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.
The eccentricity distribution of exoplanets is known from radial velocity surveys to be divergent from circular orbits beyond 0.1 AU. This is particularly the case for large planets where the radial velocity technique is most sensitive. The eccentricity of planetary orbits can have a large effect on the transit probability and subsequently the planet yield of transit surveys. The Kepler mission is the first transit survey that probes deep enough into period-space to allow this effect to be seen via the variation in transit durations. We use the Kepler planet candidates to show that the eccentr…
Most giant exoplanets discovered by radial velocity surveys have much higher eccentricities than those in the solar system. The planet--planet scattering mechanism has been shown to match the broad eccentricity distribution, but the highest-eccentricity planets are often attributed to Kozai-Lidov oscillations induced by a stellar companion. Here we investigate whether the highly eccentric exoplanet population can be produced entirely by scattering. We ran 500 N-body simulations of closely packed giant-planet systems that became unstable under their own mutual perturbations. We find that the su…
The known population of exoplanets exhibits a much wider range of orbital eccentricities than Solar System planets and has a much higher average eccentricity. These facts have been widely interpreted to indicate that the Solar System is an atypical member of the overall population of planetary systems. We report here on a strong anti-correlation of orbital eccentricity with multiplicity (number of planets in the system) among catalogued radial velocity (RV) systems. The mean, median and rough distribution of eccentricities of Solar System planets fits an extrapolation of this anti-correlation …
Exoplanet discoveries over recent years have shown that terrestrial planets are exceptionally common. Many of these planets are in compact systems that result in complex orbital dynamics. A key step toward determining the surface conditions of these planets is understanding the latitudinally dependent flux incident at the top of the atmosphere as a function of orbital phase. The two main properties of a planet that influence the time-dependent nature of the flux are the obliquity and orbital eccentricity of the planet. We derive the criterion for which the flux variation due to obliquity is eq…
We use the super Earth 55 Cnc e as a case study to address an observable effect of tidal heating. We investigate whether planet-planet interactions can force the eccentricity of this planet to a level affecting the eclipse depth observed with Spitzer. Using the constant time lag tidal model, we first calculate the observed planet flux as a function of albedo and eccentricity, for different tidal dissipation constants and for two extreme cases: a planet with no heat redistribution and a planet with full heat redistribution. We derive the values of albedo and eccentricity that match the observed…
In this paper, we show that the eccentricity of a planet on an inclined orbit with respect to a disc can be pumped up to high values by the gravitational potential of the disc, even when the orbit of the planet crosses the disc plane. This process is an extension of the Kozai effect. If the orbit of the planet is well inside the disc inner cavity, the process is formally identical to the classical Kozai effect. If the planet's orbit crosses the disc but most of the disc mass is beyond the orbit, the eccentricity of the planet grows when the initial angle between the orbit and the disc is large…
Eccentricity is an important orbital parameter. Understanding its effect on planetary climate and habitability is critical for us to search for a habitable world beyond our solar system. The orbital configurations of M-dwarf planets are always tidally-locked at resonance states, which are quite different from those around Sun-like stars. M-dwarf planets need to be investigated separately. Here we use a comprehensive three-dimensional atmospheric general circulation model to systematically investigate how eccentricity influences climate and habitability of M-dwarf exoplanets. The simulation res…
Thermal, orbital, and rotational dynamics of tidally loaded exoplanets are interconnected by intricate feedback. The rheological structure of the planet determines its susceptibility to tidal deformation and, as a consequence, participates in shaping its orbit. The orbital parameters and the spin state, conversely, control the rate of tidal dissipation and may lead to substantial changes of the interior. We investigate the coupled thermal-orbital evolution of differentiated rocky exoplanets governed by the Andrade viscoelastic rheology. The coupled evolution is treated by a semi-analytical mod…
It is suggested that the distribution of orbital eccentricities for extrasolar planets is well-described by the Beta distribution. Several properties of the Beta distribution make it a powerful tool for this purpose. For example, the Beta distribution can reproduce a diverse range of probability density functions (PDFs) using just two shape parameters (a and b). We argue that this makes it ideal for serving as a parametric model in Bayesian comparative population analysis. The Beta distribution is also uniquely defined over the interval zero to unity, meaning that it can serve as a proper prio…
The distribution of eccentricities of warm giant exoplanets is commonly explained through planet--planet interactions, although no physically sound argument favours the ubiquity of such interactions. No simple, generic explanation has been put forward to explain the high mean eccentricity of these planets. In this paper, we revisit a simple, plausible explanation to account for the eccentricities of warm Jupiters: migration inside a cavity in the protoplanetary disc. Such a scenario allows to excite the outer eccentric resonances, a working mechanism for higher mass planets, leading to a growt…
In this paper, we present the consistent evolution of short-period exoplanets coupling the tidal and gravothermal evolution of the planet. Contrarily to previous similar studies, our calculations are based on the complete tidal evolution equations of the Hut model, valid at any order in eccentricity, obliquity and spin. We demonstrate, both analytically and numerically, that, except if the system was formed with a nearly circular orbit (e<0.2), solving consistently the complete tidal equations is mandatory to derive correct tidal evolution histories. We show that calculations based on tidal mo…
The eccentricity of a planet's orbit and the inclination of its orbital plane encode important information about its formation and history. However, exoplanets detected via direct-imaging are often only observed over a very small fraction of their period, making it challenging to perform reliable physical inferences given wide, unconstrained posteriors. The aim of this project is to investigate biases (deviation of the median and mode of the posterior from the true values of orbital parameters, and the width and coverage of their credible intervals) in the estimation of orbital parameters of d…
Although our solar system features predominantly circular orbits, the exoplanets discovered so far indicate that this is the exception rather than the rule. This could have crucial consequences for exoplanet climates, both because eccentric terrestrial exoplanets could have extreme seasonal variation, and because giant planets on eccentric orbits could excite Milankovitch-like variations of a potentially habitable terrestrial planet,Äôs eccentricity, on timescales of thousands-to-millions of years. A particularly interesting implication concerns the fact that the Earth is thought to have gone …
Using the Andrade-derived Sundberg-Cooper rheology, we apply several improvements to the secular tidal evolution of TRAPPIST-1e and the early history of Pluto-Charon under the simplifying assumption of homogeneous bodies. By including higher-order eccentricity terms (up to and including $e^{20}$), we find divergences from the traditionally used $e^{2}$ truncation starting around $e=0.1$. Order-of-magnitude differences begin to occur for $e>0.6$. Critically, higher-order eccentricity terms activate additional spin-orbit resonances. Worlds experiencing non-synchronous rotation can fall into and …
(Abridged) The observed radial velocity (RV) eccentricity distribution for extrasolar planets in single-planet systems shows that a significant fraction of planets are eccentric ($e > 0.1$). Here we investigate the effects on an RV planet's eccentricity produced by undetected outer companions. We have carried out Monte Carlo simulations of mock RV data to understand this effect and predict its impact on the observed distribution. We first quantify the statistical effect of undetected outer companions and show that this alone cannot explain the observed distribution. We then modify the simulati…
Using numerical methods we investigate the dynamical stability of the Gliese 581 exoplanetary system. The system is known to harbour four planets (b-e). The existence of another planet (g) in the liquid water habitable zone of the star is debated after the latest analyses of the radial velocity (RV) measurements. We integrated the 4 and 5-planet model of Vogt et al. (AN 333, 561-575, 2012) with initial circular orbits. To characterize stability, the maximum eccentricity was used that the planets reached over the time of the integrations and the LCI and RLI to identify chaotic motion. Since cir…
The orbital eccentricities of directly imaged exoplanets and brown dwarf companions provide clues about their formation and dynamical histories. We combine new high-contrast imaging observations of substellar companions obtained primarily with Keck/NIRC2 together with astrometry from the literature to test for differences in the population-level eccentricity distributions of 27 long-period giant planets and brown dwarf companions between 5-100 AU using hierarchical Bayesian modeling. Orbit fits are performed in a uniform manner for companions with short orbital arcs; this typically results in …
Context: Several studies have so far placed useful constraints on planetary atmospheric properties using transmission spectrsocopy, and in the case of HD209458b even the radial velocity of the planet during the transit event has been reconstructed opening a new range of possibilities. AIMS. In this contribution we highlight the importance to account for the orbital eccentricity and longitude of periastron of the planetary orbit to accurately interpret the measured planetary radial velocity during the transit. Methods: We calculate the radial velocity of a transiting planet in an eccentric orbi…
Exoplanetary systems host giant planets on substantially non-circular, close-in orbits. We propose that these eccentricities arise in a phase of giant impacts, analogous to the final stage of Solar System assembly that formed Earth's Moon. In this scenario, the planets scatter each other and collide, with corresponding mass growth as they merge. We numerically integrate an ensemble of systems with varying total planet mass, allowing for collisional growth, to show that (1) the high-eccentricity giants observed today may have formed preferentially in systems of higher initial total planet mass,…
Exoplanet habitability is traditionally assessed by comparing a planet's semi-major axis to the location of its host star's "habitable zone," the shell around a star for which Earth-like planets can possess liquid surface water. The Kepler space telescope has discovered numerous planet candidates near the habitable zone, and many more are expected from missions such as K2, TESS and PLATO. These candidates often require significant follow-up observations for validation, so prioritizing planets for habitability from transit data has become an important aspect of the search for life in the univer…
Previous studies have shown that planets that rotate retrograde (backwards with respect to their orbital motion) generally experience less severe obliquity variations than those that rotate prograde (the same direction as their orbital motion). Here we examine retrograde-rotating planets on eccentric orbits and find a previously unknown secular spin-orbit resonance that can drive significant obliquity variations. This resonance occurs when the frequency of the planet's rotation axis precession becomes commensurate with an orbital eigenfrequency of the planetary system. The planet's eccentricit…
The angular momentum deficit (AMD) of a planetary system is a measure of its orbital excitation and a predictor of long-term stability. We adopt the AMD-stability criteria to constrain the orbital architectures for exoplanetary systems. Previously, He, Ford, & Ragozzine (2019) (arXiv:1907.07773v2) showed through forward modelling (SysSim) that the observed multiplicity distribution can be well reproduced by two populations consisting of a low and a high mutual inclination component. Here, we show that a broad distribution of mutual inclinations arising from systems at the AMD-stability limit c…
The architecture of a planetary system can influence the habitability of a planet via orbital effects, particularly in the areas of stability and eccentricity. Some of these effects are readily apparent, particularly when they occur on short timescales that are easily numerically calculable. However, the appearance and evolution of life can take place on gigayear timescales, long enough that secular effects become important. These effects are difficult to investigate, as a direct integration requires significant computational time. In this paper, we apply a semi-analytic framework in conjuncti…
Solar system planets move on almost circular orbits. In strong contrast, many massive gas giant exoplanets travel on highly elliptical orbits, whereas the shape of the orbits of smaller, more terrestrial, exoplanets remained largely elusive. Knowing the eccentricity distribution in systems of small planets would be important as it holds information about the planet's formation and evolution, and influences its habitability. We make these measurements using photometry from the Kepler satellite and utilizing a method relying on Kepler's second law, which relates the duration of a planetary trans…
The climate of a planet can be strongly affected by its eccentricity due to variations in the stellar flux. There are two limits for the dependence of the inner habitable zone boundary (IHZ) on eccentricity: (1) the mean-stellar flux approximation ($S_{\mbox{IHZ}} \propto \sqrt{1-e^2}$), in which the temperature is approximately constant throughout the orbit, and (2) the maximum-stellar flux approximation ($S_{\mbox{IHZ}} \propto (1-e)^2$), in which the temperature adjusts instantaneously to the stellar flux. Which limit is appropriate is determined by the dimensionless parameter $Π= \frac{C}{…
We present two exoplanets detected at Keck Observatory. HD 179079 is a G5 subgiant that hosts a hot Neptune planet with Msini = 27.5 M_earth in a 14.48 d, low-eccentricity orbit. The stellar reflex velocity induced by this planet has a semiamplitude of K = 6.6 m/s. HD 73534 is a G5 subgiant with a Jupiter-like planet of Msini = 1.1 M_jup and K = 16 m/s in a nearly circular 4.85 yr orbit. Both stars are chromospherically inactive and metal-rich. We discuss a known, classical bias in measuring eccentricities for orbits with velocity semiamplitudes, K, comparable to the radial velocity uncertaint…
We explore the multiplicity of exoplanet host stars with high-resolution images obtained with VLT/SPHERE. Two different samples of systems were observed: one containing low-eccentricity outer planets, and the other containing high-eccentricity outer planets. We find that 10 out of 34 stars in the high-eccentricity systems are members of a binary, while the proportion is 3 out of 27 for circular systems. Eccentric-exoplanet hosts are, therefore, significantly more likely to have a stellar companion than circular-exoplanet hosts. The median magnitude contrast over the 68 data sets is 11.26 and 9…
We present a model to study secularly and tidally evolving three-body systems composed by two low-mass planets orbiting a star, in the case where the bodies rotation axes are always perpendicular to the orbital plane. The tidal theory allows us to study the spin and orbit evolution of both stiff Earth-like planets and predominantly gaseous Neptune-like planets. The model is applied to study two recently-discovered exoplanetary systems containing potentially habitable exoplanets (PHE): LHS-1140 b-c and K2-18 b-c. For the former system, we show that both LHS-1140 b and c must be in nearly-circul…
The orbit eccentricities of the Solar System planets are unusually low compared to the average of known exoplanetary systems. A power law correlation has previously been found between the multiplicity of a planetary system and the orbital eccentricities of its components, for systems with multiplicities above two. In this study we investigate the correlation for an expanded data sample, by focusing on planetary systems as units (unlike previous studies that have focused on individual planets). Our full data sample contains 1171 exoplanets, in 895 systems, and the correlation between eccentrici…
We assess the multi-planet systems discovered by the Kepler satellite in terms of current ideas about orbital migration and eccentricity damping due to planet-disk interactions. Our primary focus is on mean motion resonances. Only a few percent of planet pairs are in close proximity to a resonance. However, predicted migration rates (parameterized by $τ_n=n/{|\dot n|}$) imply that during convergent migration most planets would have been captured into first order resonances. Eccentricity damping (parameterized by $τ_e=e/{|\dot e|}$) offers a plausible resolution. Estimates suggest $τ_e/τ_n\sim …
Exoplanets discovered over the last decades have provided a new sample of giant exoplanets, hot Jupiters. For lack of enough materials in current locations of hot Jupiters, they are perceived to form outside snowline. Then, migrate to the locations observed through interactions with gas disks or high-eccentricity mechanisms. We examined the efficiencies of different high-eccentricity mechanisms to form hot Jupiters in near coplaner multi-planet systems. These mechanisms include planet-planet scattering, Kozai-Lidov mechanism, coplanar high-eccentricity migration, secular chaos, as well as othe…
Simulation of the spin evolution of some selected exoplanets and inferences on their climate
Università di Padova（帕多瓦大学）；Università di Bari（巴里大学）；Istituto Nazionale di Fisica Nucleare（意大利国家核物理研究所）；Università del Salento（萨伦托大学）；Istituto Nazionale di Astrofisica（意大利国家天体物理研究所）
In recent years, a number of eccentric debris belts have been observed in extrasolar systems. The most common explanation for their shape is the presence of a nearby eccentric planetary companion. The gravitational perturbation from such a companion would induce periodic eccentricity variations on the planetesimals in the belt, with a range of precession frequencies. The overall expected shape is an eccentric belt with a finite minimum width. However, several observed eccentric debris discs have been found to exhibit a narrower width than the theoretical expectation. In this paper, we study tw…
Context: Seasonal variations and climate stability of a planet are very sensitive to the planet obliquity and its evolution. This is of particular interest for the emergence and sustainability of land-based life, but orbital and rotational parameters of exoplanets are still poorly constrained. Numerical explorations usually realised in this situation are thus in heavy contrast with the uncertain nature of the available data. Aims: We aim to provide an analytical formulation of the long-term spin-axis dynamics of exoplanets, linking it directly to physical and dynamical parameters, but still gi…
Observations of the youngest planets ($\sim$1-10 Myr for a transitional disk) will increase the accuracy of our planet formation models. Unfortunately, observations of such planets are challenging and time-consuming to undertake even in ideal circumstances. Therefore, we propose the determination of a set of markers that can pre-select promising exoplanet-hosting candidate disks. To this end, N-body simulations were conducted to investigate the effect of an embedded Jupiter mass planet on the dynamics of the surrounding planetesimal disk and the resulting creation of second generation collisio…
Planetary formation theories and, more specifically, migration models predict that planets can be captured in mean-motion resonances (MMRs) during the disc phase. The distribution of period ratios between adjacent planets shows an accumulation in the vicinity of the resonance, which is not centred on the nominal resonance but instead presents an offset slightly exterior to it. Here we extend on previous works by thoroughly exploring the effect of different disc and planet parameters on the resonance offset during the disc migration phase. The dynamical study is carried out for several first-or…
The mass-period or radius-period distribution of close-in exoplanets shows a paucity of intermediate mass/size (sub-Jovian) planets with periods ~< 3 days. We show that this sub-Jovian desert can be explained by the photoevaporation of highly irradiated sub-Neptunes and the tidal disruption barrier for gas giants undergoing high-eccentricity migration. The distinctive triangular shape of the sub-Jovain desert result from the fact that photoevaporation is more effective closer to the host star, and that in order for a gas giant to tidally circularise closer to the star without tidal disruption …
Radial velocity (RV) surveys have discovered giant exoplanets on au-scale orbits with a broad distribution of eccentricities. Those with the most eccentric orbits are valuable laboratories for testing theories of high eccentricity migration. However, few such exoplanets transit their host stars thus removing the ability to apply constraints on formation from their bulk internal compositions. We report the discovery of Kepler-1704 b, a transiting 4.15 $M_{\rm J}$ giant planet on a 988.88 day orbit with the extreme eccentricity of $0.921^{+0.010}_{-0.015}$. Our decade-long RV baseline from the K…
We report the detection of two exoplanets and a further tentative candidate around the M-dwarf stars Gl96 and Gl617A, based on radial velocity measurements obtained with the SOPHIE spectrograph at the Observatoire de Haute-Provence. Both stars were observed in the context of the SOPHIE exoplanet consortium's dedicated M-dwarf subprogramme, which aims to detect exoplanets around nearby M-dwarf stars through a systematic survey. For Gl96, we present the discovery of a new exoplanet at 73.9 d with a minimum mass of 19.66 earth masses. Gl96 b has an eccentricity of 0.44, placing it among the most …
We present a time-dependent radiative model for the atmosphere of extrasolar planets that takes into account the eccentricity of their orbit. In addition to the modulation of stellar irradiation by the varying planet-star distance, the pseudo-synchronous rotation of the planets may play a significant role. We include both of these time-dependent effects when modeling the planetary thermal structure. We investigate the thermal structure, and spectral characteristics for time-dependent stellar heating for two highly eccentric planets. Finally, we discuss observational aspects for those planets s…
Although the sample of exoplanets in binaries has been greatly expanded, the sample heterogeneity and observational bias are obstacles toward a clear figure of exoplanet demographics in the binary environment. To overcome the obstacles, we conduct a statistical study that focuses on S-type planetary systems detected by the Radial Velocity method. We try to account for observational biases by estimating, from available RV data, planet detection efficiencies for each individual system. Our main results are as follows: (1) Single (multiple) planetary systems are mostly found in close (wide) binar…
Improved photometric sensitivity from space-based telescopes have enabled the detection of phase variations for a small sample of hot Jupiters. However, exoplanets in highly eccentric orbits present unique opportunities to study the effects of drastically changing incident flux on the upper atmospheres of giant planets. Here we expand upon previous studies of phase functions for these planets at optical wavelengths by investigating the effects of orbital inclination on the flux ratio as it interacts with the other effects induced by orbital eccentricity. We determine optimal orbital inclinatio…
We show that the first order (non co-orbital) corotation torques are significantly modified by entropy gradients in a non-barotropic protoplanetary disk. Such non-barotropic torques can dramatically alter the balance that, for barotropic cases, results in the net eccentricity damping for giant gap-clearing planets embedded in the disk. We demonstrate that stellar illumination can heat the gap enough for the planet's orbital eccentricity to instead be excited. We also discuss the "Eccentricity Valley" noted in the known exoplanet population, where low-metallicity stars have a deficit of eccentr…
The detection of exoplanets through direct imaging has produced numerous new positive identifications in recent years. The technique is biased towards planets at wide separations due to the difficulty in removing the stellar signature at small angular separations. Planets in eccentric orbits will thus move in and out of the detectable region around a star as a function of time. Here we use the known diversity of orbital eccentricities to determine the range of orbits which may lie beneath the detection threshold of current surveys. We quantify the percentage of the orbit which yields a detecta…
Since exoplanets were detected using the radial velocity method, they have revealed a diverse distribution of orbital configurations. Amongst these are planets in highly eccentric orbits (e > 0.5). Most of these systems consist of a single planet but several have been found to also contain a longer period planet in a near-circular orbit. Here we use the latest Keplerian orbital solutions to investigate four known systems which exhibit this extreme eccentricity diversity; HD 37605, HD 74156, HD 163607, and HD 168443. We place limits on the presence of additional planets in these systems based o…
We have analysed radial velocity measurements for known transiting exoplanets to study the empirical signature of tidal orbital evolution for close-in planets. Compared to standard eccentricity determination, our approach is modified to focus on the rejection of the null hypothesis of a circular orbit. We are using a MCMC analysis of radial velocity measurements and photometric constraints, including a component of correlated noise, as well as Bayesian model selection to check if the data justifies the additional complexity of an eccentric orbit. We find that among planets with non-zero eccent…
We report the detection of a large mass planet orbiting around the K0 metal-rich subgiant HD38801 ($V=8.26$) by precise radial velocity (RV) measurements from the Subaru Telescope and the Keck Telescope. The star has a mass of $1.36M_{\odot}$ and metallicity of [Fe/H]= +0.26. The RV variations are consistent with a circular orbit with a period of 696.0 days and a velocity semiamplitude of 200.0\mps, which yield a minimum-mass for the companion of $10.7\mjup$ and semimajor axis of 1.71 AU. Such super-massive objects with very low-eccentricities and hundreds of days period are uncommon among the…
The nearly circular (mean eccentricity <e>~0.06) and coplanar (mean mutual inclination <i>~3 deg) orbits of the Solar System planets motivated Kant and Laplace to put forth the hypothesis that planets are formed in disks, which has developed into the widely accepted theory of planet formation. Surprisingly, the first several hundred extrasolar planets (mostly Jovian) discovered using the Radial Velocity (RV) technique are commonly on eccentric orbits (<e> ~ 0.3). This raises a fundamental question: Are the Solar System and its formation special? The Kepler mission has found thousands of transi…
Inferring planetary parameters from transit timing variations is challenging for small exoplanets because their transits may be so weak that determination of individual transit timing is difficult or impossible. We implement a useful combination of tools which together provide a numerically fast global photodynamical model. This is used to fit the TTV-bearing light-curve, in order to constrain the masses of transiting exoplanets in low eccentricity, multi-planet systems - and small planets in particular. We present inferred dynamical masses and orbital eccentricities in four multi-planet syste…
We present high resolution 3-D simulations of the planet-disc interaction using smoothed particle hydrodynamics, to investigate the possibility of driving eccentricity growth by this mechanism. For models with a given disc viscosity (α= 0.01), we find that for small planet masses (a few Jupiter masses) and canonical surface densities, no significant eccentricity growth is seen over the duration of our simulations. This contrasts with the limiting case of large planet mass (over twenty Jupiter masses) and extremely high surface densities, where we find eccentricity growth in agreement with prev…
Planetary obliquity and eccentricity influence climate by shaping the spatial and temporal patterns of stellar energy incident at a planet's surface, affecting both the annual mean climate and magnitude of seasonal variability. Previous work has demonstrated the importance of both planetary obliquity and eccentricity for climate and habitability, but most studies have not explicitly modeled the response of life to these parameters. While exaggerated seasons may be stressful to some types of life, a recent study found an increase in marine biological activity for moderately high obliquities <45…
