C. Beaugé

National University of Cordoba, Argentina | UNC

We analyse the distribution of known multi-planet systems (N ≥ 3) in the plane of mean-motion ratios, and compare it with the resonance web generated by two-planet mean-motion resonances (2P-MMR) and pure 3-planet commensurabilities (pure 3P-MMR). We find intriguing evidence of a statistically significant correlation between the observed distributi...

Tidal evolution of low-eccentric circumbinary planets is expected to drive the rotational evolution toward a pseudo-synchronous solution. In this work, we present a study of the oscillation amplitudes around this state by considering that the two central stars exert creep tides on the planet. These amplitudes are computed by direct numerical integr...

The present work consists of a study of the dynamical stability of a three-body system that takes advantage of the Shannon entropy approach to estimate the diffusivity (D_S ) in a Delaunay’s action-like phase space. We outline the main features of a numerical computation of D_S from the solutions of the equations of motion and, thereupon, we consid...

The present work consists on a study of the dynamical stability of a 3-body system, taking advantage of the Shannon entropy approach to estimate the diffusivity (D S) in a Delaunay's action-like phase space. We outline the main features of a numerical computation of D S from the solutions of the equations of motion, and therefrom how to estimate a...

We present a tidal model for treating the rotational evolution in the general three-body problem with arbitrary viscosities, in which all the masses are considered to be extended and all the tidal interactions between pairs are taken into account. Based on the creep tide theory, we present a set of differential equations that describes the rotation...

We present a tidal model for treating the rotational evolution in the general three-body problem with arbitrary viscosities, in which all the masses are considered to be extended and all the tidal interactions between pairs are taken into account. Based on the creep tide theory, we present the set of differential equations that describes the rotati...

In the present effort, we revisit the Shannon entropy approach for the study of both the extent and the rate of diffusion in a given dynamical system. In particular, we provide a theoretical and numerical study of the dependence of the formulation on the parameters of the method. We succeed in deriving not only a diffusion coefficient, DS\documentc...

Context. Planetary resonances are a common dynamical mechanism acting on planetary systems. However, no general model for describing their properties exists, particularly for commensurabilities of any order and arbitrary eccentricity and inclination values. Aims. We present a semianalytical model that describes the resonance strength, width, locati...

In spite of planetary resonances being a common dynamical mechanism acting on planetary systems, no general model exists for describing their properties, particularly for commensurabilities of any order and arbitrary values of the eccentricities and inclinations. The present work presents a semi-analytical model that describes the resonance strengt...

In this work it is shown that the Shannon entropy is an efficient dynamical indicator that provides a direct measure of the diffusion rate and thus a timescale for the instabilities arising when dealing with chaos. Its computation just involves the solution of the Hamiltonian flow, the variational equations are not required. After a review of the t...

In this work it is shown that the Shannon entropy is an efficient dynamical indicator that provides a direct measure of the diffusion rate and thus a time-scale for the instabilities arising when dealing with chaos. Its computation just involves the solution of the Hamiltonian flow, the variational equations are not required. After a review of the...

Accepted, CMDA

Paper on the creep tide theory and its applications to satellites and planets with emphasis on a new set of differential equations allowing easier numerical studies. The creep tide theory is a new paradigm that does not fix a priori the tidal deformation of the body, but considers the deformation as a low-Reynolds-number flow. The evolution under t...

Paper on the creep tide theory and its applications to satellites and planets with emphasis on a new set of differential equations allowing easier numerical studies. The creep tide theory is a new paradigm that does not fix a priori the tidal deformation of the body, but considers the deformation as a low-Reynolds-number flow. The evolution under t...

We present an extended version of the Constant Time Lag analytical approach for the tidal evolution of circumbinary planets introduced in our previous work. The model is self-consistent, in the sense that all tidal interactions between pairs are computed, regardless of their size. We derive analytical expressions for the variational equations gover...

We present a numerical study of the application of the Shannon entropy technique to the planar restricted three-body problem in the vicinity of first-order interior mean-motion resonances with the perturber. We estimate the diffusion coefficient for a series of initial conditions and compare the results with calculations obtained from the time evol...

Within the framework of the Restricted Three Body Problem (RTBP), we consider the orbital evolution of a circumbinary (CB) planet. We develop a simple analytical model to explain the mean behaviour of the planetary eccentricity and better identify the nature of the main contributors of eccentricity oscilations. Our theory is validated by comparing...

We present a numerical study of the application of Shannon entropy to the restricted three-body problem in the vicinity of first-order interior mean-motion resonances with the perturber. We estimate the diffusion coefficient for a series of initial conditions and compare the results with calculations obtained from the time evolution of the variance...

We present a self-consistent model for the tidal evolution of circumbinary planets that is easily extensible to any other three-body problem. Based on the weak-friction model, we derive expressions of the resulting forces and torques considering complete tidal interactions between all the bodies of the system. Although the tidal deformation suffere...

We present a self-consistent model for the tidal evolution of circumbinary planets. Based on the weak-friction model, we derive expressions of the resulting forces and torques considering complete tidal interactions between all the bodies of the system. Although the tidal deformation suffered by each extended mass must take into account the combine...

Circumbinary planets are thought to form far from the central binary and migrate inwards by interactions with the circumbinary disc, ultimately stopping near their present location either by a planetary trap near the disc inner edge or by resonance capture. Here, we analyse the second possibility, presenting a detailed numerical study on the captur...

We present a series of dynamical maps for fictitious 3-planets systems in initially circular coplanar orbits. These maps have unveiled a rich resonant structure involving two or three planets, as well as indicating possible migration routes from secular to double resonances or pure 3-planet commensurabilities. These structures are then compared to...

We present numerical evidence that diffusion in the herein studied mul- tidimensional near-integrable Hamiltonian systems depart from a normal process, at least for realistic time-scales. 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 diff...

Based on the model described in Ramos et al., 2017, we present an analytical+numerical study of the resonance capture under Type-I migration for the Kepler-25 (Marcy et al., 2014) and K2-24 (Petigura et al., 2016) Kepler systems, both close to a 2/1 mean-motion resonance. We find that, depending on the flare index and the proximity to the central s...

We present an analytical and numerical study of the orbital migration and resonance capture of fictitious two-planet systems with masses in the super-Earth range undergoing Type-I migration. We find that, depending on the flare index and proximity to the central star, the average value of the period ratio, $P_2/P_1$, between both planets may show a...

We present a new method that allows long-term and large-scale hydrodynamical simulations of migrating planets over a grid-based Eulerian code. This technique, which consists in a remapping of the disk by tracking the planetary migration, enables runs of migrating planets over a time comparable to the age of protoplanetary disks. This method also ha...

Chaotic diffusion is supposed to be responsible for orbital instabilities in planetary systems after the dissipation of the protoplanetary disk, and a natural consequence of irregular motion. In this paper we show that resonant multi-planetary systems, despite being highly chaotic, not necessarily exhibit significant diffusion in phase space, and m...

We analyse the secular dynamics of planets on S-type coplanar orbits in tight binary systems, based on first- and second-order analytical models, and compare their predictions with full N-body simulations. The perturbation parameter adopted for the development of these models depends on the masses of the stars and on the semimajor axis ratio betwee...

We review the orbital stability of the planar circular restricted three-body problem, in the case of massless particles initially located between both massive bodies. We present new estimates of the resonance overlap criterion and the Hill stability limit, and compare their predictions with detailed dynamical maps constructed with N-body simulation...

We present a series of numerical integrations of observed and fictitious Jupiter Trojan asteroids, under the gravitational effects of the four outer planets, for time-spans comparable with the age of the Solar System. From these results we calculate the escape rate from each Lagrange point, and construct dynamical maps of “permanence” time in diffe...

HD 82943 hosts a mysterious multi-planet system in the 2:1 mean-motion resonance that puzzles astronomers for more than a decade. We describe our new analysis of all radial velocity data currently available for this star, including both the most recent Keck data and the older but more numerous ELODIE measurements. Here we pay a major attention to t...

Hot Jupiters (HJs) are usually defined as giant Jovian-size planets with orbital periods $P \le 10$ days. Although they lie close to the star, several have finite eccentricities and significant misalignment angle with respect to the stellar equator. Two mechanisms have been proposed to explain the excited and misaligned sub-population of HJs: Lidov...

We study the capture and crossing probabilities into the 3:1 mean motion resonance with Jupiter for a small asteroid that migrates from the inner to the middle Main Belt under the action of the Yarkovsky effect. We use an algebraic mapping of the averaged planar restricted three-body problem based on the symplectic mapping of Hadjidemetriou (1993),...

We carry out a new analysis of the published radial velocity data for the planet-hosting star HD 82943. We include the recent Keck/HIRES measurements as well as the aged but much more numerous CORALIE data. We find that the CORALIE radial velocity measurements are polluted by a systematic annual variation which affected the robustness of many previ...

We present an algebraic map (MAMA) for the dynamical and collisional evolution of a planetesimal swarm orbiting the main star of a tight binary system. The orbital evolution of each planetesimal is dictated by the secular perturbations of the secondary star and gas drag due to interactions with a protoplanetary disc. The gas disc is assumed eccentr...

In this paper we revise the model proposed by Rein et al. (2010) for the origin of the HD45364 exoplanetary system, currently known to host two planets close to the 3/2 mean-motion commensurability (MMR). We show that, due to high surface density of the protoplanetary disk needed for Type III migration, this model could only lead to planets in a qu...

The existence of multiple planetary systems involved in mean motion conmensurabilities has increased significantly since the Kepler mission. Although most correspond to 2-planet resonances, multiple resonances have also been found. The Laplace resonance is a particular case of a three-body resonance where the period ratio between consecutive pairs...

We analyze the distribution of extrasolar planets (both confirmed and Kepler candidates) according to their orbital periods P and planetary radii R. Among confirmed planets, we find compelling evidence for a paucity of bodies with 3 R ⊕ < R < 10 R ⊕, where R ⊕ is Earth's radius and P < 2-3 days. We have christened this region a sub-Jovian Pampas. T...

20 years after the discovery of the first planets outside our solar system, the current exoplanetary population includes more than 700 confirmed planets around main sequence stars. Approximately 50% belong to multiple-planet systems in very diverse dynamical configurations, from two-planet hierarchical systems to multiple resonances that could only...

In the last years several exoplanets have been discovered that orbit one component of a compact binary system (separation < 50 astronomical units), the probably best-known case is gamma-Cephei. So far, all attempts to explain the in-situ formation of these planets has been unsuccessful, in part because of the strong gravitational perturbations of t...

We present the dynamical structure of the phase space of the planar planetary 2/1 mean-motion resonance (MMR). Inside the resonant domain, there exist two families of periodic orbits, one associated to the librational motion of the critical angle ($\sigma$-family) and the other related to the circulatory motion of the angle between the pericentres...

We analyze the possibilities of detection of hypothetical exoplanets in coorbital motion from synthetic radial velocity (RV) signals, taking into account different types of stable planar configurations, orbital eccentricities and mass ratios. For each nominal solution corresponding to small-amplitude oscillations around the periodic solution, we ge...

Exoplanets show a pile-up of Jupiter-size planets in orbits with a 3-day period. A fraction of these hot Jupiters have retrograde orbits with respect to the parent star's rotation. To explain these observations we performed a series of numerical integrations of planet scattering followed by the tidal circularization. We considered planetary systems...

The motion of two planets around a Sun-like star under the combined effects of mutual interaction and tidal dissipation is investigated. The secular behaviour of the system is analysed using two different approaches. First, we solve the exact equations of motion through the numerical simulation of the system evolution. In addition to the orbital de...

This investigation uses the excellent HARPS radial velocity measurements of CoRoT-7 to re-determine the planet masses and to explore techniques able to determine mass and elements of planets discovered around active stars when the relative variation of the radial velocity due to the star activity cannot be considered as just noise and can exceed th...

The secular dynamics of small planetesimals in tight binary systems play a fundamental role in establishing the possibility of accretional collisions in such extreme cases. The most important secular parameters are the forced eccentricity and secular frequency, which depend on the initial conditions of the particles, as well as on the mass and orbi...

The lower limit to the distribution of orbital periods P for the current population of close-in exoplanets shows a distinctive discontinuity located at approximately one Jovian mass. Most smaller planets have orbital periods longer than P~2.5 days, while higher masses are found down to P~1 day. We analyze whether this observed mass-period distribut...

We review some recent results on the long term dynamical evolution of V- type asteroids that point to their origin as fugitives from the Vesta family. Three scenarios are explored: (i) interplay of weak mean motion and non linear secular resonances in the inner Belt with the Yarkovsky effect, (ii) crossing of the 3:1 mean motion resonance with Jupi...

The meeting began at 11:00 am with a brief address by outgoing president Burns highlighting the most relevant advances in Celestial Mechanics that occurred in the last 3 years.

We analyse the dynamics of individual kilometre-size planetesimals in circumstellar orbits of a tight binary system. We include both the gravitational perturbations of the secondary star and a non-linear gas drag stemming from an eccentric gas disc with a finite precession rate. We consider several precession rates and eccentricities for the gas, a...

We investigate the motion of a two-planet coplanar system under the combined effects of mutual interaction and tidal dissipation. The secular behavior of the system is analyzed using two different approaches, restricting to the case of a more massive outer planet. First, we solve the exact equations of motion through the numerical simulation of the...

While recent simulations of the accretion of planetesimals in circumprimary disks in moderately close binary star systems point to the inefficiency of the growth of these objects to larger bodies, the detection of planets around the primaries of binary systems with stellar separation smaller than 20 AU, suggests that planet formation in such binari...

CoRoT-7b was the first super-Earth for which mass and radius have been determined and is one paradigm for the study of the physics of hot-super-Earths fixing constraints to models of their formation and evolution. It is thus important to have good radius and mass determinations. The radius determination from the transits observed by the space teles...

We study the stability regions and families of periodic orbits of two planets locked in a co-orbital configuration. We consider different ratios of planetary masses and orbital eccentricities; we also assume that both planets share the same orbital plane. Initially, we perform numerical simulations over a grid of osculating initial conditions to ma...

Constructing dynamical maps from the filtered output of numerical integrations, we analyse the structure of the ν⊙ secular resonance for fictitious irregular satellites in retrograde orbits. This commensurability is associated with the secular angle θ=ϖ−ϖ⊙, where ϖ is the longitude of the pericentre of the satellite and ϖ⊙ corresponds to the (fixed...

In this paper we present an analytical solution for the tidal equations de- veloped by Ferraz-Mello et al. (2008) when the orbital inclination is zero (ie: orbital plane coincide with both ecuator). In particular, we analize the equations governing the evolution of the semimajor axis and eccentricity of a close-in planet. We characterize the timesc...

This chapter is a review of the dynamics of two-planet systems. It includes the study of averaged models of both secular and resonant planetary configurations. The introduction describes our understanding of long-term planetary behavior and stability. The next section introduces the presently known sample of 31 extra-solar systems and the classific...

The interplay of the disc and the dark halo resonances governs the secular evolution of disc galaxies, and the properties of their bar component (Athanassoula 2002). Martinez-Valpuesta et al. (2006), Ceverino & Klypin (2007) and Athanassoula (2007b) confirm and extend this work. Ceverino & Klypin (2007) calculate the orbital frequencies of each par...

The Transit Timing Variation (TTV) method relies on monitoring changes in timing of transits of known exoplanets. Non-transiting planets in the system can be inferred from TTVs by their gravitational interaction with the transiting planet. The TTV method is sensitive to low-mass planets that cannot be detected by other means. Here we describe a fas...

Constructing dynamical maps from the filtered output of numerical integrations, we analyze the structure of the $\nu_\odot$ secular resonance for fictitious irregular satellites in retrograde orbits. This commensurability is associated to the secular angle $\theta = \varpi - \varpi_\odot$, where $\varpi$ is the longitude of pericenter of the satell...

We estimate the conditions for detectability of two planets in a 2/1 mean-motion resonance from radial velocity data, as a function of their masses, number of observations and the signal-to-noise ratio. Even for a data set of the order of 100 observations and standard deviations of the order of a few meters per second, we find that Jovian-size reso...

The published orbits of the planets HD 82943b and HD 82943c correspond to a system bound to a catastrophic event in less than 100,000 yr. Alternative sets of elements and masses, which fit the available observational data and correspond to regular motions, are presented in this paper. The planets HD 82943c and b are in a 2 : 1 mean-motion resonance...

This paper presents the second part in our study of the global structure of the planar phase space of the planetary three-body problem, when both planets lie in the vicinity of a 2/1 mean-motion resonance. While Paper I was devoted to cases where the outer planet is the more massive body, the present work is devoted to the cases where the more mass...