us to evaluate the depth of convective penetration (i.e. of undershooting below a convective envelope and of overshooting at the top of a convective core) and the variation of the amplitude of stochastically excited gravito-inertial waves as a function of stellar rotation. These results are of crucial importance since the rotation of stars strongly varies all along their evolution while its impact on convection and waves is completely ignored in current stellar evolution models.

Next, we have established a new theoretical framework to describe shear-induced turbulent transport in stellar radiation zones. Because of the combined action of stable stratification and rotation, this transport is highly anisotropic: the restoring forces for vertical and horizontal turbulent motions are buoyancy and the Coriolis acceleration, respectively. For the first time, we derive a prescription for the anisotropy of the turbulent transport of momentum and chemicals taking into account coherently the simultaneous action of these two forces. This allows us to compute a new turbulent transport coefficient that models the transport by turbulent motions generated by the instability of a vertical shear in the horizontal directions. This new theoretical prescription has been implemented in the dynamical stellar evolution code STAREVOL. This allows us to predict a potentially more efficient horizontal transport in the radiative core of low-mass stars. We are now working on instabilities of horizontal shears.

We also studied the magnetism of rotating stellar radiation zones. First, we examined the impact of rotation on their formation mechanism, the so-called turbulent relaxation, which is also studied in plasma physics experiments. This turbulent relaxation takes place just after the birth of a given stellar radiation zone, when a magnetic field generated by a previous convective phase, adjusts its configuration during the transition from a fully-developed convective turbulence to a stably stratified decaying turbulent state. We demonstrate that the horizontal geometry of the field is only weakly affected by rotation, in agreement with the observations. Moreover, rotation drives zonal and meridional flows. We also demonstrated that rotation affects the existence and stability of fossil equilibrium magnetic configurations.
Next, we have derived a new theoretical method and built the corresponding spectral numerical code allowing us to study for the first time the stability of general non-axisymmetric magnetic configurations in stellar radiation zones as those observed at the surface of early-type stars. We are now exploring the stability of these magnetic configurations with different field strengths and inclinations relatively to the rotation axis of the star.
Finally, we derived new theoretical scaling laws to evaluate the amplitude of dynamo-generated magnetic fields in the convective zones of stars as a function of their mass, age and rotation. They have been compared and validated with high-resolution 3D nonlinear global numerical simulations of stellar dynamos.

Then, we have built new 2D models of stellar radiation zones with adjacent differentially rotating convective regions. We consider the cases of the radiative cores of low-mass stars, of the radiative envelopes of early-type stars, and of sandwiched radiation zone in F-type stars. We identified the competition between the spin-up flows driven by the convectively driven shear imposed at convection/radiation boundaries, the thermal-wind driven by the stable stratification, and the Stewartson layers due to the presence of a convective core in the case of intermediate-mass and massive stars. The predicted 2D differential rotations have been compared in each case to observed rotation profiles in the different types of stars. This allows us to unravel in 2D the need for supplementary physical mechanisms to transport angular momentum both in the radial and latitudinal directions in solar-type stars and to identify the potential key role of Stewartson layers for the transport of angular momentum in stars, which have a convective core.

At each step, new theoretical prescriptions and numerical scaling laws are implemented in the dynamical stellar evolution code STAREVOL and new grids of stellar models are computed.
Until now, we have completely implemented:
- The new prescriptions for the anisotropic turbulent transport of angular momentum and chemicals in rotating stably stratified stellar radiation zones;
- The new ab-initio model for the dissipation of tidal inertial waves in the rotating convective envelope of low-mass stars (from M- to F-types) developed in Task II. We have computed corresponding complete stellar grids as a function of stellar mass, metallicity, age, and rotation.

All these results have allowed the team to provide relevant theoretical interpretation for the properties of stars that have been observed and characterised using asteroseismology with Kepler/K2 and spectropolarimetry with ESPaDOnS@CFHT, NARVAL@TBL (Pic-du-Midi, France) and HARPS-pol@ESO.

TII: Tides and integrated evolution of stellar systems

We study in a systematic way tidal waves propagating in stars hosting planetary systems or in multiple stars, both in their convective and radiative regions. This allows us to identify the important physical mechanisms for the dissipation of their energy that shape the orbital architecture of short-period systems and impact the evolution of the rotation of their components. Simultaneously, we study tidal dissipation in the interiors of planets of different types from super-Earths to gaseous giant planets. This strategy is aimed to obtain in the project all the building blocks necessary to elaborate the new generation of secular evolution models of star-planet systems needed to accompany the numerous new discoveries of exoplanetary worlds. This provides to the community the theoretical support mandatory to ensure the best scientific exploitation of current and forthcoming space missions and ground based instruments (e.g. Kepler/K2, CHEOPS, TESS, SPIRou, JWST, PLATO, ARIEL, etc.).

First, we have studied the dissipation of tidal inertial waves in stellar convection zones using semi-analytical methods and 2D hydrodynamical numerical simulations in synergies. They are driven by the rotation of the stars, through the Coriolis acceleration. We examined for the first time the impact of conical latitudinal differential rotations (with equatorial acceleration or deceleration) that correspond to rotation profiles observed in the Sun and in low-mass stars. We have showed how differential rotation modifies the frequencies and the regions of propagation of the waves. We also identified the key role played by critical layers, where resonances occur. There, energy and angular momentum is transferred from tidal waves to mean flows and tidal dissipation is enhanced when compared to the case of uniform rotation. We are now developing new simplified Cartesian and equatorial models to precisely understand their behaviors.
Next, we examined the impact of rotation on convection and on the turbulent friction it applies on tidal waves propagating in stellar (and planetary) convective regions. Because, rotation decreases the efficiency of the transport of heat by turbulent convective flows, the strength of the effective eddy-viscosity applied on tidal waves is diminished. The amplitude of the resonances between tidal inertial waves and the tidal forcing then becomes much higher but their width much sharper with potential important consequences for the evolution of orbiting short-period planets (or moons in the case of giant planets).
We also compute new and complete grids of the tidal dissipation driven by inertial waves in the convective envelope of low-mass stars (from M- to F-type stars) as a function of stellar mass, metallicity, age and uniform rotation using the dynamical stellar evolution code STAREVOL. They are used to build new models for the secular orbital and rotational evolutions of stellar/planetary systems.
Finally, the study of the effects of stellar dynamo-generated magnetic fields on tidal inertial waves that thus become magneto-inertial waves has been undertaken. We have obtained as a first important result that magnetic fields should be taken into account all along the evolution of low-mass stars to get a complete evaluation of tidal dissipation in their convective envelope.

Next, all the studies undertaken on (magneto-)gravito-inertial waves propagating in differentially rotating stellar radiation zones in the first task and the theoretical and numerical developments made for stellar convection zones allows us to be ready during the second half of the project to study in a systematic way their dissipation. In addition, we developed a new theoretical model of the nonlinear breaking of tidal internal gravity waves in stellar radiation zones. This model allowed us to derive a new prescription for the dissipation of high amplitude tidal gravity waves that break in stars hosting massive companions.

Then, we developed new ab-initio models for the dissipation of tidal waves propagating in the gaseous envelope of giant planets and the atmospheres and oceans of super-Earths.
In the case of giant planets, we first showed how tidal dissipation in Saturn (and in giant gaseous planets of the Solar system) is strongest than what was predicted thanks to scenarios for the formation and tidal evolution of their systems. Then, we studied for the first time the impact of the presence of heavy elements in their deep convective envelope that leads to the formation of stably stratified interfaces. Tidal inertial waves propagating in a fully convective envelope are then strongly modified and new families of tidal waves are excited such as tidal gravito-inertial and interfacial waves. This strongly affects tidal dissipation, which is increased, making the layered convection a good candidate to explain the high tidal dissipation observed in giant planets. Thanks to progresses obtained in the stellar case on the effects of differential rotation on tidal dissipation, its impact will also be evaluated in the case of giant planets during the second half of the project. We will take advantage of the new observational constrains obtained in the case of Jupiter by the JUNO space mission (NASA).
In the case of super-Earths, we studied tidal waves propagating in their potential atmosphere that are excited by the irradiation by their host stars. These thermal atmospheric tides can exert a torque on the planet that competes with the one applied on the telluric core and lead to asynchronous rotation. We recall that the rotation of super-Earths is a key physical parameter for their potential habitability. It impacts the length of the day, the climate and seasons, and the generation of a magnetic field that can protect the planet from stellar winds thanks to the magnetosphere it sustains. We generalized the state-of-the-art 3D semi-analytical modeling of thermal tides, which was first developed for the case of the Earth, to the case of slowly rotating planets close to the synchronization. This configuration is the one of Venus in the solar system and of telluric exoplanets orbiting in the habitable zone of low-mass stars. We took into account heat dissipation, which was until now neglected. We demonstrated that convective atmospheres are the seat of a strong atmospheric tidal torque leading to an asynchronous rotation while in convectively stable atmospheres the atmospheric torque is inhibited leading to a synchronous rotation. This prediction will benefit in a near future of observational constrains that will be provided by the JWST (NASA) and ARIEL (NASA). Indeed, these space missions will be able to probe the atmospheres of exoplanets and their stability at different depths.
In addition, we have developed a new 3D semi-analytical model for the dissipation of tides in potentially thick global oceans at the surface of telluric exoplanets. This study is strongly motivated by the case of the Earth, where oceans are the seat of ~90% of the tidal dissipation that drives the evolution of the Earth-Moon system. We provided for the first time a complete evaluation of the variation of the tidal dissipation in oceans as a function of their thickness and stratification, of the effective friction applied on tidal gravito-inertial waves, and of the rotation of the planet.

Finally, we have developed new models for the secular evolution of the orbital architecture of star-planets systems and of the rotation of their components. We have first implemented new ab-initio models of the dissipation of tidal inertial waves in the convective envelope of low-mass stars, which is computed in this task. Specifically, we take into account the evolution of the frequency-averaged dissipation as a function of the mass, the metallicity, the age and the rotation of stars. This allowed us to demonstrate how ab-initio tidal models lead to very different predictions for the evolution of the orbital architecture of planetary systems and their final states that those predicted using simplified constant tidal dissipation models. For instance, with tidal dissipation du
In each task, our objective is to achieve the best semi-analytical and numerical modeling of dynamical processes in stellar interiors that impact the evolution of stars and of their surrounding systems on secular timescales. However, it is not yet possible to compute directly this long-term evolution in 3D, taking all the needed space scales related to often highly non-axisymmetric and non-linear short timescale MHD phenomena into account. We thus model the action of each dynamical process and of its couplings developing new advanced semi-analytical methods and high-resolution numerical simulations to derive cutting-edge original equations, prescriptions, and scaling laws for secular timescales. They are implemented in the dynamical stellar evolution code STAREVOL and the secular orbital/rotational evolution code ESPEM we are developing and that are used to model observed stars and their systems, leading to a direct confrontation of the predictions of our modeling with the observables (e.g. the differential rotation in stars obtained thanks to asteroseismology, the orbital properties of star-planet and multiple star systems, the relative inclination of stellar spins and the orbits, etc.).

By construction, the SPIRE project builds the needed completely new generation of dynamical models of stars and their environment taking into account coherently the impact of MHD transport and tidal dissipation mechanisms in stellar (and planetary) interiors on their long-term evolution. Therefore, SPIRE has a strong impact on stellar physics (for single and multiple stars) and provides key groundbreaking results, for instance the value of the tidal dissipation in stars of different masses and evolutionary stages, for the studies of star-planet interactions. It also strongly contributes to change the paradigm of the study of stellar systems where the host star’s evolution and the orbital architecture dynamics have been treated separately until now. In this context, it benefits from the best observational constraints obtained by the most advanced space missions and ground-based instrumentation devoted to explore stellar systems all along the project (K2, and soon CHEOPS, TESS, SPIRou, JWST). The SPIRE project also contributes significantly to the scientific preparation of PLATO for the modeling of single and multiple stars and star-planet interactions. SPIRE thus proposes and provides a new framework for the interpretation of current and forthcoming observational programs and actively contributes to develop and put its topics in the forefront of academic research.
Because of the different physical processes it studies, the SPIRE project also contributes to the state-of-the-art in astrophysical (and geophysical) fluid dynamics, in fundamental fluid mechanics, in plasma physics and in numerical astrophysics.

From the societal point of view, it addresses key questions on the impact of the dynamics of stellar/planetary systems on planetary habitability and the conditions for the emergence of life. This provides key assets to understand the properties and the history of our Sun-Earth and solar systems in the broader context provided by exoplanetary systems.

In this framework, it participates to the efforts to strengthen the European position in this research field by training a new generation of stellar and planetary physicists working on the dynamics of stars, of exoplanets, and of their environment, which constitute an essential research field of modern Astronomy and Astrophysics.
The results obtained within the project are disseminated through peer-reviewed publications in international scientific journals, participation to international scientific conferences, lectures given by the members of the project in Universities and in Engineering schools, and public outreach.