Tidal dissipation in rotating low-mass stars hosting planetary or stellar companions. From BinaMIcS to SPIRou

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1 Tidal dissipation in rotating low-mass stars hosting planetary or stellar companions From BinaMIcS to SPIRou Stéphane MATHIS CEA Saclay Emeline BOLMONT University of Namur, NaXys Florian GALLET Observatoire de Genève In collaboration with P.-A. Desrotour, M. Guenel, C. Baruteau, M. Rieutord, C. Charbonnel, C. Le Poncin-Lafitte, A.-S. Brun, V. Reville

2 The general context A revolution in astrophysics: discovery of new planetary systems & characterisation of the dynamics of their host (multiple) stars (asteroseismology and spectropolarimetry) ESPaDOnS@CFHT LPs Kepler K2 SPIRou CHEOPS & TESS PLATO Stellar rotation & magnetism planetary dynamics Orbital architecture Kepler 11 Mercury orbit Albrecht et al. 2012; Gizon et al Lissauer et al Bolmont et al

3 State of the art In studies of star-star or star-planet systems, bodies are treated as point-mass objects or solids with ad-hoc models for tides, stellar winds and electromagnetic interactions However their complex internal structure, evolution, rotation, and magnetism impact tidal (and magnetic) Star-Planet Interactions Host star (M in M! ) Planets " Need of an ab-initio physical modeling to accompany the study of discovered systems 3

4 The engine of the tidal evolution of binary systems: friction & energy dissipation Dynamical evolution of a binary system Remus t Evol ~ 1/Dissip ~ Q Mathis & Remus 2013 Necessity to identify the dissipative processes and to evaluate their strength along the evolution of systems and of their components 4 Time-scales for circularization, synchronization, alignment, and migration (" Age)

5 Tidal velocities/displacements In stars and fluid planetary layers: - Large-scale circulation resulting from the hydrostatic adjustment to the tidal perturbation: Equilibrium Tide - Waves excited by the tidal potential: Dynamical Tide Excitation by each Fourier component of the forcing 2Ω KOI-54: Welsh et al N fl σ0 Acoustic waves Inertial waves (C.Z.) Gravito-inertial waves (Stab. strat.) Mathis & Remus 2013 Dissipative mechanisms: - Convective regions: turbulence - Stably stratified regions: heat diffusion Brun et al. 5

6 The signature of tidal interactions in exoplanetary systems & multiple stars The case of hot-jupiter systems (and binary solar-type stars) Albrecht et al " Tidal dissipation in a star varies over several orders of magnitude as a function of: - The mass - The age - The dynamics (rotation) Gizon et al. 2013; Davies et al. 2015; Gregory " need for ab-initio modeling 6

7 Tidal dissipation in low-mass star convective envelopes Fluid dynamical tide: forced (gravito-) inertial waves " resonant response η T, K 2Ω, N Dissipation spectrum by turbulent friction E.T. E=10-5 ; 10 days Porb > 1/2 P Inertial waves E.T. E.T. 2(n-Ω)/Ω Ogilvie & Lin 2004, 2007 Rieutord & Valdetarro 2010 Baruteau & Rieutord 2013 Guenel et al

8 Dissipation variations with stellar parameters As a function of stellar mass, age and rotation Sun, 10 days Sun, 3 days 0.5M!, 10 days Dissipation Ogilvie & Lin (n-Ω)/Ω 2(n-Ω)/Ω 2(n-Ω)/Ω To get an order of magnitude of tidal dissipation along the evolution of stars " a frequency-averaged dissipation Dissip = with structure rotation Ogilvie 2013; Mathis

9 The evolution of key structural and dynamical parameters Total radius Global rotation Mathis 2015; Gallet, Mathis, Charbonnel & Amard 2016 Aspect ratios: radius & mass 9

10 The tidal H-R diagram Dissipation Mathis 2015; Gallet, Mathis, Charbonnel & Amard

11 Grids of tidal dissipation for star-planet and multiple star systems In low-mass and solar-type stars, it varies over several orders of magnitude: " Stronger Dynamical Tide along the Pre-Main-Sequence and Sub-Giant phases " Its amplitude on the MS diminishes with mass (and the thickness of the CE) " Necessity to couple structural and rotational evolutions Dissipation Structural evolution Mathis 2015; Gallet, Mathis, Charbonnel & Amard 2016 Structural & rotational evolutions 11

12 Star-planet systems dynamical evolution (I) - Low-mass star-planet systems - circular & coplanar - Ab-initio frequency-averaged dissipation of stellar tides in the convective envelope Porb = P Outward migration Standard model Model Bolmont & Mathis Inward migration Mp = 1 M Dissipation M = 1 M P,i = 1.2 day Bolmont & Mathis, accepted in CeMDA 12

13 Star-planet systems dynamical evolution (II) Porb = P Porb = 1/2 P Dynamical Tide Standard model Model Bolmont & Mathis Equilibrium Tide Mp = 1 M Dissipation M = 1 M P,i = 1.2 day Bolmont & Mathis, accepted in CeMDA 13

14 Star-planet systems dynamical evolution (III) Semi-major axis (AU) Standard model Model Bolmont & Mathis Mp = 1 Mjup Dissipation σ Stellar rotation period (day) M = 1 M P,i = 1.2 day Bolmont & Mathis, accepted in CeMDA 14

15 Impact on stellar rotation (I) P,i = 1.2 day Compatible with observations (Ceillier et al., 2016) All planets here migrate outwards the star spins down Bolmont & Mathis, accepted in CeMDA 15

16 Impact on stellar rotation (II) M = 1 M P,i = 8.0 day Mp = 1 Mjup Planets migrate inwards the star spins up Rotation excess: star initially slow rotator Rotation deficiency: star initially fast rotator Bolmont & Mathis, accepted in CeMDA 16

17 Understanding hot-jupiters systems Porb = 1/2 P Porb = P Equilibrium tide Dynamical tide in radiative region? Dynamical tide in convective region McQuillan et al

18 Conclusions and perspectives Summary: Tidal dissipation in stellar convective zones varies over several orders of magnitude as a function of stellar mass, age and rotation The Dynamical Tide causes a much faster evolution than the Equilibrium Tide " Needs to be taken into account in tidal studies " Implications on the understanding of planets distribution The Dynamical Tide is strong enough so that the star s early rotation history has a strong influence on close-in planets For Mp > 10 M, the dynamical tide induced migration is strong enough to influence the star s rotation Perspectives: Treat: " Multiple systems " Eccentric orbits and inclined systems Take into account: " Tidal dissipation frequency-dependence " Tidal dissipation in stellar radiation zones and in planets " Best ab-initio models as possible of MHD stellar winds & SPI 18

19 CFHT instruments key players to guide future theoretical investigations

20 Tides in gaseous and icy giant planets in collaboration with the ENCELADE international team From astrometric constrains in the Solar SystemA&A 566, L9 (2014) Lainey et al. 2012, 2016! Rhea Dione Tethys Enceladus Saturn s k2/q Tidal dissipation in Saturn Fig. 2. Mechanisms of tidal dissipation in our two-layer planeta model:modelling the inelastic dissipation the dense rocky/icy core (left) a Topointab-initio of tidal indissipation Fig. 1. Two-layer planet A of mass Mp and mean radius Rp and Highest possible value from Sinclair (1983) 1e-05 mass tidal perturber B of mass MB orbiting with a mean motion n. The the dissipation due to the tidal inertial waves that reflect onto the co fluid convective envelope (right). rocky/icy solid core of radius Rc, density c, and rigidity G -(see Viscoelastic Eq. (4)) in the dissipation in the rocky/icy core Remus et is surrounded by a convective fluid envelope of density o. al. 2012, 2015 order Love number k22, which we call the tidal dissipatio - Completereservoir: characterization of the dissipation in the 2. Modelling tidal dissipation in gaseous giantfluid envelope Z +1 Auclair-Desrotour, 2 Le Poncin-Lafitte +1 k& h i d! ZMathis (!) d! planets Im k2 (!) = ( 2! 1 1 Q2 (!)! 2.1. Two-layer model - TurbulentThis convective rapidly rotating quantity tidal can befriction definedinfor any values of (l, m), but w planets Mathis et al To study the respective contributions to the tidal dissipation here chose to consider the simplest case of a coplanar syste of both the potential rocky/icy core and the fluid envelope of for which the tidal potential (U) reduces to the component (2, - Integrated model gaseous giant planets, we chose to adopt the simplified two- as well as thesolid+fluid quadrupolardissipations response of A. Guenel, Mathis & Remus 2014 layer model used in Remus et al. (2012) and Ogilvie (2013, see We now examine the two possible mechanisms of dissipatio Fig. 1). This model features a central planet A of mass Mp and (see Fig. 2): mean radius Rp along with a point-mass tidal perturber B of mass 1e Tidal frequency 2( -n) in rad/sec

21 Tides in telluric planets in collaboration with J. Laskar s team /ocean ATMOSPHERIC & OCEANIC TIDES Atmospheric tides A&A proofs: manuscript no. ADLM2016 Oceanic tides Vertical velocity (normalized) latitude latitude Pressure fluctuation (mbar) longitude - New general model with dissipation " allows to treat the case of Venus-like and super-earth planets close to synchronization " allows to predict their rotation Auclair-Desrotour, Laskar, Mathis 2016, in revision Auclair-Desrotour, Laskar, Mathis & Correia 2016, subm. longitude - Global oceanic tides with an effective friction applied by topography " Application to Earth-moon system " Application to water exoworlds Auclair-Desrotour, Mathis & Laskar, in prep.

22 Improving dynamical models With frequency dependence of tidal dissipation The case of tidal inertial waves With stellar internal structure and rotation evolution Evolution of a hot-jupiter orbiting an 1M! star Auclair-Desrotour, Le Poncin-Lafitte & Mathis 2014 " Explains the lack of close planets around fast rotators Bolmont & Mathis 2016

23 The ESPEM Project in collaboration with C. Le Poncin-Lafitte s team Objec'ves:! Take!into!account:!! 3 the!complex!internal!structure!of!celes'al!bodies! 3 angular!momentum!exchanges!within!their!interiors! 3 MHD!and!'dal!torques,!computed!using!ab3ini'o!models,!simultaneously! " Compute!star3planet!systems!dynamical!evolu'on! B" Penev et al Zhang & Penev 2014