A proof that tidal heating in a synchronous rotation is always larger than in an asymptotic nonsynchronous rotation state

In a recent paper, Wisdom (2007, Icarus, in press) derived concise expressions for the rate of tidal dissipation in a synchronously rotating body for arbitrary orbital eccentricity and obliquity. He provided numerical evidence than the derived rate is always larger than in an asymptotic nonsynchronous rotation state at any obliquity and eccentricity. Here, I present a simple mathematical proof of this conclusion and show that this result still holds for any spin-orbit resonance.Comment: 10 pages, 0 figure. accepted for publication in "Icarus

Secular evolution of a satellite by tidal effect. Application to Triton

Some of the satellites in the Solar System, including the Moon, appear to have been captured from heliocentric orbits at some point in their past, and then have evolved to the present configurations. The exact process of how this trapping occurred is unknown, but the dissociation of a planetesimal binary in the gravitational field of the planet, gas drag, or a massive collision seem to be the best candidates. However, all these mechanisms leave the satellites in elliptical orbits that need to be damped to the present almost circular ones. Here we give a complete description of the secular tidal evolution of a satellite just after entering a bounding state with the planet. In particular, we take into account the spin evolution of the satellite, which has often been assumed synchronous in previous studies. We apply our model to Triton and successfully explain some geophysical properties of this satellite, as well as the main dynamical features observed for the Neptunian system.Comment: 4 pages, 1 figur

Spin evolution of Earth-sized exoplanets, including atmospheric tides and core-mantle friction

Planets with masses between 0.1 and 10M(circle plus) are believed to host dense atmospheres. These atmospheres can play an important role on the planet's spin evolution, since thermal atmospheric tides, driven by the host star, may counterbalance gravitational tides. In this work, we study the long-term spin evolution of Earth-sized exoplanets. We generalize previous works by including the effect of eccentric orbits and obliquity. We show that under the effect of tides and core-mantle friction, the obliquity of the planets evolves either to 0 degrees or 180 degrees. The rotation of these planets is also expected to evolve into a very restricted number of equilibrium configurations. In general, none of these equilibria is synchronous with the orbital mean motion. The role of thermal atmospheric tides becomes more important for Earth-sized planets in the habitable zones of their systems; so they cannot be neglected when we search for their potential habitability

Stability analysis of the Martian obliquity during the Noachian era

We performed numerical simulations of the obliquity evolution of Mars during the Noachian era, at which time the giant planets were on drastically different orbits than today. For the preferred primordial configuration of the planets we find that there are two large zones where the Martian obliquity is stable and oscillates with an amplitude lower than 20$^\circ$. These zones occur at obliquities below 30$^\circ$ and above 60$^\circ$; intermediate values show either resonant or chaotic behaviour depending on the primordial orbits of the terrestrial planets

Wave Number of Maximal Growth in Viscous Magnetic Fluids of Arbitrary Depth

An analytical method within the frame of linear stability theory is presented for the normal field instability in magnetic fluids. It allows to calculate the maximal growth rate and the corresponding wave number for any combination of thickness and viscosity of the fluid. Applying this method to magnetic fluids of finite depth, these results are quantitatively compared to the wave number of the transient pattern observed experimentally after a jump--like increase of the field. The wave number grows linearly with increasing induction where the theoretical and the experimental data agree well. Thereby a long-standing controversy about the behaviour of the wave number above the critical magnetic field is tackled.Comment: 19 pages, 15 figures, RevTex; revised version with a new figure and references added. submitted to Phys Rev

Constraining Ceres' interior from its Rotational Motion

Context. Ceres is the most massive body of the asteroid belt and contains about 25 wt.% (weight percent) of water. Understanding its thermal evolution and assessing its current state are major goals of the Dawn Mission. Constraints on internal structure can be inferred from various observations. Especially, detailed knowledge of the rotational motion can help constrain the mass distribution inside the body, which in turn can lead to information on its geophysical history. Aims. We investigate the signature of the interior on the rotational motion of Ceres and discuss possible future measurements performed by the spacecraft Dawn that will help to constrain Ceres' internal structure. Methods. We compute the polar motion, precession-nutation, and length-of-day variations. We estimate the amplitudes of the rigid and non-rigid response for these various motions for models of Ceres interior constrained by recent shape data and surface properties. Results. As a general result, the amplitudes of oscillations in the rotation appear to be small, and their determination from spaceborne techniques will be challenging. For example, the amplitudes of the semi-annual and annual nutations are around ~364 and ~140 milli-arcseconds, and they show little variation within the parametric space of interior models envisioned for Ceres. This, combined with the very long-period of the precession motion, requires very precise measurements. We also estimate the timescale for Ceres' orientation to relax to a generalized Cassini State, and we find that the tidal dissipation within that object was probably too small to drive any significant damping of its obliquity since formation. However, combining the shape and gravity observations by Dawn offers the prospect to identify departures of non-hydrostaticity at the global and regional scale, which will be instrumental in constraining Ceres' past and current thermal state. We also discuss the existence of a possible Chandler mode in the rotational motion of Ceres, whose potential excitation by endogenic and/or exogenic processes may help detect the presence of liquid reservoirs within the asteroid.Comment: submitted to Astronomy and Astrophysic

Tidal dissipation within hot Jupiters: a new appraisal

Eccentricity or obliquity tides have been proposed as the missing energy source that may explain the anomalously large radius of some transiting ``hot Jupiters''. To maintain a non-zero and large obliquity, it was argued that the planets can be locked in a Cassini state, i.e. a resonance between spin and orbital precessions. We compute the tidal heating within ``inflated'' close-in giant planets with a non-zero eccentricity or obliquity. We further inspect whether the spin of a ``hot Jupiter'' could have been trapped and maintained in a Cassini state during its early despinning and migration. We estimate the capture probability in a spin-orbit resonance between $\sim$ 0.5 AU (a distance where tidal effects become significant) and 0.05 AU for a wide range of secular orbital frequencies and amplitudes of gravitational perturbations. Numerical simulations of the spin evolution are performed to explore the influence of tidal despinning and migration processes on the resonance stability. We find that tidal heating within a non-synchronous giant planet is about twice larger than previous estimates based on the hypothesis of synchronization. Chances of capture in a spin-orbit resonance are very good around 0.5 AU but they decrease dramatically with the semi-major axis. Furthermore, even if captured, both tidal despinning and migration processes cause the tidal torque to become large enough that the obliquity ultimately leaves the resonance and switches to near $0^{\circ}$. Locking a ``hot Jupiter'' in an isolated spin-orbit resonance is unlikely at 0.05 AU but could be possible at larger distances. Another mechanism is then required to maintain a large obliquity and create internal heating through obliquity tidesComment: 4 pages & 2 Figure

GJ 273: On the formation, dynamical evolution, and habitability of a planetary system hosted by an M dwarf at 3.75 parsec

Context. Planets orbiting low-mass stars such as M dwarfs are now considered a cornerstone in the search for life-harbouring planets. GJ 273 is a planetary system orbiting an M dwarf only 3.75 pc away, composed of two confirmed planets, GJ 273b and GJ 273c, and two promising candidates, GJ 273d and GJ 273e. Planet GJ 273b resides in the habitable zone. Currently, due to a lack of observed planetary transits, only the minimum masses of the planets are known: Mb sin ib=2.89 M⊕, Mc sin ic=1.18 M⊕, Md sin id=10.80 M⊕, and Me sin ie=9.30 M⊕. Despite being an interesting system, the GJ 273 planetary system is still poorly studied. Aims. We aim at precisely determine the physical parameters of the individual planets, in particular to break the mass–inclination degeneracy to accurately determine the mass of the planets. Moreover, we present thorough characterisation of planet GJ 273b in terms of its potential habitability. Methods. First, we explored the planetary formation and hydration phases of GJ 273 during the first 100 Myr. Secondly, we analysed the stability of the system by considering both the two- and four-planet configurations. We then performed a comparative analysis between GJ 273 and the Solar System, and searched for regions in GJ 273 which may harbour minor bodies in stable orbits, i.e. main asteroid belt and Kuiper belt analogues. Results. From our set of dynamical studies, we obtain that the four-planet configuration of the system allows us to break the mass– inclination degeneracy. From our modelling results, the masses of the planets are unveiled as: 2:89 ≤ Mb ≤ 3:03 M⊕, 1:18 ≤ Mc ≤ 1:24 M⊕, 10:80 ≤ Md ≤ 11:35 M⊕ and 9:30 ≤ Me ≤ 9:70 M⊕. These results point to a system likely composed of an Earth-mass planet, a super-Earth and two mini-Neptunes. From planetary formation models, we determine that GJ 273b was likely an efficient water captor while GJ 273c is probably a dry planet. We found that the system may have several stable regions where minor bodies might reside. Collectively, these results are used to comprehensively discuss the habitability of GJ 273bSpanish Ministry of Science and Education Ramón y Cajal programme ESP2017-87676-2-2 RYC-2012-09913CONICYT- FONDECYT/Chile Postdoctorado 3180405MIT’s Kavli Institut

Quantifying the Influence of Jupiter on the Earth's Orbital Cycles

A wealth of Earth-sized exoplanets will be discovered in the coming years, proving a large pool of candidates from which the targets for the search for life beyond the Solar system will be chosen. The target selection process will require the leveraging of all available information in order to maximise the robustness of the target list and make the most productive use of follow-up resources. Here, we present the results of a suite of $n$-body simulations that demonstrate the degree to which the orbital architecture of the Solar system impacts the variability of Earth's orbital elements. By varying the orbit of Jupiter and keeping the initial orbits of the other planets constant, we demonstrate how subtle changes in Solar system architecture could alter the Earth's orbital evolution -- a key factor in the Milankovitch cycles that alter the amount and distribution of solar insolation, thereby driving periodic climate change on our planet. The amplitudes and frequencies of Earth's modern orbital cycles fall in the middle of the range seen in our runs for all parameters considered -- neither unusually fast nor slow, nor large nor small. This finding runs counter to the `Rare Earth' hypothesis, which suggests that conditions on Earth are so unusual that life elsewhere is essentially impossible. Our results highlight how dynamical simulations of newly discovered exoplanetary systems could be used as an additional means to assess the potential targets of biosignature searches, and thereby help focus the search for life to the most promising targets.Comment: 19 pages; 11 figures; accepted for publication in the Astronomical Journal Version 2 - incorporates typo corrections and minor changes noted at the proofing stage, after acceptanc