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Register a new userThe Physics of Bodily Tides in Terrestrial Planets, and the Appropriate Scales of Dynamical Evolution
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Any model of tides is based on a specific hypothesis of how lagging depends on the tidal-flexure frequency. For example, Gerstenkorn (1955), MacDonald (1964), and Kaula (1964) assumed constancy of the geometric lag angle, while Singer (1968) and Mignard (1979, 1980) asserted constancy of the time lag. Thus, each of these two models was based on a certain law of scaling of the geometric lag. The actual dependence of the geometric lag on the frequency is more complicated and is determined by the rheology of the planet. Besides, each particular functional form of this dependence will unambiguously fix the appropriate form of the frequency dependence of the tidal quality factor, Q. Since at present we know the shape of the dependence of Q upon the frequency, we can reverse our line of reasoning and single out the appropriate actual frequency-dependence of the angular lag. This dependence turns out to be different from those employed hitherto, and it entails considerable alterations in the time scales of the tide-generated dynamical evolution. Phobos fall on Mars is an example we consider.
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Spin-orbit coupling is often described in the MacDonald torque approach which has become the textbook standard. Within this method, a concise expression for the additional tidal potential, derived by MacDonald (1964; Rev. Geophys. 2, 467), is combined with an assumption that the Q factor is frequency-independent (i.e., that the geometric lag angle is constant in time). This makes the approach unphysical because MacDonalds derivation of the said formula was implicitly based on keeping the time lag frequency-independent, which is equivalent to setting Q to scale as the inverse tidal frequency. The contradiction requires the MacDonald treatment of both non-resonant and resonant rotation to be rewritten. The non-resonant case was reconsidered by Efroimsky & Williams (2009; CMDA 104, 257), in application to spin modes distant from the major commensurabilities. We continue this work by introducing the necessary alterations into the MacDonald-torque-based model of falling into a 1:1 resonance. (For the original version of the model, see Goldreich 1966; AJ 71, 1.) We also study the effect of the triaxiality on both circulating and librating rotation near the synchronous state. Circulating rotation may evolve toward the libration region or toward a spin rate larger than synchronous (pseudosynchronous spin). Which behaviour depends on the eccentricity, the triaxiality of the primary, and the mass ratio of the secondary and primary bodies. The spin evolution will always stall for the oblate case. For small-amplitude librations, expressions are derived for the libration frequency, damping rate, and average orientation. However, the stability of pseudosynchronous spin hinges upon the dissipation model. Makarov and Efroimsky (2012; arXiv:1209.1616) have found that a more realistic dissipation model than the corrected MacDonald torque makes pseudosynchronous spin unstable.
Earth has a unique surface character among Solar System worlds. Not only does it harbor liquid water, but also large continents. An exoplanet with a similar appearance would remind us of home, but it is not obvious whether such a planet is more likely to bear life than an entirely ocean-covered waterworld---after all, surface liquid water defines the canonical habitable zone. In this proceeding, I argue that 1) Earths bimodal surface character is critical to its long-term climate stability and hence is a signpost of habitability, and 2) we will be able to constrain the surface character of terrestrial exoplanets with next-generation space missions.
In the present research, we study the effects of a single giant planet in the dynamical evolution of water-rich embryos and planetesimals, located beyond the snow line of systems around Sun-like stars, in order to determine what kind of terrestrial-like planets could be formed in the habitable zone (hereafter HZ) of these systems. To do this, we carry out N-body simulations of planetary accretion, considering that the gas has been already dissipated from the disk and a single giant planet has been formed beyond the snow line of the system, at 3 au. We find that a giant planet with a value of mass between Saturn-mass and Jupiter-mass, represents a limit from which the amount of water-rich embryos that moves inward from beyond the snow line starts to decrease. From this, our research suggests that giant planets more massive than one Jupiter-mass become efficient dynamical barriers to inward-migrating water-rich embryos. Moreover, we infer that the number of these embryos that survive in the HZ significantly decreases for systems that host a giant planet more massive than one Jupiter-mass. This result has important consequences concerning the formation of terrestrial-like planets in the HZ with very high water contents and could provide a selection criteria in the search of potentially habitable exoplanets in systems that host a gaseous giant around solar-type stars.
We reexamine the popular belief that a telluric planet or satellite on an eccentric orbit can, outside a spin-orbit resonance, be captured in a quasi-static tidal equilibrium called pseudosynchronous rotation. The existence of such configurations was deduced from oversimplified tidal models assuming either a constant tidal torque or a torque linear in the tidal frequency. A more accurate treatment requires that the torque be decomposed into the Darwin-Kaula series over the tidal modes, and that this decomposition be combined with a realistic choice of rheological properties of the mantle. This development demonstrates that there exist no stable equilibrium states for solid planets and moons, other than spin-orbit resonances.
Aims: The secondary atmospheres of terrestrial planets form and evolve as a consequence of interaction with the interior over geological time. We aim to quantify the influence of planetary bulk composition on the interior--atmosphere evolution for Earth-sized terrestrial planets to aid in the interpretation of future observations of terrestrial exoplanet atmospheres. Methods: We used a geochemical model to determine the major-element composition of planetary interiors (MgO, FeO, and SiO2) following the crystallization of a magma ocean after planet formation, predicting a compositional profile of the interior as an initial condition for our long-term thermal evolution model. Our 1D evolution model predicts the pressure-temperature structure of the interior, which we used to evaluate near-surface melt production and subsequent volatile outgassing. Volatiles are exchanged between the interior and atmosphere according to mass conservation. Results: Based on stellar compositions reported in the Hypatia catalog, we predict that about half of rocky exoplanets have a mantle that convects as a single layer (whole-mantle convection), and the other half exhibit double-layered convection due to the presence of a mid-mantle compositional boundary. Double-layered convection is more likely for planets with high bulk planetary Fe-content and low Mg/Si-ratio. We find that planets with low Mg/Si-ratio tend to cool slowly because their mantle viscosity is high. Accordingly, low-Mg/Si planets also tend to lose volatiles swiftly through extensive melting. Moreover, the dynamic regime of the lithosphere (plate tectonics vs. stagnant lid) has a first-order influence on the thermal evolution and volatile cycling. These results suggest that the composition of terrestrial exoplanetary atmospheres can provide information on the dynamic regime of the lithosphere and the thermo-chemical evolution of the interior.
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