Stellar scattering and the origin of the planet around gamma-cephei-A

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 the secondary star on any initial planetesimal swarm. Here we test whether planetary bodies in compact binaries, in particular gamma-Cephei, could have originated from a close encounter with a passing star, assuming initial configurations for the stellar system suitable for planetary formation. In other words, we analyze whether the orbital configuration of the current binary system might have been generated after the formation of the planet, and as a consequence of a close encounter with a third star in hyperbolic orbit. We performed a series of time-reverse N-body simulations of stellar scattering events in which the present-day configuration of gamma-Cephei was used as the initial condition plus a hypothetical third star as an impactor. We analyzed which configurations and system parameters could have given birth to the current system. Depending on the maximum impact velocity allowed for accretional collisions, we find that between 1% and 5% of stellar encounters correspond to an "original" system in which planetary formation around the primary star is not inhibited by the secondary, but is acceptable within the classical core-accretion scenario. Thus, although not highly probable, it is plausible that stellar encounters may have played a significant role in shaping these types of exoplanetary systems.Comment: 9 pages, 6 figures, 3 table

Semianalytical model for planetary resonances: Application to planets around single and binary stars

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, location and stability of fixed points, and periods of small-amplitude librations. The model is valid for any two gravitationally interacting massive bodies, and is thus applicable to planets around single or binary stars. Methods. Using a theoretical framework in the Poincaré and Jacobi reference system, we developed a semianalytical method that employs a numerical evaluation of the averaged resonant disturbing function. Validations of the model are presented that compare its predictions with dynamical maps for real and fictitious systems. Results. The model describes many dynamical features of planetary resonances very well. Notwithstanding the good agreement found in all cases, a small deviation is noted in the location of the resonance centers for circumbinary systems. As a consequence of its application to the HD 31527 system, we found that the updated best-fit solution leads to a high-eccentricity stable libration between the middle and outer planets inside the 16/3 mean-motion resonance (MMR). This is the first planetary system whose long-term dynamics appears dominated by such a high-order commensurability. In the case of circumbinary planets, the overlap of N/1 mean-motion resonances coincides very well with the size of the global chaotic region close to the binary, as well as its dependence on the mutual inclination.Fil: Gallardo, Tabaré. Universidad de la República; UruguayFil: Beauge, Cristian. Observatorio Astronomico de la Universidad Nacional de Cordoba; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Instituto de Astronomía Teórica y Experimental. Universidad Nacional de Córdoba. Observatorio Astronómico de Córdoba. Instituto de Astronomía Teórica y Experimental; ArgentinaFil: Giuppone, Cristian Andrés. Observatorio Astronomico de la Universidad Nacional de Cordoba; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Instituto de Astronomía Teórica y Experimental. Universidad Nacional de Córdoba. Observatorio Astronómico de Córdoba. Instituto de Astronomía Teórica y Experimental; Argentin

Tidal evolution of circumbinary systems with arbitrary eccentricities: Applications for Kepler systems

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 governing the spin and orbital evolution, which are expressed as high-order elliptical expansions in the semimajor axis ratio but retain closed form in terms of the binary and planetary eccentricities. These are found to reproduce the results of the numerical simulations with arbitrary eccentricities very well, as well as reducing to our previous results in the low-eccentric case. Our model is then applied to the well-characterised Kepler circumbinary systems by analysing the tidal timescales and unveiling the tidal flow around each different system. In all cases we find that the spins reach stationary values much faster than the characteristic timescale of the orbital evolution, indicating that all Kepler circumbinary planets are expected to be in a sub-synchronous state. On the other hand, all systems are located in a tidal flow leading to outward migration; thus the proximity of the planets to the orbital instability limit may have been even greater in the past. Additionally, Kepler systems may have suffered a significant tidally induced eccentricity damping, which may be related to their proximity to the capture eccentricity. To help understand the predictions of our model, we also offer a simple geometrical interpretation of our results.Fil: Zoppetti, Federico Andrés. Universidad Nacional de Córdoba. Observatorio Astronómico de Córdoba; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Instituto de Astronomía Teórica y Experimental. Universidad Nacional de Córdoba. Observatorio Astronómico de Córdoba. Instituto de Astronomía Teórica y Experimental; ArgentinaFil: Leiva, A. M.. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Instituto de Astronomía Teórica y Experimental. Universidad Nacional de Córdoba. Observatorio Astronómico de Córdoba. Instituto de Astronomía Teórica y Experimental; ArgentinaFil: Beauge, Cristian. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Instituto de Astronomía Teórica y Experimental. Universidad Nacional de Córdoba. Observatorio Astronómico de Córdoba. Instituto de Astronomía Teórica y Experimental; Argentin

A new scenario for the origin of the 3/2 resonant system HD 45364

We revise the model for the origin of the HD 45364 exoplanetary system proposed by Rein et al. (2010, A&A, 510, A4), which is currently known to host two planets close to the 3/2 mean-motion resonance (MMR). We show that due to the high surface density of the protoplanetary disk needed for type III migration, this model can only lead to planets in a quasi-resonant regime of motion and thus is not consistent with the resonant configuration obtained by Correia et al. (2009, A&A, 496, 521). Although both resonant and quasi-resonant solutions are statistically indistinguishable with respect to radial velocity measurements, their distinct dynamical behavior is intriguing. We used the semi-analytical model to confirm the quantitative difference between two configurations. To form a system that evolves inside the 3/2 resonance, we developed a different model. Our scenario includes an interaction between different (but slower) planetary migration types, planet growth, and gap formation in the protoplanetary disk. The evolutionary path was chosen due to a detailed analysis of the phase space structure in the vicinity of the 3/2 MMR that employed dynamical mapping techniques. The outcomes of our simulations are able to very closely reproduce the 3/2 resonant dynamics obtained from the best fit presented by Correia et al. In addition, by varying the strength of the eccentricity damping, we can also simulate the quasi-resonant configuration similar to that reported in Rein et al. We furthermore show that our scenario is reliable with respect to the physical parameters involved in the resonance-trapping process. However, our scenario can only be confirmed with additional radial velocities measurements.Fil: Correa Otto, J. A.. Universidade do Sao Paulo. Instituto Astronomia, Geofisica e Ciencias Atmosfericas; Brasil;Fil: Michtchenko, T. A.. Universidade do Sao Paulo. Instituto Astronomia, Geofisica e Ciencias Atmosfericas; Brasil;Fil: Beauge, Cristian. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico - CONICET - Córdoba. Instituto de Astronomía Teórica y Experimental; Argentina

Resonant capture and tidal evolution in circumbinary systems: Testing the case of Kepler-38

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 capture process, resonant dynamics, and tidal evolution of circumbinary planets in high-order mean-motion resonances (MMRs). Planetary migration was modelled as an external acceleration in an N-body code, while tidal effectswere incorporated with aweak-friction equilibrium tidemodel. As aworking example, we chose Kepler-38, a highly evolved system with a planet in the vicinity of the 5/1 MMR. Our simulations show that resonance capture is a high-probability event under a large range of system parameters, although several different resonant configuration are possible. We identified three possible outcomes: aligned librations, anti-aligned librations, and chaotic solutions. All were found to be dynamically stable, even after the dissipation of the disc, for time spans of the order of the system's age. We found that while tidal evolution decreases the binary's separation, the semimajor axis of the planet is driven outwards. Although the net effect is a secular increase in the mean-motion ratio, the system requires a planetary tidal parameter of the order of unity to reproduce the observed orbital configuration. The results presented here open an interesting outlook into the complex dynamics of high-order resonances in circumbinary systems.Fil: Zoppetti, Federico Andrés. Universidad Nacional de Córdoba. Observatorio Astronómico de Córdoba; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba; ArgentinaFil: Beauge, Cristian. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Instituto de Astronomía Teórica y Experimental. Universidad Nacional de Córdoba. Observatorio Astronómico de Córdoba. Instituto de Astronomía Teórica y Experimental; ArgentinaFil: Leiva, Alejandro Martín. Universidad Nacional de Córdoba. Observatorio Astronómico de Córdoba; Argentin

Resonance capture and dynamics of three-planet systems

We present a series of dynamical maps for fictitious three-planet 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 three-planet commensurabilities. These structures are then compared to the present-day orbital architecture of observed resonant chains. In a second part of the paper, we describe N-body simulations of type-I migration. Depending on the orbital decay time-scale, we show that three-planet systems may be trapped in different combinations of independent commensurabilities: (i) double resonances, (ii) intersection between a two-planet and a first-order three-planet resonances, and (iii) simultaneous libration in two first-order three-planet resonances. These latter outcomes are found for slow migrations, while double resonances are almost always the final outcome in high-density discs. Finally, we discuss an application to the TRAPPIST-1 system. We find that, for low migration rates and planetary masses of the order of the estimated values, most three-planet sub-systems are able to reach the observed double resonances after following evolutionary routes defined by pure three-planet resonances. The final orbital configuration shows resonance offsets comparable with present-day values without the need of tidal dissipation. For the 8/5 resonance proposed to dominate the dynamics of the two inner planets, we find little evidence of its dynamical significance; instead, we propose that this relation between mean motions could be a consequence of the interaction between a pure three-planet resonance and a two-planet commensurability between planets c and d.Instituto de Astrofísica de La Plat

Resonance capture and dynamics of three-planet systems

We present a series of dynamical maps for fictitious three-planet 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 three-planet commensurabilities. These structures are then compared to the present-day orbital architecture of observed resonant chains. In a second part of the paper, we describe N-body simulations of type-I migration. Depending on the orbital decay time-scale, we show that three-planet systems may be trapped in different combinations of independent commensurabilities: (i) double resonances, (ii) intersection between a two-planet and a first-order three-planet resonances, and (iii) simultaneous libration in two first-order three-planet resonances. These latter outcomes are found for slow migrations, while double resonances are almost always the final outcome in high-density discs. Finally, we discuss an application to the TRAPPIST-1 system. We find that, for low migration rates and planetary masses of the order of the estimated values, most three-planet sub-systems are able to reach the observed double resonances after following evolutionary routes defined by pure three-planet resonances. The final orbital configuration shows resonance offsets comparable with present-day values without the need of tidal dissipation. For the 8/5 resonance proposed to dominate the dynamics of the two inner planets, we find little evidence of its dynamical significance; instead, we propose that this relation between mean motions could be a consequence of the interaction between a pure three-planet resonance and a two-planet commensurability between planets c and d.Fil: Charalambous, Carolina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Instituto de Astronomía Teórica y Experimental. Universidad Nacional de Córdoba. Observatorio Astronómico de Córdoba. Instituto de Astronomía Teórica y Experimental; ArgentinaFil: Marti, Javier Guillermo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Astrofísica La Plata. Universidad Nacional de La Plata. Facultad de Ciencias Astronómicas y Geofísicas. Instituto de Astrofísica La Plata; ArgentinaFil: Beauge, Cristian. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Instituto de Astronomía Teórica y Experimental. Universidad Nacional de Córdoba. Observatorio Astronómico de Córdoba. Instituto de Astronomía Teórica y Experimental; ArgentinaFil: Ramos, Ximena Soledad. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Instituto de Astronomía Teórica y Experimental. Universidad Nacional de Córdoba. Observatorio Astronómico de Córdoba. Instituto de Astronomía Teórica y Experimental; Argentin

Conditions for Convergent Migration of N-Planet Systems

Given an N-planet system with coplanar, low eccentricity orbits, and under the effects of an external non-conservative force, we derive necessary conditions for the orbital migration to undergo global convergent migration and allow the formation of a mean-motion resonance chain. Since the conditions are expressed in terms of the time-derivatives of the semimajor axes, the method is applicable to any non-conservative force, including disk–planet interactions and tides. Although the number of possible conditions increase exponentially with the number of bodies, the calculations may be enormously simplified adopting a tree diagram for the decision process. We deduce explicit expressions for N= 3 and N= 4 together with applications to Kepler-60 and Kepler-223 assuming a simple prescription for Type-I migration and no inner disk edge. This disk model is chosen for simplicity and to highlight the applicability of the method. We also present all the necessary steps for the implementation of an algebraic tree algorithm for the general N-planet case, and discuss possible implications for the migration history of the TOI-178 and TRAPPIST-1 systems.Fil: Beauge, Cristian. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Instituto de Astronomía Teórica y Experimental. Universidad Nacional de Córdoba. Observatorio Astronómico de Córdoba. Instituto de Astronomía Teórica y Experimental; ArgentinaFil: Cerioni, Matías. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Instituto de Astronomía Teórica y Experimental. Universidad Nacional de Córdoba. Observatorio Astronómico de Córdoba. Instituto de Astronomía Teórica y Experimental; Argentin

Shannon entropy applied to the planar restricted three-body problem

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 evolution of the variance in the semimajor axis and eccentricity plane. Adopting adequate normalization factors, both methods yield comparable results, although much shorter integration times are required for entropy calculations. A second advantage of the use of entropy is that it is possible to obtain reliable results even without the use of ensembles or analysis restricted to surfaces of section or representative planes. This allows for a much more numerically efficient tool that may be incorporated into a working N-body code and applied to numerous dynamical problems in planetary dynamics. Finally, we estimate instability times for a series of initial conditions in the 2/1 and 3/2 mean-motion resonances and compare them with times of escape obtained from directed N-body simulations. We find very good agreement in all cases, not only with respect to average values but also in their dispersion for nearby trajectories.Fil: Beauge, Cristian. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Instituto de Astronomía Teórica y Experimental. Universidad Nacional de Córdoba. Observatorio Astronómico de Córdoba. Instituto de Astronomía Teórica y Experimental; ArgentinaFil: Cincotta, Pablo Miguel. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Astrofísica La Plata. Universidad Nacional de La Plata. Facultad de Ciencias Astronómicas y Geofísicas. Instituto de Astrofísica La Plata; Argentin