arXiv subjects

Alexandre C. M. Correia

Publications and source records attributed to Alexandre C. M. Correia.

72 records · Page 4Linked to original sources

arXiv2015

Spin-orbit coupling and chaotic rotation for circumbinary bodies. Application to the small satellites of the Pluto-Charon system

We investigate the resonant rotation of circumbinary bodies in planar quasi-circular orbits. Denoting $n_b$ and $n$ the orbital mean motion of the inner binary and of the circumbinary body, respectively, we show that spin-orbit resonances exist at the frequencies $n\pm kν/2$, where $ν= n_b - n$, and $k$ is an integer. Moreover, when the libration at natural frequency has the same magnitude as $ν$, the resonances overlap and the rotation becomes chaotic. We apply these results to the small satellites in the Pluto-Charon system, and conclude that their rotations are likely chaotic. However, the rotation can also be stable and not synchronous for small axial asymmetries.

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arXiv2014

Deformation and tidal evolution of close-in planets and satellites using a Maxwell viscoelastic rheology

In this paper we present a new approach to tidal theory. Assuming a Maxwell viscoelastic rheology, we compute the instantaneous deformation of celestial bodies using a differential equation for the gravity field coefficients. This method allows large eccentricities and it is not limited to quasi-periodic perturbations. It can take into account an extended class of perturbations, including chaotic motions and transient events. We apply our model to some already detected eccentric hot Jupiters and super-Earths in planar configurations. We show that when the relaxation time of the deformation is larger than the orbital period, spin-orbit equilibria arise naturally at half-integers of the mean motion, even for gaseous planets. In the case of super-Earths, these equilibria can be maintained for very low values of eccentricity. Our method can also be used to study planets with complex internal structures and other rheologies.

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arXiv2014

Transit light curve and inner structure of close-in planets

Planets orbiting very close to their host stars have been found, some of them on the verge of tidal disruption. The ellipsoidal shape of these planets can significantly differ from a sphere, which modifies the transit light curves. Here we present an easy method for taking the effect of the tidal bulge into account in the transit photometric observations. We show that the differences in the light curve are greater than previously thought. When detectable, these differences provide us an estimation of the fluid Love number, which is invaluable information on the internal structure of close-in planets. We also derive a simple analytical expression to correct the bulk density of these bodies, that can be 20% smaller than current estimates obtained assuming a spherical radius.

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arXiv2014

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

Planets with masses between 0.1 - 10 M_earth 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 evolve either to 0 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 this 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.

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arXiv2013

Spin-orbit coupling and chaotic rotation for coorbital bodies in quasi-circular orbits

Coorbital bodies are observed around the Sun sharing their orbits with the planets, but also in some pairs of satellites around Saturn. The existence of coorbital planets around other stars has also been proposed. For close-in planets and satellites, the rotation slowly evolves due to dissipative tidal effects until some kind of equilibrium is reached. When the orbits are nearly circular, the rotation period is believed to always end synchronous with the orbital period. Here we demonstrate that for coorbital bodies in quasi-circular orbits, stable non-synchronous rotation is possible for a wide range of mass ratios and body shapes. We show the existence of an entirely new family of spin-orbit resonances at the frequencies $n\pm kν/2$, where $n$ is the orbital mean motion, $ν$ the orbital libration frequency, and $k$ an integer. In addition, when the natural rotational libration frequency due to the axial asymmetry, $σ$, has the same magnitude as $ν$, the rotation becomes chaotic. Saturn coorbital satellites are synchronous since $ν\llσ$, but coorbital exoplanets may present non-synchronous or chaotic rotation. Our results prove that the spin dynamics of a body cannot be dissociated from its orbital environment. We further anticipate that a similar mechanism may affect the rotation of bodies in any mean-motion resonance.

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arXiv2013

On the equilibrium figure of close-in planets and satellites

Many exoplanets have been observed close to their parent stars with orbital periods of a few days. As for the major satellites of the Jovian planets, the figure of these planets is expected to be strongly shaped by tidal forces. However, contrarily to Solar System satellites, exoplanets may present high values for the obliquity and eccentricity due to planetary perturbations, and may also be captured in spin-orbit resonances different from the synchronous one. Here we give a general formulation of the equilibrium figure of those bodies, that makes no particular assumption on the spin and/or orbital configurations. The gravity field coefficients computed here are well suited for describing the figure evolution of a body whose spin and orbit undergo substantial variations in time.

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arXiv2012

Impact cratering on Mercury: consequences for the spin evolution

Impact basins identified by Mariner 10 and Messenger flyby images provide us a fossilized record of the impactor flux of asteroids on Mercury during the last stages of the early Solar System. The distribution of these basins is not uniform across the surface, and is consistent with a primordial synchronous rotation (Wieczorek et al. 2012). By analyzing the size of the impacts, we show that the distribution for asteroid diameters D < 110 km is compatible with an index power law of 1.2, a value that matches the predicted primordial distribution of the main-belt. We then derive a simple collisional model coherent with the observations, and when combining it with the secular evolution of the spin of Mercury, we are able to reproduce the present 3/2 spin-orbit resonance (about 50% of chances), as well as a primordial synchronous rotation. This result is robust with respect to variations in the dissipation and collisional models, or in the initial spin state of the planet.

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arXiv2011

A pre-Caloris synchronous rotation for Mercury

The planet Mercury is locked in a spin-orbit resonance where it rotates three times about its spin axis for every two orbits about the Sun. The current explanation for this unique state assumes that the initial rotation of this planet was prograde and rapid, and that tidal torques decelerated the planetary spin to this resonance. When core-mantle boundary friction is accounted for, capture into the 3/2 resonance occurs with a 26% probability, but the most probable outcome is capture into one of the higher-order resonances. Here we show that if the initial rotation of Mercury were retrograde, this planet would be captured into synchronous rotation with a 68% probability. Strong spatial variations of the impact cratering rate would have existed at this time, and these are shown to be consistent with the distribution of pre-Calorian impact basins observed by Mariner 10 and MESSENGER. Escape from this highly stable resonance is made possible by the momentum imparted by large basin-forming impact events, and capture into the 3/2 resonance occurs subsequently under favourable conditions.

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arXiv2011

Orbital migration induced by anisotropic evaporation. Can hot Jupiters form hot Neptunes ?

Short period planets are subject to intense energetic irradiations from their stars. It has been shown that this can lead to significant atmospheric mass-loss and create smaller mass planets. Here, we analyse whether the evaporation mechanism can affect the orbit of planets. The orbital evolution of a planet undergoing evaporation is derived analytically in a very general way. Analytical results are then compared with the period distribution of two classes of inner exoplanets: Jupiter-mass planets and Neptune-mass planets. These two populations have a very distinct period distribution, with a probability lower than 10^-4 that they were derived from the same parent distribution. We show that mass ejection can generate significant migration with an increase of orbital period that matches very well the difference of distribution of the two populations. This would happen if the evaporation emanates from above the hottest region of planet surface. Thus, migration induced by evaporation is an important mechanism that cannot be neglected.

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arXiv2011

Pumping the eccentricity of exoplanets by tidal effect

Planets close to their host stars are believed to undergo significant tidal interactions, leading to a progressive damping of the orbital eccentricity. Here we show that, when the orbit of the planet is excited by an outer companion, tidal effects combined with gravitational interactions may give rise to a secular increasing drift on the eccentricity. As long as this secular drift counterbalances the damping effect, the eccentricity can increase to high values. This mechanism may explain why some of the moderate close-in exoplanets are observed with substantial eccentricity values.

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arXiv2011

Tidal dissipation in multi-planet systems and constraints to orbit-fitting

We present here in full details the linear secular theory with tidal damping that was used to constraint the fit of the HD10180 planetary system in (Lovis et al. 2011). The theory is very general and can provide some intuitive understanding of the final state of a planetary system when one or more planets are close to their central star. We globally recover the results of (Mardling 2007), but we show that in the HD209458 planetary system, the consideration of the tides raised by the central star on the planet lead to believe that the eccentricity of HD209458b is most probably much smaller than 0.01.

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arXiv2011

Tidal evolution of hierarchical and inclined systems

We investigate the dynamical evolution of hierarchical three-body systems under the effect of tides, when the ratio of the orbital semi-major axes is small and the mutual inclination is relatively large (greater than 20 degrees). Using the quadrupolar non-restricted approximation for the gravitational interactions and the viscous linear model for tides, we derive the averaged equations of motion in a vectorial formalism which is suitable to model the long-term evolution of a large variety of exoplanetary systems in very eccentric and inclined orbits. In particular, it can be used to derive constraints for stellar spin-orbit misalignment, capture in Cassini states, tidal-Kozai migration, or damping of the mutual inclination. Because our model is valid for the non-restricted problem, it can be used to study systems of identical mass or for the outer restricted problem, such as the evolution of a planet around a binary of stars. Here, we apply our model to three distinct situations: 1) the HD80606 planetary system, for which we obtain the probability density function distribution for the misalignment angle, with two pronounced peaks of higher probability around 53 and 109 degrees; 2) the HD98800 binary system, for which we show that initial prograde orbits inside the observed disc may become retrograde and vice-versa, only because of tidal migration within the binary stars; 3) the HD11964 planetary system, for which we show that tidal dissipation combined with gravitational perturbations may lead to a decrease in the mutual inclination, and a fast circularization of the inner orbit.

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arXiv2011

Keplerian Orbits and Dynamics of Exoplanets

Understanding the consequences of the gravitational interaction between a star and a planet is fundamental to the study of exoplanets. The solution of the two-body problem shows that the planet moves in an elliptical path around the star and that each body moves in an ellipse about the common center of mass. The basic properties of such a system are derived from first principles and described in the context of detecting exoplanets.

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arXiv2010

Tidal Evolution of Exoplanets

Tidal effects arise from differential and inelastic deformation of a planet by a perturbing body. The continuous action of tides modify the rotation of the planet together with its orbit until an equilibrium situation is reached. It is often believed that synchronous motion is the most probable outcome of the tidal evolution process, since synchronous rotation is observed for the majority of the satellites in the Solar System. However, in the 19th century, Schiaparelli also assumed synchronous motion for the rotations of Mercury and Venus, and was later shown to be wrong. Rather, for planets in eccentric orbits synchronous rotation is very unlikely. The rotation period and axial tilt of exoplanets is still unknown, but a large number of planets have been detected close to the parent star and should have evolved to a final equilibrium situation. Therefore, based on the Solar System well studied cases, we can make some predictions for exoplanets. Here we describe in detail the main tidal effects that modify the secular evolution of the spin and the orbit of a planet. We then apply our knowledge acquired from Solar System situations to exoplanet cases. In particular, we will focus on two classes of planets, "Hot-Jupiters" (fluid) and "Super-Earths" (rocky with atmosphere).

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arXiv2009

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.

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arXiv2009

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

The rotation of Mercury is presently captured in a 3/2 spin-orbit resonance with the orbital mean motion. The capture mechanism is well understood as the result of tidal interactions with the Sun combined with planetary perturbations. However, it is now almost certain that Mercury has a liquid core, which should induce a contribution of viscous friction at the core-mantle boundary to the spin evolution. This last effect greatly increases the chances of capture in all spin-orbit resonances, being 100% for the 2/1 resonance, and thus preventing the planet from evolving to the presently observed configuration. Here we show that for a given resonance, as the chaotic evolution of Mercury's orbit can drive its eccentricity to very low values during the planet's history, any previous capture can be destabilized whenever the eccentricity becomes lower than a critical value. In our numerical integrations of 1000 orbits of Mercury over 4 Gyr, the spin ends 99.8% of the time captured in a spin-orbit resonance, in particular in one of the following three configurations: 5/2 (22%), 2/1 (32%) and 3/2 (26%). Although the present 3/2 spin-orbit resonance is not the most probable outcome, we also show that the capture probability in this resonance can be increased up to 55% or 73%, if the eccentricity of Mercury in the past has descended below the critical values 0.025 or 0.005, respectively.

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arXiv2008

Stellar wobble caused by a binary system: Can it really be mistaken as an extra-solar planet?

The traditional method for detecting extra-solar planets relies on measuring a small stellar wobble which is assumed to be caused by a planet orbiting the star. Recently, it was suggested that a similar stellar wobble could be caused by a close binary system (Schneider and Cabrera, 2006). Here we show that, although the effect of a close binary system can at first sight be mistaken as a planetary companion to the star, more careful analysis of the observational data should allow us to distinguish between the two effects.

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arXiv2008

On the equilibrium rotation of Earth-like extra-solar planets

The equilibrium rotation of tidally evolved "Earth-like" extra-solar planets is often assumed to be synchronous with their orbital mean motion. The same assumption persisted for Mercury and Venus until radar observations revealed their true spin rates. As many of these planets follow eccentric orbits and are believed to host dense atmospheres, we expect the equilibrium rotation to differ from the synchronous motion. Here we provide a general description of the allowed final equilibrium rotation states of these planets, and apply this to already discovered cases in which the mass is lower than twelve Earth-masses. At low obliquity and moderate eccentricity, it is shown that there are at most four distinct equilibrium possibilities, one of which can be retrograde. Because most presently known "Earth-like" planets present eccentric orbits, their equilibrium rotation is unlikely to be synchronous.

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