The equilibrium tide in viscoelastic parts of planets

International audienceEarth-like planets have viscoelastic mantles, whereas giant planets may have viscoelastic cores. As for the fluid parts of a body, the tidal dissipation of such solid regions, gravitationally perturbed by a companion body, highly depends on the tidal frequency, as well as on the rheology. Therefore, modelling tidal interactions presents a high interest to provide constraints on planet properties, and to understand their history and their evolution. Here, we examine the equilibrium tide in the solid core of a planet, taking into account the presence of a fluid envelope. We explain how to obtain the different Love numbers that describe its deformation. Next, we discuss how the quality factor Q depends on the chosen viscoelastic model. Finally, we show how the results may be implemented to describe the dynamical evolution of planetary systems

New constraints on Saturn's interior from Cassini astrometric data

This work has been supported by the European Community’s Seventh Framework Program (FP7/2007-2013) under grant agreement 263466 for the FP7-ESPaCE project, the International Space Science Institute (ISSI), PNP (INSU/CNES) and AS GRAM (INSU/CNES/INP). The work of R. A. J. was carried out at the Jet Propulsion Laboratory, California Institute of Technology, under a contract with NASA. N.C. and C.M. were supported by the UK Science and Technology Facilities Council (Grant No. ST/M001202/1) and are grateful to them for financial assistance. C.M. is also grateful to the Leverhulme Trust for the award of a Research Fellowship. N.C. thanks the Scientific Council of the Paris Observatory for funding. S. Mathis acknowledge funding by the European Research Council through ERC grant SPIRE 647383

Effets de marée dans les systèmes de planètes géantes et exoplanétaires

Le programme et les présentations de ces Journées scientifiques sont disponibles en ligne : http://www.imcce.fr/hosted_sites/js2012/programme.ph

Tides in Planetary Systems and in Multiple Stars: a Physical Picture

International audienceMany stars belong to close binary or multiple stellar systems. Moreover, since 1995, a large number of extrasolar planetary systems have been discovered where planets can orbit very close to their host star. Finally, our own Solar system is the seat of many interactions between the Sun, the planets, and their natural satellites. Therefore, in such astrophysical systems, tidal interactions are one of the key mechanisms that must be studied to understand the celestial bodies' dynamics and evolution. Indeed, tides generate displacements and flows in stellar and planetary interiors. The associated kinetic energy is then dissipated into heat because of internal friction processes. This leads to secular evolution of orbits and of spins with characteristic time-scales that are intrinsically related to the properties of dissipative mechanisms, the latter depending both on the internal structure of the studied bodies and on the tidal frequency. This lecture is thus aimed to recall the basics of the tidal dynamics and to describe the different tidal flows or displacements that can be excited by a perturber, the conversion of their kinetic energy into heat, the related exchanges of angular momentum, and the consequences for astrophysical systems evolution

Tidal dissipation in the dense anelastic core of giant planets

International audienceThe prescriptions used today in celestial mechanics to describe dynamical processes, such as tidal interactions, are somewhat crude. In particular, the quality factor Q, quantifying the tidal dissipation, is often taken as constant, despite its dependence on internal structure, and thus on the tidal frequency. In a solid layer, Efroimsky & Lainey (2007) showed the importance of using a realistic prescription of Q to estimate the evolution speed of the Mars-Phobos system. Such studies confirm the necessity to go beyond evolution models using ad-hoc Q values. Recent astrometric observations of the dynamical evolution of the Jovian and Saturnian systems have shown a higher tidal dissipation than expected (for Jupiter: Q≈3.6×10^4, and for Saturn: Q≈1.7×10^3, from Lainey et al. 2009,2012 resp.). According to a recent model of the Saturnian system formation, such a high tidal dissipation is required by the satellites to migrate up to their present location over the age of the solar system (Charnoz et al., 2011). Globally, gas giants are constituted by a large fluid envelope and a dense central icy/rocky core (Hubbard & Marley 1989). Fluid models, where the tide excites the inertial waves of the convective envelope, show that the resulting tidal dissipation is of the order of Q≈10^5-10^7 (Wu 2005, Ogilvie & Lin 2004). These models have neglected the possible dissipation by the core. Thus, we have developed a model evaluating the tidal dissipation in the anelastic central region of a two-layer planet, surrounded by a static envelope, tidally excited by the hostingstar or a satellite (Remus et al., 2012). The tide exerted by the companion deforms both the envelope and the core. Because of its anelasticity, the core also creates tidal dissipation. I will discuss how the tidal dissipation depends on the rheological parameters and the size of the core. Assuming realistic models of internal structure and taking into account the frequency dependence of the solid dissipation, I will show how this mechanism might compete with the dissipation in fluid layers, and even explain the observed values of tidal dissipation. [abridged

Tidal dissipation in the dense anelastic core of giant planets

International audienceThe prescriptions used today in celestial mechanics to describe dynamical processes, such as tidal interactions, are somewhat crude. In particular, the quality factor Q, quantifying the tidal dissipation, is often taken as constant, despite its dependence on internal structure, and thus on the tidal frequency. In a solid layer, Efroimsky & Lainey (2007) showed the importance of using a realistic prescription of Q to estimate the evolution speed of the Mars-Phobos system. Such studies confirm the necessity to go beyond evolution models using ad-hoc Q values. Recent astrometric observations of the dynamical evolution of the Jovian and Saturnian systems have shown a higher tidal dissipation than expected (for Jupiter: Q≈3.6×10^4, and for Saturn: Q≈1.7×10^3, from Lainey et al. 2009,2012 resp.). According to a recent model of the Saturnian system formation, such a high tidal dissipation is required by the satellites to migrate up to their present location over the age of the solar system (Charnoz et al., 2011). Globally, gas giants are constituted by a large fluid envelope and a dense central icy/rocky core (Hubbard & Marley 1989). Fluid models, where the tide excites the inertial waves of the convective envelope, show that the resulting tidal dissipation is of the order of Q≈10^5-10^7 (Wu 2005, Ogilvie & Lin 2004). These models have neglected the possible dissipation by the core. Thus, we have developed a model evaluating the tidal dissipation in the anelastic central region of a two-layer planet, surrounded by a static envelope, tidally excited by the hostingstar or a satellite (Remus et al., 2012). The tide exerted by the companion deforms both the envelope and the core. Because of its anelasticity, the core also creates tidal dissipation. I will discuss how the tidal dissipation depends on the rheological parameters and the size of the core. Assuming realistic models of internal structure and taking into account the frequency dependence of the solid dissipation, I will show how this mechanism might compete with the dissipation in fluid layers, and even explain the observed values of tidal dissipation. [abridged

Tidal dissipation in the dense anelastic core of giant planets

International audienceThe prescriptions used today in celestial mechanics to describe dynamical processes, such as tidal interactions, are somewhat crude. In particular, the quality factor Q, quantifying the tidal dissipation, is often taken as constant, despite its dependence on internal structure, and thus on the tidal frequency. In a solid layer, Efroimsky & Lainey (2007) showed the importance of using a realistic prescription of Q to estimate the evolution speed of the Mars-Phobos system. Such studies confirm the necessity to go beyond evolution models using ad-hoc Q values. Recent astrometric observations of the dynamical evolution of the Jovian and Saturnian systems have shown a higher tidal dissipation than expected (for Jupiter: Q≈3.6×10^4, and for Saturn: Q≈1.7×10^3, from Lainey et al. 2009,2012 resp.). According to a recent model of the Saturnian system formation, such a high tidal dissipation is required by the satellites to migrate up to their present location over the age of the solar system (Charnoz et al., 2011). Globally, gas giants are constituted by a large fluid envelope and a dense central icy/rocky core (Hubbard & Marley 1989). Fluid models, where the tide excites the inertial waves of the convective envelope, show that the resulting tidal dissipation is of the order of Q≈10^5-10^7 (Wu 2005, Ogilvie & Lin 2004). These models have neglected the possible dissipation by the core. Thus, we have developed a model evaluating the tidal dissipation in the anelastic central region of a two-layer planet, surrounded by a static envelope, tidally excited by the hostingstar or a satellite (Remus et al., 2012). The tide exerted by the companion deforms both the envelope and the core. Because of its anelasticity, the core also creates tidal dissipation. I will discuss how the tidal dissipation depends on the rheological parameters and the size of the core. Assuming realistic models of internal structure and taking into account the frequency dependence of the solid dissipation, I will show how this mechanism might compete with the dissipation in fluid layers, and even explain the observed values of tidal dissipation. [abridged

The fluid Equilibrium Tide In Stars And Giant Planets

International audienceMany extrasolar planets orbit very close to their parent star, so that they experience strong tidal interactions; by converting mechanical energy into heat, these tides contribute to the dynamical evolution of such systems. This motivates us to acquire a deeper understanding of the processes that cause tidal dissipation, which depend both on the structure and the physical properties of the considered body

The fluid Equilibrium Tide In Stars And Giant Planets

International audienceMany extrasolar planets orbit very close to their parent star, so that they experience strong tidal interactions; by converting mechanical energy into heat, these tides contribute to the dynamical evolution of such systems. This motivates us to acquire a deeper understanding of the processes that cause tidal dissipation, which depend both on the structure and the physical properties of the considered body

The fluid equilibrium tide in stars and giant planets

International audienceMany extrasolar planets orbit very close to their parent star, so that they experience strong tidal interactions; by converting mechanical energy into heat, these tides contribute to the dynamical evolution of such systems. This motivates us to acquire a deeper understanding of the processes that cause tidal dissipation, which depend both on the structure and the physical properties of the considered body. Here we examine the equilibrium tide, i.e. the hydrostatic adjustment to the tidal potential, in a rotating fluid planet or star. We first present the equations governing the problem, and show how to rigorously separate the equilibrium tide from the dynamical tide, which is due to the excited eigenmodes. We discuss in particular how the quality factor Q is linked whith the turbulent viscosity of the convection zone. Finally we show how the results may be implemented to describe the dynamical evolution of the system