arXiv subjects

Pierre Auclair-Desrotour

Publications and source records attributed to Pierre Auclair-Desrotour.

At least 19 recordsLinked to original sources

arXiv2025

An analytical framework for atmospheric tides on rocky planets. I. Formulation

Atmospheric thermal tides arise from the diurnal contrast in stellar irradiation. They exert a significant influence on the long-term rotational evolution of rocky planets because they can accelerate the planetary spin, thereby counteracting the decelerating effect of classical gravitational tides. Consequently, equilibrium tide-locked states may emerge, as exemplified by Venus and hypothesised for Precambrian Earth. Quantifying the atmospheric thermal torque and elucidating its dependence on tidal frequency -- both in the low- and high-frequency regimes -- is therefore essential. In particular, we focus here on the resonance that affected early Earth, which is associated with a forced Lamb wave. Within the framework of linear theory, we develop a new analytical model of the atmospheric response to both gravitational an thermal tidal forcings for two representative vertical temperature profiles that bracket the atmospheres of rocky planets: (i) an isothermal profile (uniform temperature) and (ii) an isentropic profile (uniform potential temperature). Dissipative processes are incorporated via Newtonian cooling. We demonstrate that the isothermal and isentropic cases are governed by the same general closed-form solution, and we derive explicit expressions for the three-dimensional tidal fields (pressure, temperature, density and wind velocities) throughout the spherical atmospheric shell. These results constitute the foundation for two forthcoming papers, in which analytical formulae for the thermotidal torque will be presented and compared with numerical solutions obtained from General Circulation Models (GCMs).

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arXiv2024

Anisotropic tidal dissipation in misaligned planetary systems

Tides are the main driving force behind the long-term evolution of planetary systems. The associated energy dissipation and momentum exchanges are commonly described by Love numbers, which relate the exciting potential to the tidally perturbed potential. These transfer functions are generally assumed to depend solely on tidal frequency and body rheology, following the isotropic assumption, which presumes invariance of properties by rotation about the centre of mass. We examine the limitations of the isotropic assumption for fluid bodies, where Coriolis acceleration breaks spherical symmetry, resulting in rotational scattering and complex tidal responses. Using angular momentum theory, we derive a new formalism to calculate the tidal rates of energy and momentum transfers in non-isotropic cases. We apply this formalism to the Earth-Moon system to assess the effects of anisotropy in planet-satellite systems with misaligned spin and orbital angular momenta. Our findings indicate that the isotropic assumption can introduce significant errors in planetary evolution models, particularly in the dynamical tide regime. These errors stem from forced wave resonances, with inaccuracies in energy dissipation scaling in proportion to resonance amplification factors.

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arXiv2024

Tides on Lava Worlds: Application to Close-in Exoplanets and the Early Earth-Moon System

Understanding the physics of planetary magma oceans has been the subject of growing efforts, in light of the increasing abundance of Solar system samples and extrasolar surveys. A rocky planet harboring such an ocean is likely to interact tidally with its host star, planetary companions, or satellites. To date, however, models of the tidal response and heat generation of magma oceans have been restricted to the framework of weakly viscous solids, ignoring the dynamical fluid behavior of the ocean beyond a critical melt fraction. Here we provide a handy analytical model that accommodates this phase transition, allowing for a physical estimation of the tidal response of lava worlds. We apply the model in two settings: The tidal history of the early Earth-Moon system in the aftermath of the giant impact; and the tidal interplay between short-period exoplanets and their host stars. For the former, we show that the fluid behavior of the Earth's molten surface drives efficient early Lunar recession to ${\sim} 25$ Earth radii within $10^4{-} 10^5$ years, in contrast with earlier predictions. For close-in exoplanets, we report on how their molten surfaces significantly change their spin-orbit dynamics, allowing them to evade spin-orbit resonances and accelerating their track towards tidal synchronization from a Gyr to Myr timescale. Moreover, we re-evaluate the energy budgets of detected close-in exoplanets, highlighting how the surface thermodynamics of these planets are likely controlled by enhanced, fluid-driven tidal heating, rather than vigorous insolation, and how this regime change substantially alters predictions for their surface temperatures.

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arXiv2024

Thermal tides on rocky planets through a novel fully analytical solution

Thermal tides are atmospheric tides caused by variations in day-night insolation, similar to gravitational tides but with key differences. While both result in delayed mass redistribution, energy dissipation, and angular momentum exchanges between the planet and its host star, thermal tides can drive a planet's dynamics away from the rotational equilibrium states predicted by classical tidal theory. In this work, we present a novel closed-form solution for the thermotidal response of rocky planets. This general solution is derived from first principles, assuming either dry or moist adiabatic temperature profiles for the planet's atmosphere, and can be readily applied to study the long-term evolution of exoplanets in the habitable zones of their host stars. Despite relying on a small number of parameters, the model successfully captures the key features of the thermotidal torque predicted by General Circulation Models (GCMs). It also accurately predicts Earth's current semidiurnal thermotidal response and provides new insights into the evolution of the length of day during the Precambrian era.

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arXiv2023

Can one hear supercontinents in the tides of ocean planets?

Recent observations and theoretical progress made about the history of the Earth-Moon system suggest that tidal dissipation in oceans primarily drives the long term evolution of orbital systems hosting ocean planets. Particularly, they emphasise the key role played by the geometry of land-ocean distributions in this mechanism. However, the complex way continents affect oceanic tides still remains to be elucidated. In the present study, we investigate the impact of a single supercontinent on the tidal response of an ocean planet and the induced tidally dissipated energy. The adopted approach is based on the linear tidal theory. By simplifying the continent to a spherical cap of given angular radius and position on the globe, we proceed to a harmonic analysis of the whole planet's tidal response including the coupling with the solid part due to ocean loading and self-attraction variations. In this framework, tidal flows are formulated analytically in terms of explicitly defined oceanic eigenmodes, as well as the resulting tidal Love numbers, dissipated power, and torque. The analysis highlights the symmetry breaking effect of the continent, which makes the dependence of tidal quantities on the tidal frequency become highly irregular. The metric introduced to quantify this continentality effect reveals abrupt transitions between polar and non-polar configurations, and between small-sized and medium-sized continents. Additionally, it predicts that a continent similar to South America or smaller (30°-angular radius) does not alter qualitatively the tidal response of a global ocean whatever its position on the planet.

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arXiv2023

Did atmospheric thermal tides cause a daylength locking in the Precambrian? A review on recent results

After the initial suggestion by Zahnle and Walker (1987) that the torque accelerating the spin rate of the Earth and produced by the heating of the atmosphere by the Sun could counteract the braking lunir-solar gravitational torque in the Precambrian, several authors have recently revisited this hypothesis. In these studies, it is argued that the geological evidences of the past spin state of the Earth play in favor of this atmospheric tidal locking of the length of the day (LOD). In the present review of the recent literature, we show that the drawn conclusions depend crucially on the consideration of the stromatolite geological LOD estimates obtained by Pannella at 1.88 and 2.0 Ga, which are subject to large uncertainties. When only the most robust cyclostatigraphic estimates of the LOD are retained, the LOD locking hypothesis is not supported. Moreover, the consideration of the published General Circulation Model numerical simulations and of new analytical models for the thermal atmospheric tides suggest that the atmospheric tidal resonance, which is the crucial ingredient for the LOD locking in the Precambrian, was never of sufficiently large amplitude to allow for this tidal LOD lock.

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arXiv2023

Thermal tides in neutrally stratified atmospheres: Revisiting the Earth's Precambrian rotational equilibrium

Rotational dynamics of the Earth, over geological timescales, have profoundly affected local and global climatic evolution, probably contributing to the evolution of life. To better retrieve the Earth's rotational history, and motivated by the published hypothesis of a stabilized length of day during the Precambrian, we examine the effect of thermal tides on the evolution of planetary rotational motion. The hypothesized scenario is contingent upon encountering a resonance in atmospheric Lamb waves, whereby an amplified thermotidal torque cancels the opposing torque of the oceans and solid interior, driving the Earth into a rotational equilibrium. With this scenario in mind, we construct an ab initio model of thermal tides on rocky planets describing a neutrally stratified atmosphere. The model takes into account dissipative processes with Newtonian cooling and diffusive processes in the planetary boundary layer. We retrieve from this model a closed-form solution for the frequency-dependent tidal torque which captures the main spectral features previously computed using 3D general circulation models. In particular, under longwave heating, diffusive processes near the surface and the delayed thermal response of the ground prove to be responsible for attenuating, and possibly annihilating, the accelerating effect of the thermotidal torque at the resonance. When applied to the Earth, our model prediction suggests the occurrence of the Lamb resonance in the Phanerozoic, but with an amplitude that is insufficient for the rotational equilibrium. Interestingly, though our study was motivated by the Earth's history, the generic tidal solution can be straightforwardly and efficiently applied in exoplanetary settings.

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arXiv2022

The Resonant Tidal Evolution of the Earth-Moon Distance

Due to tidal interactions in the Earth-Moon system, the spin of the Earth slows down and the Moon drifts away. This recession of the Moon is now measured with great precision, but it has been realized, more than fifty years ago, that simple tidal models extrapolated back in time lead to an age of the Moon that is by far incompatible with the geochronological and geochemical evidence. In order to evade this problem, more elaborate models have been proposed, taking into account the oceanic tidal dissipation. However, these models did not fit both the estimated lunar age and the present rate of lunar recession simultaneously. Here we present a physical model that reconciles these two constraints and yields a unique solution of the tidal history. This solution fits well the available geological proxies for the history of the Earth-Moon system and consolidates the cyclostratigraphic method. The resulting evolution involves multiple crossings of resonances in the oceanic dissipation that are associated with significant and rapid variations in the lunar orbital distance, the Earth's length of the day, and the Earth's obliquity.

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arXiv2022

Meta-modelling the climate of dry tide locked rocky planets

Rocky planets hosted by close-in extrasolar systems are likely to be tidally locked in 1:1 spin-orbit resonance, a configuration where they exhibit permanent dayside and nightside. Because of the resulting day-night temperature gradient, the climate and large-scale circulation of these planets are strongly determined by their atmospheric stability against collapse, which designates the runaway condensation of greenhouse gases. To better constrain the surface conditions of rocky planets located in the habitable zone of their host star, it is therefore crucial to elucidate the mechanisms that govern the day-night heat redistribution. As a first attempt to bridge the gap between multiple modelling approaches ranging from idealised models to 3-D General Circulation Models (GCM), we developed a General Circulation Meta-Model (GCMM) able to reproduce both the closed-form solutions provided by analytical models and the numerical solutions obtained from GCM simulations. We used this approach to characterise the atmospheric stability of Earth-sized rocky planets with dry atmospheres containing CO2, and we benchmarked it against 3-D GCM simulations using THOR GCM. We observe that the collapse pressure below which collapse occurs can vary by ~40% around the value predicted by analytical scaling laws depending on the mechanisms taken into account among radiative transfer, atmospheric dynamics, and turbulent diffusion. Particularly, we find (i) that the turbulent diffusion taking place in the dayside planetary boundary layer (PBL) globally tends to warm up the nightside surface hemisphere except in the transition zone between optically thin and optically thick regimes, (ii) that the PBL also significantly affects the day-night advection timescale, and (iii) that the slow rotator approximation holds from the moment that the normalised equatorial Rossby deformation radius is greater than 2.

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arXiv2021

Lithologic Controls on Silicate Weathering Regimes of Temperate Planets

Weathering of silicate rocks at a planetary surface can draw down CO$_2$ from the atmosphere for eventual burial and long-term storage in the planetary interior. This process is thought to provide an essential negative feedback to the carbonate-silicate cycle (carbon cycle) to maintain clement climates on Earth and potentially similar temperate exoplanets. We implement thermodynamics to determine weathering rates as a function of surface lithology (rock type). These rates provide upper limits that allow estimating the maximum rate of weathering in regulating climate. This modeling shows that the weathering of mineral assemblages in a given rock, rather than individual minerals, is crucial to determine weathering rates at planetary surfaces. By implementing a fluid-transport controlled approach, we further mimic chemical kinetics and thermodynamics to determine weathering rates for three types of rocks inspired by the lithologies of Earth's continental and oceanic crust, and its upper mantle. We find that thermodynamic weathering rates of a continental crust-like lithology are about one to two orders of magnitude lower than those of a lithology characteristic of the oceanic crust. We show that when the CO$_2$ partial pressure decreases or surface temperature increases, thermodynamics rather than kinetics exerts a strong control on weathering. The kinetically- and thermodynamically-limited regimes of weathering depend on lithology, whereas, the supply-limited weathering is independent of lithology. Our results imply that the temperature-sensitivity of thermodynamically-limited silicate weathering may instigate a positive feedback to the carbon cycle, in which the weathering rate decreases as the surface temperature increases.

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arXiv2020

Atmospheric stability and collapse on tidally locked rocky planets

Over large timescales, a terrestrial planet may be driven towards spin-orbit synchronous rotation by tidal forces. In this particular configuration, the planet exhibits permanent dayside and nightside, which may induce strong day-night temperature gradients. The nightside temperature depends on the efficiency of the day-night heat redistribution and determines the stability of the atmosphere against collapse. To better constrain the atmospheric stability, climate, and surface conditions of rocky planets located in the habitable zone of their host star, it is thus crucial to understand the complex mechanism of heat redistribution. Building on early works and assuming dry thermodynamics, we developed a hierarchy of analytic models taking into account the coupling between radiative transfer, dayside convection, and large-scale atmospheric circulation in the case of slowly rotating planets. There are two types of these models: a zero-dimensional two-layer approach and a two-column radiative-convective-subsiding-upwelling (RCSU) model. They yield analytical solutions and scaling laws characterising the dependence of the collapse pressure on physical features, which are compared to the results obtained by early works using 3D global climate models (GCMs). The analytical theory captures (i) the dependence of temperatures on atmospheric opacities and scattering in the shortwave and in the longwave, (ii) the behaviour of the collapse pressure observed in GCM simulations at low stellar fluxes that are due to the non-linear dependence of the atmospheric opacity on the longwave optical depth at the planet's surface, (iii) the increase of stability generated by dayside sensible heating, and (iv) the decrease of stability induced by the increase of the planet size.

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arXiv2020

On the impact of tides on the transit-timing fits to the TRAPPIST-1 system

Transit Timing Variations, or TTVs, can be a very efficient way of constraining masses and eccentricities of multi-planet systems. Recent measurements of the TTVs of TRAPPIST-1 led to an estimate of the masses of the planets, enabling an estimate of their densities. A recent TTV analysis using data obtained in the past two years yields a 34% and 13% increase in mass for TRAPPIST-1b and c, respectively. In most studies to date, a Newtonian N-body model is used to fit the masses of the planets, while sometimes general relativity is accounted for. Using the Posidonius N-body code, we show that in the case of the TRAPPIST-1 system, non-Newtonian effects might be also relevant to correctly model the dynamics of the system and the resulting TTVs. In particular, using standard values of the tidal Love number $k_2$ (accounting for the tidal deformation) and the fluid Love number $k_{2f}$ (accounting for the rotational flattening) leads to differences in the TTVs of TRAPPIST-1b and c similar to the differences caused by general relativity. We also show that relaxing the values of tidal Love number $k_2$ and the fluid Love number $k_{2f}$ can lead to TTVs which differ by as much as a few 10~s on a $3-4$-year timescale, which is a potentially observable level. The high values of the Love numbers needed to reach observable levels for the TTVs could be achieved for planets with a liquid ocean, which, if detected, might then be interpreted as a sign that TRAPPIST-1b and TRAPPIST-1c could have a liquid magma ocean. For TRAPPIST-1 and similar systems, the models to fit the TTVs should potentially account for general relativity, for the tidal deformation of the planets, for the rotational deformation of the planets and, to a lesser extent, for the rotational deformation of the star, which would add up to 7x2+1 = 15 additional free parameters in the case of TRAPPIST-1.

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arXiv2019

Final spin states of eccentric ocean planets

Eccentricity tides generate a torque that can drive an ocean planet towards asynchronous rotation states of equilibrium when enhanced by resonances associated with the oceanic tidal modes. We investigate the impact of eccentricity tides on the rotation of rocky planets hosting a thin uniform ocean and orbiting cool dwarf stars such as TRAPPIST-1, with orbital periods ~1-10 days. Combining the linear theory of oceanic tides in the shallow water approximation with the Andrade model for the solid part of the planet, we develop a global model including the coupling effects of ocean loading, self-attraction, and deformation of the solid regions. We derive from this model analytic solutions for the tidal Love numbers and torque exerted on the planet. These solutions are used with realistic values of parameters provided by advanced models of the internal structure and tidal oscillations of solid bodies to explore the parameter space both analytically and numerically. Our model allows us to fully characterise the frequency-resonant tidal response of the planet, and particularly the features of resonances associated with the oceanic tidal modes (eigenfrequencies, resulting maxima of the tidal torque and Love numbers) as functions of the planet parameters (mass, radius, Andrade parameters, ocean depth and Rayleigh drag frequency). Resonances associated with the oceanic tide decrease the critical eccentricity beyond which asynchronous rotation states distinct from the usual spin-orbit resonances can exist. We provide an estimation and scaling laws for this critical eccentricity, which is found to be lowered by roughly one order of magnitude, switching from ~0.3 to ~0.06 in typical cases and to ~0.01 in extremal ones.

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arXiv2019

A generic frequency dependence for the atmospheric tidal torque of terrestrial planets

Thermal atmospheric tides have a strong impact on the rotation of terrestrial planets. They can lock these planets into an asynchronous rotation state of equilibrium. We aim at characterizing the dependence of the tidal torque resulting from the semidiurnal thermal tide on the tidal frequency, the planet orbital radius, and the atmospheric surface pressure. The tidal torque is computed from full 3D simulations of the atmospheric climate and mean flows using a generic version of the LMDZ general circulation model (GCM) in the case of a nitrogen-dominated atmosphere. Numerical results are discussed with the help of an updated linear analytical framework. Power scaling laws governing the evolution of the torque with the planet orbital radius and surface pressure are derived. The tidal torque exhibits i) a thermal peak in the vicinity of synchronization, ii) a resonant peak associated with the excitation of the Lamb mode in the high frequency range, and iii) well defined frequency slopes outside these resonances. These features are well explained by our linear theory. Whatever the star-planet distance and surface pressure, the torque frequency spectrum -- when rescaled with the relevant power laws -- always presents the same behaviour. This allows us to provide a single and easily usable empirical formula describing the atmospheric tidal torque over the whole parameter space. With such a formula, the effect of the atmospheric tidal torque can be implemented in evolutionary models of the rotational dynamics of a planet in a computationally efficient, and yet relatively accurate way.

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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.

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arXiv2018

Consequences of semidiurnal thermal tides on hot Jupiters zonal mean flows

Hot Jupiters are submitted to an intense stellar heating. The resulting thermal tides can torque their atmospheres into asynchronous rotation, while these planets are usually assumed to be locked into spin-orbit synchronization with their host star. Particularly, the thermal atmospheric torque can be greatly enhanced by the dynamical component of the tidal response, that is the component associated with the propagation of internal waves. Owing to the involved complex dynamics, semi-analytical approaches are crucial to understand the physical mechanisms that are responsible for the frequency-resonant behavior of thermal tides, and quantify the atmospheric tidal torque. In this work, we revisit the early works by Arras \& Socrates (2010) and present an improved modeling of thermal tides taking into account rotation and radiative cooling. Using this new modeling, we compute analytically the atmospheric tidal response of hot Jupiters and show that resonances associated with low-frequency internal gravity waves are able to drive asynchronous zonal flows in the range 1-30 days.

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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.

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arXiv2018

Semidiurnal thermal tides in asynchronously rotating hot Jupiters

Thermal tides can torque the atmosphere of hot Jupiters into asynchronous rotation, while these planets are usually assumed to be locked into spin-orbit synchronization with their host star. In this work, our goal is to characterize the tidal response of a rotating hot Jupiter to the tidal semidiurnal thermal forcing of its host star, by identifying the structure of tidal waves responsible for variation of mass distribution, their dependence on the tidal frequency and their ability to generate strong zonal flows. We develop an ab initio global modeling that generalizes the early approach of Arras & Socrates (2010) to rotating and non-adiabatic planets. We derive analytically the torque exerted on the body and the associated timescales of evolution, as well as the equilibrium tidal response of the atmosphere in the zero-frequency limit. Finally, we integrate numerically the equations of thermal tides for three cases including dissipation and rotation step by step. The resonances associated with tidally generated gravito-inertial waves amplify significantly the resulting tidal torque in the range 1-30 days. This torque can drive globally the atmosphere into asynchronous rotation, as its sign depends on the tidal frequency. The resonant behaviour of the tidal response is enhanced by rotation, which couples the forcing to several Hough modes in the general case, while the radiative cooling tends to regularize it and diminish its amplitude.

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