Eccentricity Of Planet Research Articles

The SOPHIE search for northern extrasolar planets

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 eccentric planets orbiting M stars. For Gl617A we independently confirm a recently reported exoplanet at 86.7 d with a minimum mass of 31.29 earth masses. Both Gl96 b and Gl617A b are potentially within the habitable zone, although the high eccentricity of Gl96 b may take it too close to the star at periapsis.

Migration of planets into and out of mean motion resonances in protoplanetary discs: overstability of capture and non-linear eccentricity damping

A number of multiplanet systems are observed to contain planets very close to mean motion resonances, although there is no significant pileup of precise resonance pairs. We present theoretical and numerical studies on the outcome of capture into first-order mean motion resonances (MMRs) using a parametrized planet migration model that takes into account nonlinear eccentricity damping due to planet-disk interaction. This parametrization is based on numerical hydrodynamical simulations and is more realistic than the simple linear parametrization widely used in previous analytic studies. We find that nonlinear eccentricity damping can significantly influence the stability and outcome of resonance capture. In particular, the equilibrium eccentricity of the planet captured into MMRs become larger, and the captured MMR state tends to be more stable compared to the prediction based on the simple migration model. In addition, when the migration is sufficiently fast or/and the planet mass ratio is sufficiently small, we observe a novel phenomenon of eccentricity overshoot, where the planet's eccentricity becomes very large before settling down to the lower equilibrium value. This can lead to the ejection of the smaller planet if its eccentricity approaches unity during the overshoot. This may help explain the lack of low-mass planet companion of hot Jupiters when compared to warm Jupiters.

The HADES RV Programme with HARPS-N at TNG

We present 20 yr of radial velocity (RV) measurements of the M1 dwarf Gl15A, combining five years of intensive RV monitoring with the HARPS-N spectrograph with 15 yr of archival HIRES/Keck RV data. We have carried out an MCMC-based analysis of the RV time series, inclusive of Gaussian Process (GP) approach to the description of stellar activity induced RV variations. Our analysis confirms the Keplerian nature and refines the orbital solution for the 11.44-day period super Earth, Gl15A b, reducing its amplitude to 1.68−0.18+0.17 m s−1 (M sin i = 3.03−0.44+0.46 M⊕), and successfully models a long-term trend in the combined RV dataset in terms of a Keplerian orbit with a period around 7600 days and an amplitude of 2.5−1.0+1.3 m s−1, corresponding to a super-Neptune mass (M sin i = 36−18+25 M⊕) planetary companion. We also discuss the present orbital configuration of Gl15A planetary system in terms of the possible outcomes of Lidov–Kozai interactions with the wide-separation companion Gl15B in a suite of detailed numerical simulations. In order to improve the results of the dynamical analysis, we have derived a new orbital solution for the binary system, combining our RV measurements with astrometric data from the WDS catalogue. The eccentric Lidov–Kozai analysis shows the strong influence of Gl15B on the Gl15A planetary system, which can produce orbits compatible with the observed configuration for initial inclinations of the planetary system between 75° and 90°, and can also enhance the eccentricity of the outer planet well above the observed value, even resulting in orbital instability, for inclinations around 0° and 15°−30°. The Gl15A system is the multi-planet system closest to Earth, at 3.56 pc, and hosts the longest period RV sub-Jovian mass planet discovered so far. Its orbital architecture constitutes a very important laboratory for the investigation of formation and orbital evolution scenarios for planetary systems in binary stellar systems.

A Criterion for the Onset of Chaos in Systems of Two Eccentric Planets

Abstract We derive a criterion for the onset of chaos in systems consisting of two massive, eccentric, coplanar planets. Given the planets’ masses and separation, the criterion predicts the critical eccentricity above which chaos is triggered. Chaos occurs where mean motion resonances overlap, as in Wisdom's pioneering work. But whereas Wisdom considered the overlap of first-order resonances only, limiting the applicability of his criterion to nearly circular planets, we extend his results to arbitrarily eccentric planets (up to crossing orbits) by examining resonances of all orders. We thereby arrive at a simple expression for the critical eccentricity. We do this first for a test particle in the presence of a planet and then generalize to the case of two massive planets, based on a new approximation to the Hamiltonian. We then confirm our results with detailed numerical simulations. Finally, we explore the extent to which chaotic two-planet systems eventually result in planetary collisions.

Dynamics and Formation of the Near-resonant K2-24 System: Insights from Transit-timing Variations and Radial Velocities

Abstract While planets between the size of Uranus and Saturn are absent within the solar system, the star K2-24 hosts two such planets, K2-24b and c, with radii equal to 5.4 and 7.5 , respectively. The two planets have orbital periods of 20.9 days and 42.4 days, residing only 1% outside the nominal 2:1 mean-motion resonance. In this work, we present results from a coordinated observing campaign to measure planet masses and eccentricities that combines radial velocity measurements from Keck/HIRES and transit-timing measurements from K2 and Spitzer. K2-24b and c have low, but nonzero, eccentricities of . The low observed eccentricities provide clues to the formation and dynamical evolution of K2-24b and K2-24c, suggesting that they could be the result of stochastic gravitational interactions with a turbulent protoplanetary disk, among other mechanisms. K2-24b and c are and , respectively; K2-24c is 20% less massive than K2-24b, despite being 40% larger. Their large sizes and low masses imply large envelope fractions, which we estimate at % and %. In particular, K2-24c’s large envelope presents an intriguing challenge to the standard model of core-nucleated accretion that predicts the onset of runaway accretion when ≈ 50%.

Feasibility of a Resonance-based Planet Nine Search

Abstract It has been proposed that mean-motion resonances (MMRs) between Planet Nine and distant objects of the scattered disk might inform the semimajor axis and instantaneous position of Planet Nine. Within the context of this hypothesis, the specific distribution of occupied MMRs largely determines the available constraints. Here we characterize the behavior of scattered Kuiper Belt objects arising in the presence of an eccentric Planet Nine (e 9 ∈ 0.1, 0.7), focusing on relative sizes of populations occupying particular commensurabilities. Highlighting the challenge of predicting the exact MMR of a given object, we find that the majority of resonant test particles have period ratios with Planet Nine other than those of the form P 9/P = N/1, N/2 . Taking into account the updated prior distribution of MMRs outlined in this work, we find that the close spacing of high-order resonances, as well as chaotic transport, preclude resonance-based Planet Nine constraints from current observational data.

Catching drifting pebbles

Context.Coagulation theory predicts that micron-sized dust grains grow into pebbles, which drift inward towards the star when they reach sizes of mm−cm. When they cross the orbit of a planet, a fraction of these drifting pebbles will be accreted. In the pebble accretion mechanism, the combined effects of the planet’s gravitational attraction and gas drag greatly increase the accretion rate.Aims.We calculate the pebble accretion efficiencyε2D– the probability that a pebble is accreted by the planet – in the 2D limit (pebbles reside in the midplane). In particular, we investigate the dependence ofε2Don the planet eccentricity and its implications for planet formation models.Methods.We conduct N-body simulations to calculate the pebble accretion efficiency in both the local frame and the global frame. With the global method we investigate the pebble accretion efficiency when the planet is on an eccentric orbit.Results.We find that the local and the global methods generally give consistent results. However, the global method becomes more accurate when the planet is more massive than a few Earth masses or when the aerodynamic size (Stokes number) of the pebble is larger than 1. The efficiency increases with the planet’s eccentricity once the relative velocity between the pebble and the planet is determined by the planet’s eccentric velocity. At high eccentricities, however, the relative velocity becomes too high for pebble accretion. The efficiency then drops significantly and the accretion enters the ballistic regime. We present general expressions forε2D. Applying the obtained formula to the formation of a secondary planet, in resonance with an already-formed giant planet, we find that the embryo grows quickly due to its higher eccentricity.Conclusions.The maximumε2Dfor a planet on an eccentric orbit is several times higher than for a planet on a circular orbit, but this increase gives the planet an important headstart and boosts its following mass growth. The recipe forε2Dthat we have obtained is designed to be implemented into N-body codes to simulate the growth and evolution of planetary systems.

Puzzling out the coexistence of terrestrial planets and giant exoplanets

Aims. Hundreds of giant planets have been discovered so far and the quest of exo-Earths in giant planet systems has become intriguing. In this work, we aim to address the question of the possible long-term coexistence of a terrestrial companion on an orbit interior to a giant planet, and explore the extent of the stability regions for both non-resonant and resonant configurations. Methods. Our study focuses on the restricted three-body problem, where an inner terrestrial planet (massless body) moves under the gravitational attraction of a star and an outer massive planet on a circular or elliptic orbit. Using the detrended fast Lyapunov indicator as a chaotic indicator, we constructed maps of dynamical stability by varying both the eccentricity of the outer giant planet and the semi-major axis of the inner terrestrial planet, and identify the boundaries of the stability domains. Guided by the computation of families of periodic orbits, the phase space is unravelled by meticulously chosen stable periodic orbits, which buttress the stability domains. Results. We provide all possible stability domains for coplanar symmetric configurations and show that a terrestrial planet, either in mean-motion resonance or not, can coexist with a giant planet, when the latter moves on either a circular or an (even highly) eccentric orbit. New families of symmetric and asymmetric periodic orbits are presented for the 2/1 resonance. It is shown that an inner terrestrial planet can survive long time spans with a giant eccentric outer planet on resonant symmetric orbits, even when both orbits are highly eccentric. For 22 detected single-planet systems consisting of a giant planet with high eccentricity, we discuss the possible existence of a terrestrial planet. This study is particularly suitable for the research of companions among the detected systems with giant planets, and could assist with refining observational data.

The role of general relativity on icy body reservoirs under the effects of an inner eccentric Jupiter

Context. Recent studies have analyzed the dynamical evolution of outer small body populations under the effects of an eccentric inner massive perturber, which result from a planetary scattering event. These investigations suggest that such outer reservoirs are composed of particles on prograde and retrograde orbits, as well as particles whose orbit flips from prograde to retrograde and back again showing a coupling between the inclination i and the ascending node longitude Ω (Type-F particles). Aims. We analyze the role of the general relativity (GR) on the dynamics of outer particles under the influence of an inner eccentric Jupiter-mass planet produced by a planetary scattering event. In particular, we are interested in studying how the GR affects the dynamical evolution of the outer Type-F particles, which experience an eccentric Lidov–Kozai mechanism. Methods. To do this, we carried out N-body simulations with and without GR effects. Such a detailed comparative analysis allows us to strengthen our understanding concerning the GR and eccentric Lidov–Kozai combined effects on the dynamical evolution of outer particles. Results. When the GR is included, the extreme values of Ω are obtained for retrograde inclinations, while the minimum and maximum inclinations allowed for Type-F particles increase in comparison with that derived without GR effects. According to this, if the GR is included in the simulations, the range of prograde (retrograde) inclinations of the libration region is reduced (increased) with respect to that obtained in absence of GR. We find two new classes of particles when GR effects are included in the simulations. On the one hand, there are particles whose orbital plane flips from prograde to retrograde and back again without experiencing a coupling between i and Ω. On the other hand, retrograde particles show a strong coupling between i and Ω. We infer that GR may significantly modify the dynamical properties of the outer reservoirs that evolve under the effects of an eccentric inner perturber.

Modal Decomposition of TTV: Inferring Planet Masses and Eccentricities

Abstract Transit timing variations (TTVs) are a powerful tool for characterizing the properties of transiting exoplanets. However, inferring planet properties from the observed timing variations is a challenging task, which is usually addressed by extensive numerical searches. We propose a new, computationally inexpensive method for inverting TTV signals in a planetary system of two transiting planets. To the lowest order in planetary masses and eccentricities, TTVs can be expressed as a linear combination of three functions, which we call the TTV modes. These functions depend only on the planets’ linear ephemerides, and can be either constructed analytically, or by performing three orbital integrations of the three-body system. Given a TTV signal, the underlying physical parameters are found by decomposing the data as a sum of the TTV modes. We demonstrate the use of this method by inferring the mass and eccentricity of six Kepler planets that were previously characterized in other studies. Finally we discuss the implications and future prospects of our new method.

The HARPS search for southern extra-solar planets

We report the discovery of four super-Earth planets around HD 215152, with orbital periods of 5.76, 7.28, 10.86, and 25.2 d, and minimum masses of 1.8, 1.7, 2.8, and 2.9 M⊕ respectively. This discovery is based on 373 high-quality radial velocity measurements taken by HARPS over 13 yr. Given the low masses of the planets, the signal-to-noise ratio is not sufficient to constrain the planet eccentricities. However, a preliminary dynamical analysis suggests that eccentricities should be typically lower than about 0.03 for the system to remain stable. With two pairs of planets with a period ratio lower than 1.5, with short orbital periods, low masses, and low eccentricities, HD 215152 is similar to the very compact multi-planet systems found by Kepler, which is very rare in radial-velocity surveys. This discovery proves that these systems can be reached with the radial-velocity technique, but characterizing them requires a huge amount of observations.

Eccentricities and inclinations of multiplanet systems with external perturbers

Compact multi-planet systems containing super-Earths or sub-Neptunes, commonly found around solar-type stars, may be surrounded by external giant planet or stellar companions, which can shape the architechture and observability of the inner systems. We present a comprehensive study on the evolution of the inner planetary system subject to the gravitational influence of an eccentric, misaligned outer perturber. Analytic results are derived for the inner planet eccentricities ($e_i$) and mutual inclination ($\theta_{12}$) of the "2-planet + perturber" system, calibrated with numerical secular and N-body integrations, as a function of the perturber mass $m_p$, semi-major axis $a_p$ and inclination angle $\theta_p$. We find that the dynamics of the inner system is determined by the dimensionless parameter $\epsilon_{12}$, given by the ratio between the differential precession rate driven by the perturber and the mutual precession rate of the inner planets. Loosely packed systems (corresponding to $\epsilon_{12} \gg 1$) are more susceptible to eccentricity/inclination excitations by the perturber than tightly packed inner systems (with $\epsilon_{12} \ll 1$) (or singletons), although resonance may occur around $\epsilon_{12}\sim 1$, leading to large $e_i$ and $\theta_{12}$. Dynamical instability may set in for inner planet systems with large excited eccentricities and mutual inclinations. We present a formalism to extend our analytical results to general inner systems with $N>2$ planets and apply our results to constrain possible external companions to the Kepler-11 system. Eccentricity and inclination excitation by external companions may help explain the observational trend that systems with fewer transiting planets are dynamically hotter than those with more transiting planets.

Properties of the single Jovian planet population and the pursuit of Solar system analogues

While the number of exoplanets discovered continues to increase at a rapid rate, we are still to discover any system that truly resembles the Solar system. Existing and near future surveys will likely continue this trend of rapid discovery. To see if these systems are Solar system analogues, we will need to efficiently allocate resources to carry out intensive follow-up observations. We seek to uncover the properties and trends across systems that indicate how much of the habitable zone is stable in each system to provide focus for planet hunters. We study the dynamics of all known single Jovian planetary systems, to assess the dynamical stability of the habitable zone around their host stars. We perform a suite of simulations of all systems where the Jovian planet will interact gravitationally with the habitable zone, and broadly classify these systems. Besides the system's mass ratio (Mpl/Mstar), and the Jovian planet's semi-major axis (apl) and eccentricity (epl), we find that there are no underlying system properties which are observable that indicate the potential for planets to survive within the system's habitable zone. We use Mpl/Mstar, apl and epl to generate a parameter space over which the unstable systems cluster, thus allowing us to predict which systems to exclude from future observational or numerical searches for habitable exoplanets. We also provide a candidate list of 20 systems that have completely stable habitable zones and Jovian planets orbiting beyond the habitable zone as potential first order Solar system analogues.

Chemical fingerprints of hot Jupiter planet formation

Context. The current paradigm to explain the presence of Jupiter-like planets with small orbital periods (P < 10 days; hot Jupiters), which involves their formation beyond the snow line following inward migration, has been challenged by recent works that explore the possibility of in situ formation. Aims. We aim to test whether stars harbouring hot Jupiters and stars with more distant gas-giant planets show any chemical peculiarity that could be related to different formation processes. Methods. Our methodology is based on the analysis of high-resolution échelle spectra. Stellar parameters and abundances of C, O, Na, Mg, Al, Si, S, Ca, Sc, Ti, V, Cr, Mn, Co, Ni, Cu, and Zn for a sample of 88 planet hosts are derived. The sample is divided into stars hosting hot (a < 0.1 au) and cool (a > 0.1 au) Jupiter-like planets. The metallicity and abundance trends of the two sub-samples are compared and set in the context of current models of planet formation and migration. Results. Our results show that stars with hot Jupiters have higher metallicities than stars with cool distant gas-giant planets in the metallicity range +0.00/+0.20 dex. The data also shows a tendency of stars with cool Jupiters to show larger abundances of α elements. No abundance differences between stars with cool and hot Jupiters are found when considering iron peak, volatile elements or the C/O, and Mg/Si ratios. The corresponding p-values from the statistical tests comparing the cumulative distributions of cool and hot planet hosts are 0.20, <0.01, 0.81, and 0.16 for metallicity, α, iron-peak, and volatile elements, respectively. We confirm previous works suggesting that more distant planets show higher planetary masses as well as larger eccentricities. We note differences in age and spectral type between the hot and cool planet host samples that might affect the abundance comparison. Conclusions. The differences in the distribution of planetary mass, period, eccentricity, and stellar host metallicity suggest a different formation mechanism for hot and cool Jupiters. The slightly larger α abundances found in stars harbouring cool Jupiters might compensate their lower metallicities allowing the formation of gas-giant planets.

Chaotic Excitation and Tidal Damping in the GJ 876 System

Abstract The M-dwarf GJ 876 is the closest known star to harbor a multi-planetary system. With three outer planets locked in a chaotic Laplace-type resonance and an appreciably eccentric short-period super-Earth, this system represents a unique exposition of extrasolar planetary dynamics. A key question that concerns the long-term evolution of this system, and the fate of close-in planets in general, is how the significant eccentricity of the inner-most planet is maintained against tidal circularization on timescales comparable to the age of the universe. Here, we employ stochastic secular perturbation theory and N-body simulations to show that the orbit of the inner-most planet is shaped by a delicate balance between extrinsic chaotic forcing and tidal dissipation. As such, the planet’s orbital eccentricity represents an indirect measure of its tidal quality factor. Based on the system’s present-day architecture, we estimate that the extrasolar super-Earth GJ 876 d has a tidal Q ∼ 104–105, a value characteristic of solar system gas giants.

On the chaotic diffusion in multidimensional Hamiltonian systems

We present numerical evidence that diffusion in the herein studied multidimensional near-integrable Hamiltonian systems departs from a normal process, at least for realistic timescales. Therefore, the derivation of a diffusion coefficient from a linear fit on the variance evolution of the unperturbed integrals fails. We review some topics on diffusion in the Arnold Hamiltonian and yield numerical and theoretical arguments to show that in the examples we considered, a standard coefficient would not provide a good estimation of the speed of diffusion. However, numerical experiments concerning diffusion would provide reliable information about the stability of the motion within chaotic regions of the phase space. In this direction, we present an extension of previous results concerning the dynamical structure of the Laplace resonance in Gliese-876 planetary system considering variations of the orbital parameters accordingly to the error introduced by the radial velocity determination. We found that a slight variation of the eccentricity of planet c would destabilize the inner region of the resonance that, though chaotic, shows stable when adopting the best fit values for the parameters.

Eccentricity evolution during planet–disc interaction

During the process of planet formation, the planet-discs interactions might excite (or damp) the orbital eccentricity of the planet. In this paper, we present two long ($t\sim 3\times 10^5$ orbits) numerical simulations: (a) one (with a relatively light disc, $M_{\rm d}/M_{\rm p}=0.2$) where the eccentricity initially stalls before growing at later times and (b) one (with a more massive disc, $M_{\rm d}/M_{\rm p}=0.65$) with fast growth and a late decrease of the eccentricity. We recover the well-known result that a more massive disc promotes a faster initial growth of the planet eccentricity. However, at late times the planet eccentricity decreases in the massive disc case, but increases in the light disc case. Both simulations show periodic eccentricity oscillations superimposed on a growing/decreasing trend and a rapid transition between fast and slow pericentre precession. The peculiar and contrasting evolution of the eccentricity of both planet and disc in the two simulations can be understood by invoking a simple toy model where the disc is treated as a second point-like gravitating body, subject to secular planet-planet interaction and eccentricity pumping/damping provided by the disc. We show how the counterintuitive result that the more massive simulation produces a lower planet eccentricity at late times can be understood in terms of the different ratios of the disc-to-planet angular momentum in the two simulations. In our interpretation, at late times the planet eccentricity can increase more in low-mass discs rather than in high-mass discs, contrary to previous claims in the literature.

The Pan-Pacific Planet Search. VII. The Most Eccentric Planet Orbiting a Giant Star

Abstract Radial velocity observations from three instruments reveal the presence of a 4 M Jup planet candidate orbiting the K giant HD 76920. HD 76920b has an orbital eccentricity of 0.856 ± 0.009, making it the most eccentric planet known to orbit an evolved star. There is no indication that HD 76920 has an unseen binary companion, suggesting a scattering event rather than Kozai oscillations as a probable culprit for the observed eccentricity. The candidate planet currently approaches to about four stellar radii from its host star, and is predicted to be engulfed on a ∼100 Myr timescale due to the combined effects of stellar evolution and tidal interactions.

Characterization of the K2-18 multi-planetary system with HARPS

The bright M dwarf K2-18 at 34 pc is known to host a transiting super-Earth-sized planet orbiting within the star's habitable zone; K2-18b. Given the superlative nature of this system for studying an exoplanetary atmosphere receiving similar levels of insolation as the Earth, we aim to characterize the planet's mass which is required to interpret atmospheric properties and infer the planet's bulk composition. We obtain precision radial velocity measurements with the HARPS spectrograph and couple those measurements with the K2 photometry to jointly model the observed radial velocity variation with planetary signals and a radial velocity jitter model based on Gaussian process regression. We measure the mass of K2-18b to be $8.0 \pm 1.9$ M$_{\oplus}$ with a bulk density of $3.7 \pm 0.9$ g/cm$^3$ which may correspond to a predominantly rocky planet with a significant gaseous envelope or an ocean planet with a water mass fraction $\gtrsim 50$%. We also find strong evidence for a second, warm super-Earth K2-18c at $\sim 9$ days with a semi-major axis 2.4 times smaller than the transiting K2-18b. After re-analyzing the available light curves of K2-18 we conclude that K2-18c is not detected in transit and therefore likely has an orbit that is non-coplanar with K2-18b. A suite of dynamical integrations with varying simulated orbital eccentricities of the two planets are used to further constrain each planet's eccentricity posterior from which we measure $e_b < 0.43$ and $e_c < 0.47$ at 99% confidence. The discovery of the inner planet K2-18c further emphasizes the prevalence of multi-planet systems around M dwarfs. The characterization of the density of K2-18b reveals that the planet likely has a thick gaseous envelope which along with its proximity to the Solar system makes the K2-18 planetary system an interesting target for the atmospheric study of an exoplanet receiving Earth-like insolation.

Obliquity and Eccentricity Constraints for Terrestrial Exoplanets

Abstract 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 equivalent to the flux variation due to orbital eccentricity. This equivalence is computed for both the maximum and average flux scenarios, the latter of which includes the effects of the diurnal cycle. We apply these calculations to four known multi-planet systems (GJ 163, K2-3, Kepler-186, and Proxima Centauri), where we constrain the eccentricity of terrestrial planets using orbital dynamics considerations and model the effect of obliquity on incident flux. We discuss the implications of these simulations on climate models for terrestrial planets and outline detectable signatures of planetary obliquity.