arXiv subjects

Mohammad Farhat

Publications and source records attributed to Mohammad Farhat.

13 recordsLinked to original sources

arXiv2026

Magma Ocean Waves and Thermal Variability on Lava Worlds

Lava worlds are rocky planets with dayside skins made molten by stellar irradiation. Tidal heating on these shortest-period planets is more than skin deep. We show how orbital eccentricities of just a few percent (within current observed bounds and maintained secularly by exterior companions) can create deep magma oceans. ``Lava tidal waves'' slosh across these oceans; we compute the multi-modal response of the ocean to tidal forcing, subject to a coastline at the day-night terminator and a parameterized viscous drag. Wave interference produces a dayside heat map that is spatially irregular and highly time-variable; hotspots can wander both east and west of the substellar point, and thermal light curves can vary and spike aperiodically, from orbit to orbit and within an orbit. Heat deposited by tides is removed in steady state by a combination of fluid, mushy, and solid-state convection in the mantle. For Earth-sized planets with sub-day periods, the entire mantle may be tidally liquified.

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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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arXiv2025

Capture into Apsidal Resonance and the Decimation of Planets around In-spiraling Binaries

Transiting circumbinary planets (CBPs) are conspicuously rare, and entirely absent around stellar binaries with periods $\leq 7$ days. Here, we exploit a secular resonance to stimulate the orbit of a CBP into strong, disruptive interactions with the host binary. The process requires no tertiary companion and is triggered when the general-relativistic precession of a tightening binary matches the Newtonian precession it induces in its companion planet. Adiabatic capture in this resonance sees the binary draining angular momentum from the CBP's orbit which grows steadily in eccentricity until destabilization, and eventual ejection or engulfment. We map this resonance in phase space, then investigate the dynamical outcomes of encounter in the course of tidally shrinking binaries. With the help of orbit averaged simulations of a suite of systems, we find that, around tightening binaries: eight out of ten CBPs encounter and are captured in the resonance; three out of four are `destroyed'; and survivors lurk on remote, low-transit-probability orbits. This suggests that the very process which forms tight binaries effectively clears the region where transiting CBPs could reside.

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arXiv2025

Interior redox state effects on the stability of secondary atmospheres and observational manifestations: LP 791-18 d as a case study for outgassing rocky exoplanets

Recent advances in space and ground-based facilities now enable atmospheric characterization of a selected sample of rocky exoplanets. These atmospheres offer key insights into planetary formation and evolution, but their interpretation requires models that couple atmospheric processes with both the planetary interior and the surrounding space environment. This work focuses on the Earth-size planet LP791 18d, which is estimated to receive continuous tidal heating due to the orbital configuration of the system; thus, it is expected to exhibit volcanic activity. We estimate the mantle temperature of 1680-1880 K. Our results show that the atmospheric mean molecular weight gradient is controlled by oxygen fugacity rather than bulk metallicity. Furthermore, we use the atmospheric steady-state solutions produced from the interior redox state versus surface pressure parameter space and explore their atmospheric stability. We find that stability is achieved only in highly oxidized scenarios while reduced interior states fall into the hydrodynamic escape regime with mass loss rates on the order of 10^5-10^8 kg/s. We argue that scenarios with reduced interior states are likely to have exhausted their volatile budget during the planets lifetime. Furthermore, we predict the atmospheric footprint of the planets interior based on its oxidation state and assess its detectability using current or forthcoming tools to constrain the internal and atmospheric composition. We show that the degeneracy between bare rock surfaces and thick atmospheres can be resolved by using three photometric bands to construct a color-color diagram that accounts for potential effects from photochemical hazes and clouds. Our modeling approach connects interior and atmospheric processes, providing a basis to explore volatile evolution and potential habitability.

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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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arXiv2023

The case of HD 106906 debris disc: A binary's revenge

Debris disc architecture presents [exo-]planetary scientists with precious clues for processes of planet formation and evolution, including constraints on planetary mass perturbers. This is particularly true of the disc in HD 106906, which in early HST, then follow up polarimetric observations, presented asymmetries and needle-like features that have been attributed to perturbations by a massive, and unusually distant external planetary companion. Here, we revisit the long-term secular dynamical evolution of the HD 106906 disc allowing for the combined gravitational action of the planetary companion and the inner stellar binary which holds the system together. We argue that the binary is strong enough to impose a dynamical break at the disc's location, resulting in distinctive observational signatures which we render via simulated surface density maps and vertical structure profiles. Within uncertainties on the planet's orbit, we show that the disc can go from being fully dominated by the inner binary to significantly so, and is hardly ever outside its reach. The extent of binary dominance impacts the disc's mean eccentricity, a metric which we map as a function of the planet's semi-major axis and orbital eccentricity, with and without radiation pressure. We can thus constrain the planet's orbit to ease the tension between evident axisymmetry in the millimeter, and apparent asymmetry in scattered light. We discuss phase space structure, then inclination distribution, arguing for the relevance of our results to a variety of hierarchical systems, as we set the stage for generalizations that allow for disc self-gravity and collisional evolution.

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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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arXiv2021

Laplace surface dynamics, revisited: satellites, exo-planets and debris with distant, eccentric companions

To date, studies of $\textit{Laplace Surface}$ dynamics have concerned themselves with test particle orbits of fixed shape and orientation in the combined field of an oblate central body (to which the particle is bound) and a distant, inclined, companion which is captured to quadrupolar order. While amply sufficient for satellites around planets on near-circular orbits, the quadrupolar approximation fails to capture essential dynamical features induced by a wide binary companion (be it a star, a planet or a black hole) on a fairly eccentric orbit. With similar such astronomical settings in mind, we extend the classical Laplace framework to higher multipoles, and map out the backbone of stationary orbits, now complexified by the broken axial symmetry. Eccentric and inclined Laplace equilibria, which had been presaged in systems of large enough mutual inclination, are here delineated over a broad range of mutually inclined perturbations. We recover them for test particles in the field of a hot Jupiter and a wide eccentric stellar binary, highlighting their relevance for the architecture of multi-planet systems in binaries. We then extend and deploy our machinery closer to home, as we consider the secular dynamics of Trans-Neptunian Objects (TNOs) in the presence of a putative ninth planet. We show how generalized Laplace equilibria seed islands for Trans-Neptunian objects to be sheltered around, islands within chaotic seas which we capture via Poincar$é$ sections, while highlighting a beautiful interplay between Laplace and Kozai-Lidov secular dynamical structures. An eminently classical tale revived for the exo-planetary 21st century!

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arXiv2021

Constraining the Earth's Dynamical Ellipticity from Ice Age Dynamics

The dynamical ellipticity of a planet expresses the departure of its mass distribution from spherical symmetry. It enters as a parameter in the description of a planet's precession and nutation, as well as other rotational normal modes. In the case of the Earth, uncertainties in this quantity's history produce an uncertainty in the solutions for the past evolution of the Earth-Moon system. Constraining this history has been a target of interdisciplinary efforts as it represents an astro-geodetic parameter whose variation is shaped by geophysical processes, and whose imprints can be found in the geological signal. We revisit the classical problem of its variation during ice ages, where glacial cycles exerted a varying surface loading that had altered the shape of the geoid. In the framework of glacial isostatic adjustment, and with the help of a recent paleoclimatic proxy of ice volume, we present the evolution of the dynamical ellipticity over the Cenozoic ice ages. We map out the problem in full generality identifying major sensitivities to surface loading and internal variations in parameter space. This constrained evolution is aimed to be used in future astronomical computations of the orbital and insolation quantities of the Earth.

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