Improving tidal modeling for rocky worlds

This work studies the evolution of several Distant Retrograde Orbits (DROs) of varying size in the Earth-Moon system over durations up to tens of millennia. This analysis is relevant for missions requiring a completely hands off, long duration quarantine orbit, such as a Mars Sample Return mission or the Asteroid Redirect Mission. Four DROs are selected from four stable size regions and are propagated for up to 30,000 years with an integrator that uses extended precision arithmetic techniques and a high fidelity dynamical model. The evolution of the orbit’s size, shape, orientation, period, out-of-plane amplitude, and Jacobi constant are tracked. It has been found that small DROs, with minor axis amplitudes of approximately 45,000 km or less decay in size and period largely due to the Moon’s solid tides. Larger DROs (62,000 km and up) are more influenced by the gravity of bodies external to the Earth-Moon system, and remain bound to the Moon for significantly less time.

Mercury is locked into a 3/2 spin-orbit resonance where it rotates three times on its axis for every two orbits around the sun. The stability of this equilibrium state is well established, but our understanding of how this state initially arose remains unsatisfactory. Unless one uses an unrealistic tidal model with constant torques (which cannot account for the observed damping of the libration of the planet) the computed probability of capture into 3/2 resonance is very low (about 7 per cent). This led to the proposal that core-mantle friction may have increased the capture probability, but such a process requires very specific values of the core viscosity. Here we show that the chaotic evolution of Mercury's orbit can drive its eccentricity beyond 0.325 during the planet's history, which very efficiently leads to its capture into the 3/2 resonance. In our numerical integrations of 1,000 orbits of Mercury over 4 Gyr, capture into the 3/2 spin-orbit resonant state was the most probable final outcome of the planet's evolution, occurring 55.4 per cent of the time.

<p>Earth and atmospheric tides are prevalent across the land-surface and provide natural forcing to characterise the hydro-geomechanical confined subsurface by using their groundwater response. Since tides are harmonic, their individual influences on the pressure head can be separated into complex components containing level or pressure magnitudes and phases. The approximated planar strain from Earth tides, and the uniaxial loading from atmospheric tides, allow the estimation of a wide range of values based on hydraulic and poroelastic relationships. With recent research advances, tidal analysis can be used to estimate hydro-geomechanical properties including specific storage, hydraulic conductivity, porosity, shear, Young’s and Bulk moduli, Skempton’s and Biot-Willis coefficients and undrained/drained Poisson’s ratios. This approach does not require any assumption on mineral grain compressibility for unconsolidated systems. However, consolidated materials currently require an a priori estimate of grain compressibility. We applied this method to pressure measurements from different geological settings. The estimated hydro-geomechanical properties comply with theoretically expected values except for Poisson’s ratio, which differs from laboratory values due to differing confining pressures, and comparatively low frequencies of the Earth and Atmospheric tide signals. However, these estimated values from in-situ data are likely more realistic of the natural hydrogeological response. We anticipate that, by developing methods that routinely can derive engineering geotechnical values through the monitoring of hydraulic head variations, the collection of groundwater pressures will become a priority for large civic excavations or construction, such as mining, in addition to environmental studies and regulatory compliance.</p>

The effects of the earth and ocean tides on the semi-diurnal lunar tide in the atmosphere have been ignored in nearly all studies of this air tide. Elementary arguments show that these boundary effects are not trivial. Using linear theory we calculated the combined effect of the lunar potential, the earth tide, and the ocean tide on a realistic model atmosphere. Love's theory was used to represent the earth tide. Numerical calculations by Bogdanov and Magarik and by Pekeris and Accad were used to represent the ocean tide. Our results indicate that the ocean tide has a significant and probably a dominant effect on the lunar air tide. The ocean tide of Pekeris and Accad yielded results that agreed better with the observations. We calculated the effect of a tide in a “small” or “point” ocean on the atmosphere and found that its effects were global. Hence, differences between the observations and our calculations of the lunar air tide cannot easily be reduced by simple manipulation of the forcing fun...

Aims. The aim of this work is to develop a formalism for the study of the secular evolution of a binary system which includes interaction due to the tides that each body imparts on the other. We also consider the influence of the J2-related secular terms on the orbital evolution and the torque, caused by the triaxiality, on the rotational evolution, both of which are associated only to one of the bodies. We apply these set of equations to the study of the orbital and rotational evolution of a binary system composed of a rocky planet and its host star in order to characterize the dynamical evolution at work, particularly near spin-orbit resonances. Methods. We used the equations of motion that give the time evolution of the orbital elements and the spin rates of each body to study the dynamical evolution of the Kepler-21 system as an example of how the formalism that we have developed can be applied. Results. We obtained a set of equations of motion without singularities for vanishing eccentricities and inclinations. This set gives, on one hand, the time evolution of the orbital elements due to the tidal potentials generated by both members of the system as well as the oblateness of one of them. On the other hand, it gives the time evolution of the stellar spin rate due to the corresponding tidal torque and of the planet’s rotation angle due to both the tidal and triaxiality-induced torques. We found that for the parameters and the initial conditions explored here, the tidally and triaxiality-induced modifications of the tidal modes can be more significative than expected and that the time of tidal synchronization strongly depends on the values of the rheological parameters.

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. (2016a) and Auclair-Desrotour et al. (2016b).

Mercury's capture into the 3/2 spin–orbit resonance including the effect of core–mantle friction

<p>Observations of the Venus Climate Orbiter “Akatsuki” provide us with horizontal distributions of the horizontal winds derived from cloud tracking of the Ultraviolet Imager (UVI) and of temperature observed by the Longwave Infrared Camera (LIR). However, these observations are limited in altitude, local time (day or night side), and frequency. Then it is difficult to elucidate the general circulation of the Venus atmosphere, including various temporal and spatial scales, only from observations. In this study, we produced a Venus dataset (analysis) that has high temporal and spatial resolutions by assimilating horizontal winds derived by the Akatsuki observations. At the top of the cloud layer of Venus, there are planetary-scale atmospheric waves that are excited by the solar heating and move with the sun, called the thermal tides. In this presentation, we focused on thermal tides to verify the analysis.</p> <p>We use the Venus atmospheric data assimilation system “ALEDAS-V" (Sugimoto et al., 2017) [1] for assimilation and the Venus atmospheric general circulation model “AFES-Venus" (Sugimoto et al., 2014) [2] for ensemble forecasts. AFES-Venus is a full nonlinear dynamical GCM on the assumption of hydrostatic balance, designed for the Venus atmosphere. ALEDAS-V uses the Local Ensemble Transform Kalman Filter, and is the first data assimilation system for the Venus atmosphere. We assimilated the cloud top (~70km) zonal and meridional winds obtained by tracking morphology, using Akatsuki UVI data (Horinouchi et al., 2021) [3] from September 1st to December 31st, 2018. The assimilation data (analysis) from October 1st to November 30th, 2018, is analyzed, because the root-mean-square-deviations (RMSD) from FR (free run; the case without data assimilation) are stable.</p> <p>Figures (a) and (d) show the observed zonal and meridional winds, respectively. The zonal wind has a local minimum near 11 LT (local time) around the equator (Figure a). The meridional wind is the weakest at the equator and increases with latitude, and the amplitude is maximum around noon (Figure d) in the local time direction. Note that these winds obtained from observations exist only the dayside equatorward of 50° latitudes (Figure a and d).</p> <p>Figures (b) and (e) show the deviations from the zonal means of zonal and meridional winds at an altitude of 70 km in the FR, respectively. For zonal wind, diurnal (zonal wavenumber 1) and semidiurnal (zonal wavenumber 2) tides are dominant at latitudes poleward and equatorward of 30, respectively (Figure b). The zonal wind deviation has a local minimum at 14-15LT, which is ~ 2 hours behind the observation (Figures a and b). The meridional wind deviation is polar and equatorial on the dayside and nightside, respectively (Figure e), and this distribution is consistent with Akatsuki's observation (Figure d).</p> <p>Figures (c) and (f) show the zonal and meridional winds as a result of assimilation, respectively. The zonal wind in the equatorial region have a local minimum near 11 LT. The assimilation improved the semidiurnal tide closer to the observations (Figures a and c). The meridional wind is not so different from FR. This is probably because FR was originally very similar to observations (Figures d and f). These results are consistent with a previous study by Sugimoto et al. (2019) [4]. In addition, while the observed winds exist only on the dayside, the results of assimilation show that the horizontal winds field is modified significantly even on the nightside. It is suggested that spatially limited data assimilation can improve the general circulation of GCM.</p> <p>In the future work, we are planning to release the assimilation dataset as the “objective analysis data” of Venus for the first time in the world.</p> <p><img src="" alt="" width="743" height="482" /></p> <p>[1] Sugimoto, N., et al. Development of an ensemble Kalman filter data assimilation system for the Venusian atmosphere. Scientific Reports 7(1), 9321 (2017).</p> <p>[2] Sugimoto, N., et al. Baroclinic instability in the Venus atmosphere simulated by GCM. J. Geophys. Res. Planets 119, 1950–1968 (2014).</p> <p>[3] Horinouchi, T., et al. Venus Climate Orbiter Akatsuki Cloud Motion Vector Data Set v1.0, JAXA Data Archives and Transmission System (2021).</p> <p>[4] Sugimoto, N., et al. Impact of data assimilation on thermal tides in the case of Venus Express wind observation. Geophys. Res. Lett. 46, 4573–4580 (2019).</p>

The long-term monitoring records of hydraulic heads frequently contain fluctuations originating from different cyclic drivers. Fourier analysis applied to these records can reveal connected surface-water/groundwater system characteristics. The various components of the atmospheric tides, the earth tides and the presence of diurnal responses to evapotranspiration are identified and isolated through band-pass filtering of data recorded from both vented and absolute gauge transducers. The signature of the different cyclic drivers is contained in amplitude and phase of the various signal components and can be used to determine the degree of system confinement. A methodology is described for the calculation of barometric efficiency in confined aquifers based upon the amplitude of the M2 and S2 components of the earth and atmospheric tides. It is demonstrated that Fourier analysis of water-level fluctuations is a simple but underused tool that can help to characterise shallow groundwater systems.

The viscosity of Venus’ mantle inferred from its rotational state

A constant daylength during the Precambrian era?

Close-in planets evolve under extreme conditions, which raises questions about their origins and current nature. Two evolutionary mechanisms thought to play a predominant role are orbital migration, which brings them close to their star, and atmospheric escape under the resulting increased irradiation. Yet their relative roles remain poorly understood, in part because we lack numerical models that couple the two mechanisms with high precision and on secular timescales. To address this need, we developed the Joining Atmosphere and Dynamics for Exoplanets (JADE) code, which simulates the secular atmospheric and dynamical evolution of a specific planet around its star, and can include the perturbation induced by a distant third body. On the dynamical side, the three dimensional evolution of the orbit is modeled under stellar and planetary tidal forces, a relativistic correction, and the action of the distant perturber. On the atmospheric side, the vertical structure of the atmosphere is integrated over time based on its thermodynamical properties, inner heating, and the evolving stellar irradiation, which results, in particular, in extreme ultraviolet induced photo-evaporation. The JADE code is benchmarked on GJ436 b, which is a prototype of the evaporating giants on eccentric, misaligned orbits at the edge of the hot Neptunes desert. We confirm previous results that the orbital architecture of GJ436 b is well explained by Kozai migration and bring to light a strong interplay between its atmospheric and orbital evolution. During the resonance phase, the atmosphere pulsates in tune with the Kozai cycles, which leads to stronger tides and an earlier migration. This triggers a strong atmospheric evaporation several billion years after the planet formed, refining the paradigm that mass loss is dominant in the early age of close-in planets. These results suggest that the edge of the desert could be formed of warm Neptunes whose evaporation was delayed by Kozai migration. They strengthen the importance of coupling atmospheric and dynamical evolution over secular timescales, which the JADE code will allow for one to simulate for a wide range of systems.

<p>Groundwater resources are under increasing threat from human activity and climate change, making sustainable management critical. However, appropriate management generally requires extensive knowledge of the properties and characteristics of aquifers. In recent years, research into passive investigation methods utilising the impact of Earth and atmospheric tides (EAT) on the groundwater response have gained momentum. EAT occur at known frequencies of daily and sub-daily cycles per day (cpd) and present an inexpensive and viable opportunity for the characterization of groundwater systems at an unprecedented spatial and temporal resolution (McMillan et al., 2019). However, quantifying aquifer properties relies on accurate and reliable extraction of the harmonic properties (amplitude and phase) of tidal components embedded in groundwater level and atmospheric pressure records that are dominated by larger magnitude variations as well as other noise. Here, we use synthetic signals and real measurements to test and compare the performance of the Discrete Fourier Transform (DFT) with a generalised harmonic least squares amplitude and phase estimation (APES) approach for the harmonic tidal components. APES was implemented in Python in conjunction with a windowed de-trending function that serves as a high pass filter. The analysis focuses on three realistic aspects often encountered in groundwater monitoring: (1) the minimum record length required to reliably separate tidal components at nearby frequencies, (2) signal quantisation as a proxy for measurement resolution, and (3) the amount of sampling gaps or irregularly spaced sampling. Results indicate that APES outperforms DFT in quantifying the amplitude of the major tidal components M2 (1.93227 cpd) and S2 (2.0 cpd) on regularly sampled data, because it is not subject to spectral leakage. Furthermore, APES is superior in handling data gaps, missing values and outliers, yielding accurate amplitude estimates even for comparably small amounts of data and without requiring pre-processing such as data interpolation or resampling. This increases the data volume for the tidal analysis considerably and enables a much more extensive use of tidal analysis. Further investigation will focus on the methods’ performance in quantifying the phase of the M2 and S2 components.</p><p> </p><p>McMillan, T. C., Rau, G. C., Timms, W. A., & Andersen, M. S. ( 2019). Utilizing the impact of Earth and atmospheric tides on groundwater systems: A review reveals the future potential. Reviews of Geophysics, 57, 281– 315. https://doi.org/10.1029/2018RG000630.</p>

Planets in the liquid-water habitable zone of low-mass stars experience large tidal forces, 103–104 times those on Earth, due to the small distance between the habitable zone and the host stars. Therefore, interior solid tides, ocean tides, and atmospheric tides on these planets could be much stronger than those on Earth, but little work has been done to explicitly simulate the ocean tides. Here, for the first time, we perform global ocean tide simulations and show that ocean tides on asynchronously rotating planets with large eccentricities can reach O ( 1000 ) m in height and O ( 10 ) m s − 1 in flow speed. Interactions between tide and bottom topography can induce large energy dissipation, ∼ O ( 100 ) W m − 2 in the global mean. This tidal energy dissipation can strongly accelerate orbital evolution by 1–2 orders of magnitude. However, for planets with small eccentricities, the ocean tides are much weaker but still comparable to those on modern Earth. Our results suggest that ocean tides on eccentric planets orbiting low-mass stars are orders of magnitude more powerful than those on Earth and can dramatically influence surface geography and orbital evolution.

The formation of massive black hole binaries (MBHBs) is an unavoidable outcome of galaxy evolution via successive mergers. However, the mechanism that drives their orbital evolution from parsec separations down to the gravitational wave (GW) dominated regime is poorly understood, and their final fate is still unclear. If such binaries are embedded in gas-rich and turbulent environments, as observed in remnants of galaxy mergers, the interaction with gas clumps (such as molecular clouds) may efficiently drive their orbital evolution. Using numerical simulations, we test this hypothesis by studying the dynamical evolution of an equal-mass, circular MBHB accreting infalling molecular clouds. We investigate different orbital configurations, modelling a total of 13 systems to explore different possible impact parameters and relative inclinations of the cloud-binary encounter. We focus our study on the prompt, transient phase during the first few orbits when the dynamical evolution of the binary is fastest, finding that this evolution is dominated by the exchange of angular momentum through gas capture by the individual black holes and accretion. Building on these results, we construct a simple model for evolving a MBHB interacting with a sequence of clouds, which are randomly drawn from reasonable populations with different levels of anisotropy in their angular momenta distributions. We show that the binary efficiently evolves down to the GW emission regime within a few hundred million years, overcoming the 'final parsec' problem regardless of the stellar distribution.