Spin states and climates of eccentric exoplanets

The known extrasolar planets exhibit a wide range of orbital eccentricities e. This has a profound influence on their rotations and climates. Because of tides in their interiors, mostly solid exoplanets are expected eventually to despin to a state of spin-orbit resonance, where the orbital period is some integer or half-integer times the rotation period. The most important of these resonances is the synchronous state, where the planet's spin period exactly equals its orbital period (like Earth's Moon, and indeed most of the regular satellites in the Solar System). Such planets seem doomed to roast on one side and freeze on the other. However, synchronous planets rock back and forth by an angle of ∼2Arcsine with respect to the sub-stellar point. For e=0.055 (as for the Moon), this optical libration amounts to only ∼6°; but for a synchronous planet with e=0.50, for example, it would rise to ∼59°. This greatly expands the temperate “twilight zone” near the terminator and considerably improves the planet's prospects for habitability. For e?0.72389, the optical libration exceeds 90°; for such planets, the sector of permanent night vanishes, while the sunniest region splits in two. Furthermore, the synchronous state is not the only possible spin resonance. For example, Mercury (with e≈0.206) has an orbital period exactly 1.5 times its rotation period. A terrestrial exoplanet with e=0.40, say, is liable to have an orbital period of 2.0, 2.5, or 3.0 times its spin period. The corresponding insolation patterns are generally complicated, and all different from the synchronous state. Yet these non-synchronous resonances also protect certain longitudes from the worst extremes of temperature and solar radiation, and improve the planet's habitability, compared to non-resonant rotation. These results also have implications for the direct detectability of extrasolar planets, and the interpretation of their thermal emissions.     

Obliquity evolution of extrasolar terrestrial planets

We have investigated the obliquity evolution of terrestrial planets in habitable zones (at ∼1 AU) in extrasolar planetary systems, due to tidal interactions with their satellite and host star with wide varieties of satellite-to-planet mass ratio (m/Mp) and initial obliquity (γ₀), through numerical calculations and analytical arguments. The obliquity, the angle between planetary spin axis and its orbit normal, of a terrestrial planet is one of the key factors in determining the planetary surface environments. A recent scenario of terrestrial planet accretion implies that giant impacts of Mars-sized or larger bodies determine the planetary spin and form satellites. Since the giant impacts would be isotropic, tilted spins (sinγ₀∼1) are more likely to be produced than straight ones (sinγ₀∼0). The ratio m/Mp is dependent on the impact parameters and impactors' mass. However, most of previous studies on tidal evolution of the planet-satellite systems have focused on a particular case of the Earth-Moon systems in which m/Mp?0.0125 and γ₀∼10° or the two-body planar problem in which γ₀=0° and stellar torque is neglected. We numerically integrated the evolution of planetary spin and a satellite orbit with various m/Mp (from 0.0025 to 0.05) and γ₀ (from 0° to 180°), taking into account the stellar torques and precessional motions of the spin and the orbit. We start with the spin axis that almost coincides with the satellite orbit normal, assuming that the spin and the satellite are formed by one dominant impact. With initially straight spins, the evolution is similar to that of the Earth-Moon system. The satellite monotonically recedes from the planet until synchronous state between the spin period and the satellite orbital period is realized. The obliquity gradually increases initially but it starts decreasing down to zero as approaching the synchronous state. However, we have found that the evolution with initially tiled spins is completely different. The satellite's orbit migrates outward with almost constant obliquity until the orbit reaches the critical radius ∼10-20 planetary radii, but then the migration is reversed to inward one. At the reversal, the obliquity starts oscillation with large amplitude. The oscillation gradually ceases and the obliquity is reduced to ∼0° during the inward migration. The satellite eventually falls onto the planetary surface or it is captured at the synchronous state at several planetary radii. We found that the character change of precession about total angular momentum vector into that about the planetary orbit normal is responsible for the oscillation with large amplitude and the reversal of migration. With the results of numerical integration and analytical arguments, we divided the m/Mp-γ₀ space into the regions of the qualitatively different evolution. The peculiar tidal evolution with initially tiled spins give deep insights into dynamics of extrasolar planet-satellite systems and discussions of surface environments of the planets.     

Obliquity variations of terrestrial planets in habitable zones

We have investigated obliquity variations of possible terrestrial planets in habitable zones (HZs) perturbed by a giant planet(s) in extrasolar planetary systems. All the extrasolar planets so far discovered are inferred to be jovian-type gas giants. However, terrestrial planets could also exist in extrasolar planetary systems. In order for life, in particular for land-based life, to evolve and survive on a possible terrestrial planet in an HZ, small obliquity variations of the planet may be required in addition to its orbital stability, because large obliquity variations would cause significant climate change. It is known that large obliquity variations are caused by spin-orbit resonances where the precession frequency of the planet's spin nearly coincides with one of the precession frequencies of the ascending node of the planet's orbit. Using analytical expressions, we evaluated the obliquity variations of terrestrial planets with prograde spins in HZs. We found that the obliquity of terrestrial planets suffers large variations when the giant planet's orbit is separated by several Hill radii from an edge of the HZ, in which the orbits of the terrestrial planets in the HZ are marginally stable. Applying these results to the known extrasolar planetary systems, we found that about half of these systems can have terrestrial planets with small obliquity variations (smaller than 10°) over their entire HZs. However, the systems with both small obliquity variations and stable orbits in their HZs are only 1/5 of known systems. Most such systems are comprised of short-period giant planets. If additional planets are found in the known planetary systems, they generally tend to enhance the obliquity variations. On the other hand, if a large/close satellite exists, it significantly enhances the precession rate of the spin axis of a terrestrial planet and is likely to reduce the obliquity variations of the planet. Moreover, if a terrestrial planet is in a retrograde spin state, the spin-orbit resonance does not occur. Retrograde spin, or a large/close satellite might be essential for land-based life to survive on a terrestrial planet in an HZ.     

When and where were the satellites of uranus formed?

Uranus exhibits an unusually large obliquity compared to other planets of the solar system; its equator is inclined by 98° to the plane of its orbit. However its five satellites are remarkably regular, with eccentricities and inclinations very nearly zero, but of course with orbit planes that are tilted by ～98° to the plane of the ecliptic. This circumstance is used here to relate the formation of satellites to planet formation. Six different cases are discussed, of which two can be ruled out and two others are highly improbable. In the analysis, use is made of the fact that satellites in near-equatorial orbits could not follow a rapid (“non-adiabatic”) change of the planet's obliquity. We assume, also, that the observed obliquity is the result of the last stages of planet accumulation. We can therefore exclude contemporaneous formation of planet and satellites, and conclude instead that the satellites were formed or acquired after the planet's axis had been tilted. A plausible scenario involves the tidal capture of a body having 5% to 10% of the planet's mass—sufficient to account for the tilt—followed by its accretion. However, tidal forces break up the body into chunks, slow the accretion, and allow ～1% of the chunks to form the satellites through interaction with a temporary dense atmosphere. The same reasoning may apply also for Saturn and Jupiter. It should be noted that the synchronous orbit it well within the Roche limit for all three planets.     

On the oscillations in Mercury's obliquity

Mercury's capture into the 3:2 spin–orbit resonance can be explained as a result of its chaotic orbital dynamics. One major objective of MESSENGER and BepiColombo spatial missions is to accurately measure Mercury's rotation and its obliquity in order to obtain constraints on internal structure of the planet. Analytical approaches at the first-order level using the Cassini state assumptions give the obliquity constant or quasi-constant. Which is the obliquity's dynamical behavior deriving from a complete spin–orbit motion of Mercury simultaneously integrated with planetary interactions? We have used our SONYR model (acronym of Spin–Orbit N-bodY Relativistic model) integrating the spin–orbit N-body problem applied to the Solar System (Sun and planets). For lack of current accurate observations or ephemerides of Mercury's rotation, and therefore for lack of valid initial conditions for a numerical integration, we have built an original method for finding the libration center of the spin–orbit system and, as a consequence, for avoiding arbitrary amplitudes in librations of the spin–orbit motion as well as in Mercury's obliquity. The method has been carried out in two cases: (1) the spin–orbit motion of Mercury in the 2-body problem case (Sun–Mercury) where an uniform precession of the Keplerian orbital plane is kinematically added at a fixed inclination (S_2K case), (2) the spin–orbit motion of Mercury in the N-body problem case (Sun and planets) (S_n case). We find that the remaining amplitude of the oscillations in the S_n case is one order of magnitude larger than in the S_2K case, namely 4 versus 0.4 arcseconds (peak-to-peak). The mean obliquity is also larger, namely 1.98 versus 1.80 arcminutes, for a difference of 10.8 arcseconds. These theoretical results are in a good agreement with recent radar observations but it is not excluded that it should be possible to push farther the convergence process by drawing nearer still more precisely to the libration center. We note that the dynamically driven spin precession, which occurs when the planetary interactions are included, is more complex than the purely kinematic case. Nevertheless, in such a N-body problem, we find that the 3:2 spin–orbit resonance is really combined to a synchronism where the spin and orbit poles on average precess at the same rate while the orbit inclination and the spin axis orientation on average decrease at the same rate. As a consequence and whether it would turn out that there exists an irreducible minimum of the oscillation amplitude, quasi-periodic oscillations found in Mercury's obliquity should be to geometrically understood as librations related to these synchronisms that both follow a Cassini state. Whatever the open question on the minimal amplitude in the obliquity's oscillations and in spite of the planetary interactions indirectly acting by the solar torque on Mercury's rotation, Mercury remains therefore in a stable equilibrium state that proceeds from a 2-body Cassini state.     

Spin axis of (2953) Vysheslavia and its implications

Photometric observations made during the years 2000-2005 are used to determine the pole orientation of (2953) Vysheslavia, a ?15-km size member of the Koronis family. We find admissible solutions for ecliptic latitude and longitude of the rotation pole P₃: βp=−64°±10° and λp=11°±8° or P₄: βp=−68°±8° and λp=192°±8°. These imply obliquity values γ=154°±14° and γ=157°±11°, respectively. The sidereal rotation period is Psid=0.2622722±0.0000018 day. This result is interesting for two reasons: (i) the obliquity value between 90° and 180° is consistent with a prediction done by Vokrouhlický et al. [Vokrouhlický, D., Bro?, M., Farinella, P., Kne?evi?, Z., 2001. Icarus 150, 78-93] that Vysheslavia might have been transported to its unstable orbit by the Yarkovsky effect, and (ii) with the obliquity close to 180°, Vysheslavia seems to belong to one of the two distinct groups in the Koronis family found recently by Slivan [Slivan, S.M., 2002. Nature 419, 49-51], further supporting the case of dichotomy in the spin axis distribution in this family. We also argue against the possibility that Vysheslavia reached its current orbit by a recent collisional breakup.     

The spin state of 433 Eros and its possible implications

In this paper, we show that Asteroid (433) Eros is currently residing in a spin-orbit resonance, with its spin axis undergoing a small-amplitude libration about the Cassini state 2 of the proper mode in the nonsingular orbital element sinI/2exp(?Ω), where I the orbital inclination and Ω the longitude of the node. The period of this libration is ?53.4 kyr. By excluding these libration wiggles, we find that Eros' pole precesses with the proper orbital plane in inertial space with a period of ?61.4 kyr. Eros' resonant state forces its obliquity to oscillate with a period of ?53.4 kyr between ?76° and ?89.5°. The observed value of ?89° places it near the latter extreme of this cycle. We have used these results to probe Eros' past orbit and spin evolution. Our computations suggest that Eros is unlikely to have achieved its current spin state by solar and planetary gravitational perturbations alone. We hypothesize that some dissipative process such as thermal torques (e.g., the so-called YORP effect) may be needed in our model to obtain a more satisfactory match with data. A detailed study of this problem is left for future work.     

Dynamic habitability for Earth-like planets in 86 extrasolar planetary systems

In this paper we estimate the likelihood to find habitable Earth-like planets on stable orbits for 86 selected extrasolar planetary systems, where luminosity, effective temperature and stellar age are known. For determining the habitable zone (HZ) an integrated system approach is used taking into account a variety of climatological, biogeochemical, and geodynamical processes. Habitability is linked to the photosynthetic activity on the planetary surface. We find that habitability strongly depends on the age of the stellar system and the characteristics of a virtual Earth-like planet. In particular, the portion of land/ocean coverages plays an important role. We approximated the conditions for orbital stability using a method based on the Hill radius. Almost 60% of the investigated systems could harbour habitable Earth-like planets on stable orbits. In 18 extrasolar systems we find even better prerequisites for dynamic habitability than in our own solar system. In general our results are comparable to those with an HZ determination based only on climatic constraints. However, there are remarkable differences for land worlds and for systems older than about 7 Gyr.     

Giant planet migration through the action of disk torques and planet-planet scattering

This paper presents a parametric study of giant planet migration through the combined action of disk torques and planet-planet scattering. The torques exerted on planets during Type II migration in circumstellar disks readily decrease the semi-major axes a, whereas scattering between planets increases the orbital eccentricities ?. This paper presents a parametric exploration of the possible parameter space for this migration scenario using two (initial) planetary mass distributions and a range of values for the time scale of eccentricity damping (due to the disk). For each class of systems, many realizations of the simulations are performed in order to determine the distributions of the resulting orbital elements of the surviving planets; this paper presents the results of ∼8500 numerical experiments. Our goal is to study the physics of this particular migration mechanism and to test it against observations of extrasolar planets. The action of disk torques and planet-planet scattering results in a distribution of final orbital elements that fills the a-? plane, in rough agreement with the orbital elements of observed extrasolar planets. In addition to specifying the orbital elements, we characterize this migration mechanism by finding the percentages of ejected and accreted planets, the number of collisions, the dependence of outcomes on planetary masses, the time spent in 2:1 and 3:1 resonances, and the effects of the planetary IMF. We also determine the distribution of inclination angles of surviving planets and the distribution of ejection speeds for exiled planets.     

Atmospheric circulations of terrestrial planets orbiting low-mass stars

Circulations and habitable zones of planets orbiting low-mass stars are investigated. Many of these planets are expected to rotate synchronously relative to their parent stars, thereby raising questions about their surface temperature distributions and habitability. We use a global circulation model to study idealized, synchronously rotating (tidally locked) planets of various rotation periods, with surfaces of all land or all water, but with an Earth-like atmosphere and solar insolation. The dry planets exhibit wide variations in surface temperature: >80 °C on the dayside to <−110 °C on the nightside for the 240-h rotator, for example. The water-covered aquaplanets are warmer and exhibit narrower ranges of surface temperatures, e.g., ∼40 °C to >−60 °C for the 240-h orbiter. They also have a larger habitable area, defined here as the region where average surface temperatures are between 0 °C and 50 °C. This concept has little relevance for either dry or aquaplanets, but might become relevant on a planet with both land area and oceans.The circulations on these tidally locked planets exhibit systematic changes as the rotation period is varied. However, they also reveal abrupt transitions between two different circulation regimes and multiple equilibria. For the dry planet, the transition occurs between a 4-day and a 5-day period, while for the aquaplanet, it occurs between a 3-day and a 4-day period. For both dry and aqua planets, this transition occurs when the Rossby deformation radius exceeds half the planetary radius. Further investigation on the dry planet reveals that multiple equilibria exist between 100- and 221-h periods. These multiple equilibria may be relevant for real planets within the habitable zones of late K and M stars, because these planets are expected to have rotation periods between 8 and 100 Earth days.     

Long-term evolution of the spin of Mercury: I. Effect of the obliquity and core-mantle friction

The present obliquity of Mercury is very low (less than 0.1°), which led previous studies to always adopt a nearly zero obliquity during the planet’s past evolution. However, the initial orientation of Mercury’s rotation axis is unknown and probably much different than today. As a consequence, we believe that the obliquity could have been significant when the rotation rate of the planet first encountered spin-orbit resonances. In order to compute the capture probabilities in resonance for any evolutionary scenario, we present in full detail the dynamical equations governing the long-term evolution of the spin, including the obliquity contribution.The secular spin evolution of Mercury results from tidal interactions with the Sun, but also from viscous friction at the core-mantle boundary. Here, this effect is also regarded with particular attention. Previous studies show that a liquid core enhances drastically the chances of capture in spin-orbit resonances. We confirm these results for null obliquity, but we find that the capture probability generally decreases as the obliquity increases. We finally show that, when core-mantle friction is combined with obliquity evolution, the spin can evolve into some unexpected configurations as the synchronous or the 1/2 spin-orbit resonance.     

Orbital change experiments with a Mars general circulation model

We use a Mars general circulation model to examine the effect of orbital changes on the planet’s general circulation and climate system. Experiments are performed for obliquities ranging from 0° to 60° for two different longitudes of perihelion. Each experiment simulates a full Mars year assuming a fixed atmospheric dust distribution and fixed amount of CO₂ in the atmosphere/cap system. We find that global mean surface temperatures and pressures decline with increasing obliquity due to the increasing extent of the winter polar caps. The seasonal CO₂ cycle and intensity of the solstice circulation amplify considerably with increasing obliquity such that global dust storms are likely at both solstices. The most significant feature of the high obliquity solstice circulations is the development of an intense low-level jet associated with the return branch of the Hadley circulation.Model surface stresses are used to map regions of preferred dust lifting, which are defined in terms of an annual deflation potential. For the present obliquity, the model-predicted regions of high deflation potential are in good agreement with Cantor et al.’s (2001, J. Geophys. Res.106, 23653-23688) observations, which gives us some confidence in the model’s ability to predict where lifting might occur when Mars’ orbit parameters are different than they are today. In general we find that the dust lifting potential increases sharply with obliquity and is greatest at times of high obliquity when perihelion coincides with northern summer solstice. Over an obliquity cycle, the model global annual deflation potential ranges from several tenths of a millimeter at 0° obliquity to almost 15 mm at 60° obliquity. Much higher values are possible when the atmosphere is very dusty.We find a strong correlation between the deflation potential and surface thermal inertia: regions of high deflation potential correspond to regions of high thermal inertia (high rock abundance), and regions of low deflation potential correspond to regions of low thermal inertia (high dust/sand abundance). Furthermore, while the regions of preferred lifting (high deflation potential) expand somewhat with increasing obliquity and dust loading, the central parts of Tharsis, Arabia, and Elysium show no tendency for significant lifting at any obliquity or longitude of perihelion. These regions may therefore be very old and represent net long-term sinks for atmospheric dust. It is the topography of the planet, through its influence on surface pressure and wind systems, which ultimately determines where dust accumulates.Finally, as was found by Fenton and Richardson (2001, J. Geophys. Res.106, 32885-32909), we find no tendency for the development of east-southeasterly winds at the Pathfinder site for any of our orbital change experiments. This suggests that the ancient wind regime discussed by Greeley et al. (2000, J. Geophys. Res.105, 1829-1840) was produced by other factors, such as polar wander.     

Orbital Evolution of Extrasolar Planets

The recent discovery of extrasolar planets and planetary systems has raised many new research problems for astronomers. It has become apparent that the newly discovered systems differ significantly from the Solar System. In particular, many massive planets of other stars, in contrast to Jupiter, have large orbital eccentricities. In the present paper, we investigate several dynamic implications of this finding. Numerical integration results show that the orbits of low-mass planets in such systems usually have large evolving eccentricities. If the motion remains regular and no close encounters occur, the orbital evolution can be described analytically by using secular perturbations of Laplace–Lagrange equations. In terms of the Lagrange variables, the trajectories are circles, and the semimajor axis remains constant. The loss of the regularity of motion is normally followed by a nonmonotone synchronous increase in the semimajor axis and eccentricity, and the orbit becomes similar to that of a large-period comet. Narrow resonance-related regions include more complex motions.     

Colour-differential interferometry for the observation of extrasolar planets

We present the high angular resolution technique of colour-differential interferometry for direct detection of extrasolar giant planets (EGPs). The measurement of differential phase with long-baseline ground-based interferometers in the near-infrared could allow the observation of several hot giant extrasolar planets in tight orbit around the nearby stars, and thus yield their low- or mid-resolution spectroscopy, complete orbital data set and mass. Estimates of potentially achievable signal-to-noise ratios are presented for a number of planets already discovered by indirect methods. The limits from the instrumental and atmospheric instability are discussed, and a subsequent observational strategy is proposed.     

Eccentricity evolution of giant planet orbits due to circumstellar disk torques

The extrasolar planets discovered to date possess unexpected orbital elements. Most orbit their host stars with larger eccentricities and smaller semi-major axes than similarly sized planets in our own Solar System do. It is generally agreed that the interaction between giant planets and circumstellar disks (Type II migration) drives these planets inward to small radii, but the effect of these same disks on orbital eccentricity, ?, is controversial. Several recent analytic calculations suggest that disk-planet interactions can excite eccentricity, while numerical studies generally produce eccentricity damping. This paper addresses this controversy using a quasi-analytic approach, drawing on several preceding analytic studies. This work refines the current treatment of eccentricity evolution by removing several approximations from the calculation of disk torques. We encounter neither uniform damping nor uniform excitation of orbital eccentricity, but rather a function d?/dt that varies in both sign and magnitude depending on eccentricity and other Solar System properties. Most significantly, we find that for every combination of disk and planet properties investigated herein, corotation torques produce negative values of d?/dt for some range in ? within the interval [0.1, 0.5]. If corotation torques are saturated, this region of eccentricity damping disappears, and excitation occurs on a short timescale of less than 0.08 Myr. Thus, our study does not produce eccentricity excitation on a timescale of a few Myr—we obtain either eccentricity excitation on a short time scale, or eccentricity damping on a longer time scale. Finally, we discuss the implications of this result for producing the observed range in extrasolar planet eccentricity.     

Eccentric Extrasolar Planets: The Jumping Jupiter Model

Most extrasolar planets discovered to date are more massive than Jupiter, in surprisingly small orbits (semimajor axes less than 3 AU). Many of these have significant orbital eccentricities. Such orbits may be the product of dynamical interactions in multiplanet systems. We examine outcomes of such evolution in systems of three Jupiter-mass planets around a solar-mass star by integration of their orbits in three dimensions. Such systems are unstable for a broad range of initial conditions, with mutual perturbations leading to crossing orbits and close encounters. The time scale for instability to develop depends on the initial orbital spacing; some configurations become chaotic after delays exceeding 10⁸ y. The most common outcome of gravitational scattering by close encounters is hyperbolic ejection of one planet. Of the two survivors, one is moved closer to the star and the other is left in a distant orbit; for systems with equal-mass planets, there is no correlation between initial and final orbital positions. Both survivors may have significant eccentricities, and the mutual inclination of their orbits can be large. The inner survivor's semimajor axis is usually about half that of the innermost starting orbit. Gravitational scattering alone cannot produce the observed excess of “hot Jupiters” in close circular orbits. However, those scattered planets with large eccentricities and small periastron distances may become circularized if tidal dissipation is effective. Most stars with a massive planet in an eccentric orbit should have at least one additional planet of comparable mass in a more distant orbit.     

The rotation of Janus and Epimetheus

Epimetheus, a small moon of Saturn, has a rotational libration (an oscillation about synchronous rotation) of 5.9°±1.2°, placing Epimetheus in the company of Earth’s Moon and Mars’ Phobos as the only natural satellites for which forced rotational libration has been detected. The forced libration is caused by the satellite’s slightly eccentric orbit and non-spherical shape.Detection of a moon’s forced libration allows us to probe its interior by comparing the measured amplitude to that predicted by a shape model assuming constant density. A discrepancy between the two would indicate internal density asymmetries. For Epimetheus, the uncertainties in the shape model are large enough to account for the measured libration amplitude. For Janus, on the other hand, although we cannot rule out synchronous rotation, a permanent offset of several degrees between Janus’ minimum moment of inertia (long axis) and the equilibrium sub-Saturn point may indicate that Janus does have modest internal density asymmetries.The rotation states of Janus and Epimetheus experience a perturbation every 4 years, as the two moons “swap” orbits. The sudden change in the orbital periods produces a free libration about synchronous rotation that is subsequently damped by internal friction. We calculate that this free libration is small in amplitude (<0.1°) and decays quickly (a few weeks, at most), and is thus below the current limits for detection using Cassini images.     

Forced obliquity and moments of inertia of Titan

The obliquity of Titan is small, but certainly non-zero, and may be used to place constraints on Titan's internal structure. The measured gravity coefficients of Titan imply that it is non-hydrostatic and thus the normal Darwin-Radau approach to determining internal structure cannot be applied. However, if the obliquity is assumed to be tidally damped (that is, in a Cassini state) then combining the obliquity with the measured gravity coefficients allows Titan's moment of inertia to be determined without invoking hydrostatic equilibrium. For polar moment values in the range (0.3<C/MR²<0.4), tidally-damped obliquity values of (0.115°<|ε|<0.177°) result. If the inferred moment value exceeds 0.4, this strongly suggests the presence of a near-surface ice shell decoupled from the interior, probably by a subsurface ocean.     

Obliquity tides do not significantly heat Enceladus

Recently, Tyler [Tyler, R.H., 2009. Geophys. Res. Lett. 36, L15205; Tyler, R., 2011. Icarus, 211, 770-779] proposed that the tide due to an obliquity of greater than 0.1° might drive resonant flow in a liquid ocean at Enceladus, and that dissipation of the ocean’s kinetic energy may be an alternate source for the observed global heat flux. While there is currently no measurement of Enceladus’ obliquity, dissipation is expected to drive the spin pole to a Cassini state. Under this assumption, we find that Enceladus should occupy Cassini state 1 and that the obliquity of Enceladus should be less than 0.0015° for values of the degree-2 gravity coefficient C_2,2 between 1.0 × 10⁻³ and 2.5 × 10⁻³. Unless there is a significant free obliquity or the gravity coefficient C_2,2 has been significantly overestimated, it is unlikely that obliquity-driven flow in a subsurface ocean is the source of the extreme heat on Enceladus.     

Eccentricities of Planets in Binary Systems

The most puzzling property of the extrasolar planets discovered by recent radial velocity surveys is their high orbital eccentricities, which are very difficult to explain within our current theoretical paradigm for planet formation. Current data reveal that at least 25% of these planets, including some with particularly high eccentricities, are orbiting a component of a binary star system. The presence of a distant companion can cause significant secular perturbations in the orbit of a planet. At high relative inclinations, large-amplitude, periodic eccentricity perturbations can occur. These are known as “Kozai cycles” and their amplitude is purely dependent on the relative orbital inclination. Assuming that every planet host star also has a (possibly unseen, e.g., substellar) distant companion, with reasonable distributions of orbital parameters and masses, we determine the resulting eccentricity distribution of planets and compare it to observations? We find that perturbations from a binary companion always appear to produce an excess of planets with both very high (?0.6) and very low (e ? 0.1) eccentricities. The paucity of near-circular orbits in the observed sample implies that at least one additional mechanism must be increasing eccentricities. On the other hand, the overproduction of very high eccentricities observed in our models could be combined with plausible circularization mechanisms (e.g., friction from residual gas) to create more planets with intermediate eccentricities (e? 0.1–0.6).