Researchers extend analytical model of atmospheric tides on rocky planets

Researchers Pierre Auclair-Desrotour, Jacques Laskar, Mohammad Farhat, and Gwenaël Boué wrote an analytical framework on atmospheric tides, the pressure and temperature waves driven by cycles of heating in an atmosphere; Pierre Auclair-Desrotour uploaded the first version to arXiv, a preprint server where researchers share papers before formal publication, on Nov. 4, 2026, at 19:19:17 UTC, Astrobiology Web reported on Nov. 7, 2026.

Astrobiology Web reported that the study extends earlier work that produced a fully analytical formulation of how rocky-planet atmospheres respond to tides, expressed in mathematical equations rather than numerical simulation. That earlier work serves as the foundation for the new analysis. The authors apply the framework to two idealized atmosphere types: isentropic atmospheres, in which entropy stays constant, and isothermal atmospheres, in which temperature stays constant; entropy measures how energy disperses in a system. Testing both lets the authors examine how the framework behaves under different thermodynamic assumptions, or ideas about how heat and energy move through the air.

The paper states that heat-driven atmospheric tides create thermodynamic acceleration that strongly shapes the spin of temperate rocky planets where gravitational and radiative forcings balance each other, Astrobiology Web reported. Thermodynamic acceleration is the change in motion produced by heat-driven atmospheric motion. Tidal forcing refers to the influence that raises tides, here from both gravity and starlight. The authors focus on cases where those two forcings are comparable, a situation that sets up the paper’s relevance to exoplanets not locked in synchronous rotation, in which one side permanently faces the star.

Astrobiology Web reported that this acceleration drives planets away from synchronous rotation and alters their climate, broad atmospheric circulation, and conditions at the surface. Observable planetary properties are traits that astronomers can measure. The authors link the torque mechanism directly to observable planetary properties. Exoplanets not locked in synchronous rotation are therefore the primary setting for the effect.

Because that relationship is not sufficiently understood, scientists must better constrain how thermotidal torque depends on tidal frequency and star-planet physical parameters, Astrobiology Web reports. Thermotidal torque is the twisting force on a planet’s spin produced by atmospheric tides driven by heating, and tidal frequency describes how often the tidal forcing repeats. Star-planet physical parameters describe properties of the star and planet together. The authors present this constraint work as necessary because current understanding remains incomplete.

The abstract singles out resonantly excited Lamb waves as a process that needs clarification, Astrobiology Web reported. Lamb waves are large-scale atmospheric waves trapped near a planet’s surface. The authors note these waves may have affected Earth’s length of day during the Precambrian era, an interval in Earth’s early history. Earth’s length of day is how long the planet takes to spin once on its axis, and understanding that connection is part of the paper’s motivation.

Understanding that connection better is part of the paper’s motivation.

Astrobiology Web reported that the authors work out the torque as a function of variables and check their analytical predictions against numerical results from earlier general circulation model studies. General circulation models are computer simulations of planetary atmospheres and climates. Functional analysis examines how one quantity changes as a function of another, and the authors combine it with benchmarking against earlier GCM simulations to test whether the analytical expressions reproduce numerical model behavior.

The authors’ analytical model agrees well with general circulation model results and reproduces how tidal torque varies with frequency for both paleo-Earth and present-day Earth, Astrobiology Web reported. Frequency dependence describes how a quantity changes as the repetition rate of the forcing changes. Paleo-Earth refers to an earlier climate state of the planet, while present-day Earth refers to the modern climate. The agreement spans two planetary climate states and supports using the model across different planetary climate conditions.

The solutions produce a peak torque close to synchronous rotation and stronger amplification tied to Lamb-wave resonance, Astrobiology Web reported. Amplification means an increase in strength. Resonance occurs when the atmosphere’s natural response lines up with the repeating tidal forcing. These features appear in the model output across the analyzed cases, and the peak and the enhancement are general characteristics of the torque solutions.

Near resonance, general circulation model results show a braking torque that is stronger than the accelerating torque, Astrobiology Web reported. Braking torque slows a planet’s spin, while accelerating torque speeds it up. Net braking means the rotational effect slows the planet rather than speeds it. This asymmetry, which the analytical work seeks to explain, appears as net braking that exceeds net acceleration in the GCM results near resonance.

The model reproduces this imbalance by allowing tidal heating to lag behind insolation, the incoming sunlight absorbed by the planet, Astrobiology Web reported. The paper states that introducing a lag between tidal heating and incoming insolation reproduces the GCM asymmetry. The paper presents that time delay as the physical reason for stronger braking near resonance.

Matching general circulation model spectra indicates that indirect thermal forcing with time delay mainly drives benchmark thermal tides rather than direct sunlight absorption, which governs semidiurnal tides on present-day Earth, Astrobiology Web reported. GCM spectra show how tidal strength varies across frequencies, and benchmark means the reference cases the authors test against. Indirect heating means warmth reaches the atmosphere through steps such as surface absorption before driving tides. Semidiurnal tides occur twice each day, and the spectral agreement supports the delayed-indirect-heating picture for the benchmark cases.

Astrobiology Web reported that the manuscript contains 26 pages and 7 figures, and Astronomy & Astrophysics has accepted it for publication. The comments field on the page gives the manuscript’s length and publication status, meaning whether it has been accepted or is still under consideration. The author line appears at the end of the abstract on the Astrobiology Web page, and it lists the four names without institutional affiliations.

The paper carries arXiv tags for Earth and Planetary Astrophysics (astro-ph.EP) and Geophysics (physics.geo-ph), plus mathematics subject class 85-02, a code used to classify research listed directly below the author list, and the tags place the paper in Earth and planetary astrophysics and geophysics, Astrobiology Web reported. The citation is arXiv:2611.07060 [astro-ph.EP], or arXiv:2611.07060v1 for this version, with DOI https://doi.org/10.48550/arXiv.2611.07060, a permanent digital identifier for the paper. The v1 label distinguishes this first version from later revisions. Pierre Auclair-Desrotour uploaded the first version, and it is 3,309 KB, with KB a unit of digital file size.