arXiv subjects

Jacques Laskar

Publications and source records attributed to Jacques Laskar.

At least 55 records · Page 3Linked to original sources

arXiv2019

Secular spin-axis dynamics of exoplanets

Context: Seasonal variations and climate stability of a planet are very sensitive to the planet obliquity and its evolution. This is of particular interest for the emergence and sustainability of land-based life, but orbital and rotational parameters of exoplanets are still poorly constrained. Numerical explorations usually realised in this situation are thus in heavy contrast with the uncertain nature of the available data. Aims: We aim to provide an analytical formulation of the long-term spin-axis dynamics of exoplanets, linking it directly to physical and dynamical parameters, but still giving precise quantitative results if the parameters are well known. Together with bounds for the poorly constrained parameters of exoplanets, this analysis is designed to allow a quick and straightforward exploration of the spin-axis dynamics. Methods: The long-term orbital solution is decomposed in quasi-periodic series and the spin-axis Hamiltonian is expanded in powers of eccentricity and inclination. Chaotic zones are measured by the resonance overlap criterion. Bounds for the poorly known parameters of exoplanets are obtained from physical grounds (rotational breakup) and dynamical considerations (equipartition of AMD). Results: This method gives accurate results when the orbital evolution is well known. The chaotic zones for planets of the Solar System can be retrieved in details from simple analytical formulas. For less constrained planetary systems, the maximal extent of the chaotic regions can be computed, requiring only the mass, the semi-major axis and the eccentricity of the planets present in the system. Additionally, some estimated bounds of the precession constant allow to classify which observed exoplanets are necessarily out of major spin-orbit secular resonances (unless the precession rate is affected by the presence of massive satellites).

astro-ph.EP↗

arXiv2018

Tidal dissipation in deep oceanic shells: from telluric planets to icy satellites

Oceanic tides are a major source of tidal dissipation. They are a key actor for the orbital and rotational evolution of planetary systems, and contribute to the heating of icy satellites hosting a subsurface ocean. Oceanic tides are characterized by a highly frequency-resonant behavior, which is mainly due to the propagation of surface gravity waves in the case of thin oceans, and internal waves when they are deeper. In this work, we derive self-consistent ab initio expressions of the oceanic tidal torque as a function of the key physical parameters of the system (the ocean depth, the Brunt-Väisälä stratification frequency, the rotation rate, the tidal frequency, the Rayleigh friction). These solutions include the coupled mechanisms of internal and surface gravito-inertial waves, which allows us to study the case of planets hosting deep oceans and offer interesting prospects for the coupling between subsurface oceans and ice shells in the case of icy satellites.

astro-ph.EP↗

arXiv2018

Hill stability in the AMD framework

In a two-planet system, due to Sundman (1912) inequality, a topological boundary can forbid close encounters between the two planets for infinite time. A system is said Hill stable if it verifies this topological condition. Hill stability is widely used in the study of extra solar planets dynamics. However people often use the coplanar and circular orbits approximation. In this paper, we explain how the Hill stability can be understood in the framework of Angular Momentum Deficit (AMD). In the secular approximation, the AMD allows to discriminate between a priori stable systems and systems for which a more in depth dynamical analysis is required. We show that the general Hill stability criterion can be expressed as a function of only the semi major axes, the masses and the total AMD of the system. The proposed criterion is only expanded in the planets-to-star mass ratio $ε$ and not in the semi-major axis ratio, in eccentricities nor in the mutual inclination. Moreover the expansion in $ε$ remains excellent up to values of about $10^{-3}$ even for two planets with very different mass values. We performed numerical simulations in order to highlight the sharp change of behaviour between Hill stable and Hill unstable systems. We show that Hill stable systems tend to be very regular whereas Hill unstable ones often lead to rapid planet collisions. We also remind that Hill stability does not protect from the ejection of the outer planet.

astro-ph.EP↗

arXiv2018

Long-Term Cyclicities in Phanerozoic Sea-Level Sedimentary Record and their Potential Drivers (Does the Phanerozoic sea level encode the motion of solar system in the Milky Way ?)

Cyclic sedimentation has varied at several timescales and this variability has been geologically well documented at Milankovitch timescales, controlled in part by climatically (insolation) driven sea-level changes. At the longer (tens of Myr) timescales connection between astronomical parameters and sedimentation via cyclic solar-system motions within the Milky Way has also been proposed, but this hypothesis remains controversial because of the lack of long geological records. The absence of a physical mechanism that could explain the connection between climate and astronomy at these longer timescales led to the explanation of plate motions as the main driver of climate on Earth. Here we statistically show a prominent and persistent ~36 Myr sedimentary cyclicity superimposed on two megacycles (~250 Myr) in a relatively well-constrained sea-level (SL) record of the past 542 Myr (Phanerozoic eon). Given the possible link between amplitudes of the ~36 and ~250 Myr cyclicities in SL record and the potential that these periodicities fall into the frequency band of solar system motions, we suggest an astronomical origin, and model these periodicities as originating from the path of the solar system in the Milky Way as vertical and radial periods that modulate the flux of cosmic rays on Earth. Our finding of the ~36 Myr SL cyclicity lends credibility to the existing hypothesis about the imprint of solar-system vertical period on the geological record. The ~250 Myr megacycles are tentatively attributed to a radial period. However, the tectonic drivers also remain potentially plausible. The potential existence of a correlation between the modeled astronomical signal and the geological record may offer an indirect proxy to understand the structure and history of the Milky Way by providing a 542 Myr long record of the path of the Sun in our Galaxy.

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arXiv2018

Oceanic tides from Earth-like to ocean planets

Oceanic tides are a major source of tidal dissipation. They drive the evolution of planetary systems and the rotational dynamics of planets. However, 2D models commonly used for the Earth cannot be applied to extrasolar telluric planets hosting potentially deep oceans because they ignore the three-dimensional effects related to the ocean vertical structure. Our goal is to investigate in a consistant way the importance of the contribution of internal gravity waves in the oceanic tidal response and to propose a modeling allowing to treat a wide range of cases from shallow to deep oceans. A 3D ab initio model is developed to study the dynamics of a global planetary ocean. This model takes into account compressibility, stratification and sphericity terms, which are usually ignored in 2D approaches. An analytic solution is computed and used to study the dependence of the tidal response on the tidal frequency and on the ocean depth and stratification. In the 2D asymptotic limit, we recover the frequency-resonant behaviour due to surface inertial-gravity waves identified by early studies. As the ocean depth and Brunt-Väisälä frequency increase, the contribution of internal gravity waves grows in importance and the tidal response become three-dimensional. In the case of deep oceans, the stable stratification induces resonances that can increase the tidal dissipation rate by several orders of magnitude. It is thus able to affect significantly the evolution time scale of the planetary rotation.

astro-ph.EP↗

arXiv2017

Repercussions of thermal atmospheric tides on the rotation of terrestrial planets in the habitable zone

Semidiurnal atmospheric thermal tides are important for terrestrial exoplanets in the habitable zone of their host stars. With solid tides, they torque these planets, thus contributing to determine their rotation states as well as their climate. Given the complex dynamics of thermal tides, analytical models are essential to understand its dependence on the structure and rotation of planetary atmospheres and the tidal frequency. In this context, the state of the art model proposed in the 60's by Lindzen and Chapman explains well the properties of thermal tides in the asymptotic regime of Earth-like rapid rotators but predicts a non-physical diverging tidal torque in the vicinity of the spin-orbit synchronization. In this work, we present a new model that addresses this issue by taking into account dissipative processes through a Newtonian cooling. First, we recover the tidal torque recently obtained with numerical simulations using General Circulation Models (GCM). Second, we show that the tidal response is very sensitive to the atmospheric structure, particularly to the stability with respect to convection. A strong stable stratification is able to annihilate the atmospheric tidal torque, leading to synchronization, while a convective atmosphere will be submitted to a strong torque, leading to a non-synchronized rotation state.

astro-ph.EP↗

arXiv2017

Des premiers travaux de Le Verrier à la découverte de Neptune

(in english): Urbain-Jean-Joseph Le Verrier was born in Saint-Lô on March 11, 1811. He entered the Ecole Polytechnique in 1831, from which he was to emerge 8th two years later. After first devoting himself to chemistry, in 1836 he obtained a position as an astronomy assistant at the Ecole Polytechnique. This choice will decide his future career which culminates with the discovery of Neptune in 1846. Le Verrier wrote more than 200 contributions in the Comptes Rendus de l'Académie des Sciences. These contributions are very varied: some original articles but also reports on publications published elsewhere, sometimes even simple notes of a single page. The whole set gives a very vivid vision of the development of the science of the XIXth century. At that time, the Comptes Rendus are really a reflection of the debates of the sessions of the Academy. They are published very quickly, and leave a large freedom of speech to the authors. They are therefore a snapshot of the sometimes lively polemics which animated the sessions of the Academy of Sciences. In this limited essay, we will look to the first years of the career of Le Verrier until the discovery of Neptune. (in french) Le Verrier a écrit plus de 200 contributions dans les Comptes Rendus de l'Académie des Sciences . Ces contributions sont le reflet des débats des séances de l'Académie. Ils sont publiés très rapidement, et laissent une très grande liberté de parole aux auteurs. On y retrouve de manière instantanée les polémiques parfois vives qui ont animé les séances de l'Académie des sciences. Dans cet essai nous survolerons les premières années de la carrière de Le Verrier jusqu'à la découverte de Neptune.

physics.hist-ph↗

arXiv2017

Atmospheric thermal tides and planetary spin I. The complex interplay between stratification and rotation

Thermal atmospheric tides can torque telluric planets away from spin-orbit synchronous rotation, as observed in the case of Venus. They thus participate to determine the possible climates and general circulations of the atmospheres of these planets. In this work, we write the equations governing the dynamics of thermal tides in a local vertically-stratified section of a rotating planetary atmosphere by taking into account the effects of the complete Coriolis acceleration on tidal waves. This allows us to derive analytically the tidal torque and the tidally dissipated energy, which we use to discuss the possible regimes of tidal dissipation and examine the key role played by stratification. In agreement with early studies, we find that the frequency dependence of the thermal atmospheric tidal torque in the vicinity of synchronization can be approximated by a Maxwell model. This behaviour corresponds to weakly stably stratified or convective fluid layers, as observed in ADLM2016a. A strong stable stratification allows gravity waves to propagate, which makes the tidal torque become negligible. The transition is continuous between these two regimes. The traditional approximation appears to be valid in thin atmospheres and in regimes where the rotation frequency is dominated by the forcing or the buoyancy frequencies. Depending on the stability of their atmospheres with respect to convection, observed exoplanets can be tidally driven toward synchronous or asynchronous final rotation rates. The domain of applicability of the traditional approximation is rigorously constrained by calculations.

astro-ph.EP↗

arXiv2017

Atmospheric tides and their consequences on the rotational dynamics of terrestrial planets

Atmospheric tides can have a strong impact on the rotational dynamics of planets. They are of most importance for terrestrial planets located in the habitable zone of their host star, where their competition with solid tides is likely to drive the body towards non-synchronized rotation states of equilibrium, as observed in the case of Venus. Contrary to other planetary layers, the atmosphere is sensitive to both gravitational and thermal forcings, through a complex dynamical coupling involving the effects of Coriolis acceleration and characteristics of the atmospheric structure. These key physics are usually not taken into account in modelings used to compute the evolution of planetary systems, where tides are described with parametrised prescriptions. In this work, we present a new ab initio modeling of atmospheric tides adapting the theory of the Earth's atmospheric tides (Chapman & Lindzen 1970) to other terrestrial planets. We derive analytic expressions of the tidal torque, as a function of the tidal frequency and parameters characterizing the internal structure (e.g. the Brunt-Väisälä frequency, the radiative frequency, the pressure heigh scale). We show that stratification plays a key role, the tidal torque being strong in the case of convective atmospheres (i.e. with a neutral stratification) and weak in case of atmosphere convectively stable. In a second step, the model is used to determine the non-synchronized rotation states of equilibrium of Venus-like planets as functions of the physical parameters of the system. These results are detailed in Auclair-Desrotour et al. (2017a) and Auclair-Desrotour et al. (2017b).

astro-ph.EP↗

arXiv2017

AMD-stability in presence of first order Mean Motion Resonances

The AMD-stability criterion allows to discriminate between a-priori stable planetary systems and systems for which the stability is not granted and needs further investigations. AMD-stability is based on the conservation of the Angular Momentum Deficit (AMD) in the averaged system at all orders of averaging. While the AMD criterion is rigorous, the conservation of the AMD is only granted in absence of mean-motion resonances (MMR). Here we extend the AMD-stability criterion to take into account mean-motion resonances, and more specifically the overlap of first order MMR. If the MMR islands overlap, the system will experience generalized chaos leading to instability. The Hamiltonian of two massive planets on coplanar quasi-circular orbits can be reduced to an integrable one degree of freedom problem for period ratios close to a first order MMR. We use the reduced Hamiltonian to derive a new overlap criterion for first order MMR. This stability criterion unifies the previous criteria proposed in the literature and admits the criteria obtained for initially circular and eccentric orbits as limit cases. We then improve the definition of AMD-stability to take into account the short term chaos generated by MMR overlap. We analyze the outcome of this improved definition of AMD-stability on selected multi-planet systems from the Extrasolar Planets Encyclopeadia.

astro-ph.EP↗

arXiv2017

Theia: Faint objects in motion or the new astrometry frontier

In the context of the ESA M5 (medium mission) call we proposed a new satellite mission, Theia, based on relative astrometry and extreme precision to study the motion of very faint objects in the Universe. Theia is primarily designed to study the local dark matter properties, the existence of Earth-like exoplanets in our nearest star systems and the physics of compact objects. Furthermore, about 15 $\%$ of the mission time was dedicated to an open observatory for the wider community to propose complementary science cases. With its unique metrology system and "point and stare" strategy, Theia's precision would have reached the sub micro-arcsecond level. This is about 1000 times better than ESA/Gaia's accuracy for the brightest objects and represents a factor 10-30 improvement for the faintest stars (depending on the exact observational program). In the version submitted to ESA, we proposed an optical (350-1000nm) on-axis TMA telescope. Due to ESA Technology readiness level, the camera's focal plane would have been made of CCD detectors but we anticipated an upgrade with CMOS detectors. Photometric measurements would have been performed during slew time and stabilisation phases needed for reaching the required astrometric precision.

astro-ph.IM↗

arXiv2017

Universality of free fall versus ephemeris

When a light scalar field with gravitational strength interacts with matter, the weak equivalence principle is in general violated, leading for instance to a violation of the universality of free fall. This has been known and tested for a while. However, recent developments [Minazzoli & Hees, PRD 2016] showed that a novel manifestation of the universality of free fall can appear in some models. Here we discuss this new scenario and expose how we intend to constrain it with INPOP ephemeris.

gr-qc↗

arXiv2017

AMD-stability and the classification of planetary systems

We present here in full detail the evolution of the angular momentum deficit (AMD) during collisions as it was described in (Laskar, PRL,2000). Since then, the AMD has been revealed to be a key parameter for the understanding of the outcome of planetary formation models. We define here the AMD-stability criterion that can be easily verified on a newly discovered planetary system. We show how AMD-stability can be used to establish a classification of the multiplanet systems in order to exhibit the planetary systems that are long-term stable because they are AMD-stable, and those that are AMD-unstable which then require some additional dynamical studies to conclude on their stability. The AMD-stability classification is applied to the 131 multiplanet systems from The Extrasolar Planet Encyclopaedia database (exoplanet.eu) for which the orbital elements are sufficiently well known.

astro-ph.EP↗

arXiv2017

Frequency analysis and the representation of slowly diffusing planetary solutions

Over short time intervals planetary ephemerides have been traditionally represented in analytical form as finite sums of periodic terms or sums of Poisson terms that are periodic terms with polynomial amplitudes. Nevertheless, this representation is not well adapted for the evolution of the planetary orbits in the solar system over million of years as they present drifts in their main frequencies, due to the chaotic nature of their dynamics. The aim of the present paper is to develop a numerical algorithm for slowly diffusing solutions of a perturbed integrable Hamiltonian system that will apply to the representation of the chaotic planetary motions with varying frequencies. By simple analytical considerations, we first argue that it is possible to recover exactly a single varying frequency. Then, a function basis involving time-dependent fundamental frequencies is formulated in a semi-analytical way. Finally, starting from a numerical solution, a recursive algorithm is used to numerically decompose the solution on the significant elements of the function basis. Simple examples show that this algorithm can be used to give compact representations of different types of slowly diffusing solutions. As a test example, we show how this algorithm can be successfully applied to obtain a very compact approximation of the La2004 solution of the orbital motion of the Earth over 40 Myr ([-35Myr,5Myr]). This example has been chosen as this solution is widely used for the reconstruction of the climates of the past.

astro-ph.IM↗

arXiv2016

Complete spin and orbital evolution of close-in bodies using a Maxwell viscoelastic rheology

In this paper, we present a formalism designed to model tidal interaction with a viscoelastic body made of Maxwell material. Our approach remains regular for any spin rate and orientation, and for any orbital configuration including high eccentricities and close encounters. The method is to integrate simultaneously the rotation and the position of the planet as well as its deformation. We provide the equations of motion both in the body frame and in the inertial frame. With this study, we generalize preexisting models to the spatial case and to arbitrary multipole orders using a formalism taken from quantum theory. We also provide the vectorial expression of the secular tidal torque expanded in Fourier series. Applying this model to close-in exoplanets, we observe that if the relaxation time is longer than the revolution period, the phase space of the system is characterized by the presence of several spin-orbit resonances, even in the circular case. As the system evolves, the planet spin can visit different spin-orbit configurations. The obliquity is decreasing along most of these resonances, but we observe a case where the planet tilt is instead growing. These conclusions derived from the secular torque are successfully tested with numerical integrations of the instantaneous equations of motion on HD 80606b. Our formalism is also well adapted to close-in super-Earths in multiplanet systems which are known to have non-zero mutual inclinations.

astro-ph.EP↗

arXiv2016

Andoyer construction for Hill and Delaunay variables

Andoyer variables are well known for the study of rotational dynamics. These variables were derived by Andoyer through a procedure that can be also used to obtain the Hill variables of the Kepler problem. Andoyer construction can also forecast the Delaunay variables which canonicity is then obtained without the use of a generating function.

astro-ph.IM↗

arXiv2016

The rotation of planets hosting atmospheric tides: from Venus to habitable super-earths

The competition between the torques induced by solid and thermal tides drives the rotational dynamics of Venus-like planets and super-Earths orbiting in the habitable zone of low-mass stars. The tidal responses of the atmosphere and telluric core are related to their respective physical properties and strongly depend on the tidal frequency. The resulting torque determines the possible equilibrium states of the planet's spin. We compute here an analytic expression for the total tidal torque exerted on a Venus-like planet. This expression is used to characterize the equilibrium rotation of the body. Close to the star, the solid tide dominates. Far from it, the thermal tide drives the rotational dynamics of the planet. The transition regime corresponds to the habitable zone, where prograde and retrograde equilibrium states appear. We demonstrate the strong impact of the atmospheric properties and of the rheology of the solid part on the rotational dynamics of Venus-like planets, highlighting the key role played by dissipative mechanisms in the stability of equilibrium configurations.

astro-ph.EP↗

arXiv2016

Atmospheric tides in Earth-like planets

Atmospheric tides can strongly affect the rotational dynamics of planets. In the family of Earth-like planets, such as Venus, this physical mechanism coupled with solid tides makes the angular velocity evolve over long timescales and determines the equilibrium configurations of their spin. Contrary to the solid core, the atmosphere is submitted to both tidal gravitational potential and insolation flux coming from the star. The complex response of the gas is intrinsically linked to its physical properties. This dependence has to be characterized and quantified to study the large variety of extrasolar planetary systems. We develop a theoretical global model where radiative losses, which are predominant in slowly rotating atmospheres, are taken into account. We analytically compute the tidal perturbation of pressure, density, temperature and velocity field from which we deduce the expressions of atmospheric Love numbers and tidal torque exerted by the star. The dynamics of atmospheric tides depends on the frequency regime of the tidal perturbation: the thermal regime near synchronization and the dynamical regime characterizing fast-rotating planets. The dependence of the torque on the tidal frequency is quantified for Earth-like and Venus-like exoplanets and is in good agreement with the results given by Global Climate Models (GCM) simulations. Introducing dissipative processes such as radiation regularizes the tidal response of the atmosphere, otherwise it is singular at synchronization. We demonstrate the important role played by the physical and dynamical properties of a super-Earth atmosphere (e.g. Coriolis, stratification, background pressure, density, temperature, radiative emission) and point out the key parameters defining tidal regimes (e.g. inertia, Brunt-Väisälä, radiative frequencies, tidal frequency) and characterize the behaviour of the fluid shell with dissipation.

astro-ph.EP↗