Co-orbital planets have not yet been discovered, although they constitute a frequent by-product of planetary formation and evolution models. This lack may be due to observational biases, since the main detection methods are unable to spot co-orbital companions when they are small or near the Lagrangian equilibrium points. However, for a system with one known transiting planet (with mass m1), we can detect a co-orbital companion (with mass m2) by combining the time of mid-transit with the radial-velocity data of the star. Here, we propose a simple method that allows the detection of co-orbital companions, valid for eccentric orbits, that relies on a single parameter α, which is proportional to the mass ratio m2/m1. Therefore, when α is statistically different from zero, we have a strong candidate to harbour a co-orbital companion. We also discuss the relevance of false positives generated by different planetary configurations. © 2017 ESO.

We investigate the resonant rotation of co-orbital bodies in eccentric and planar orbits. We develop a simple analytical model to study the impact of the eccentricity and orbital perturbations on the spin dynamics. This model is relevant in the entire domain of horseshoe and tadpole orbit, for moderate eccentricities. We show that there are three different families of spin-orbit resonances, one depending on the eccentricity, one depending on the orbital libration frequency, and another depending on the pericenter's dynamics. We can estimate the width and the location of the different resonant islands in the phase space, predicting which are the more likely to capture the spin of the rotating body. In some regions of the phase space the resonant islands may overlap, giving rise to chaotic rotation.

Determining the architecture of multi-planetary systems is one of the cornerstones of understanding planet formation and evolution. Resonant systems are especially important as the fragility of their orbital configuration ensures that no significant scattering or collisional event has taken place since the earliest formation phase when the parent protoplanetary disc was still present. In this context, TOI-178 has been the subject of particular attention since the first TESS observations hinted at a 2:3:3 resonant chain. Here we report the results of observations from CHEOPS, ESPRESSO, NGTS, and SPECULOOS with the aim of deciphering the peculiar orbital architecture of the system. We show that TOI-178 harbours at least six planets in the super-Earth to mini-Neptune regimes, with radii ranging from 1.152(-0.070/+0.073) to 2.87(-0.13/+0.14) Earth radii and periods of 1.91, 3.24, 6.56, 9.96, 15.23, and 20.71 days. All planets but the innermost one form a 2:4:6:9:12 chain of Laplace resonances, and the planetary densities show important variations from planet to planet, jumping from 1.02(+0.28/-0.23) to 0.177(+0.055/-0.061) times the Earth's density between planets c and d. Using Bayesian interior structure retrieval models, we show that the amount of gas in the planets does not vary in a monotonous way, contrary to what one would expect from simple formation and evolution models and unlike other known systems in a chain of Laplace resonances. The brightness of TOI-178 allows for a precise characterisation of its orbital architecture as well as of the physical nature of the six presently known transiting planets it harbours. The peculiar orbital configuration and the diversity in average density among the planets in the system will enable the study of interior planetary structures and atmospheric evolution, providing important clues on the formation of super-Earths and mini-Neptunes.

We study the phase space of eccentric coplanar co-orbitals in the non-restricted case. Departing from the quasi-circular case, we describe the evolution of the phase space as the eccentricities increase. We find that over a given value of the eccentricity, around 0.5 for equal mass co-orbitals, important topological changes occur in the phase space. These changes lead to the emergence of new co-orbital configurations and open a continuous path between the previously distinct trojan domains near the L_4 and L_5 eccentric Lagrangian equilibria. These topological changes are shown to be linked with the reconnection of families of quasi-periodic orbits of non-maximal dimension.

We study the spin evolution of close-in planets in compact multi-planetary systems. The rotation period of these planets is often assumed to be synchronous with the orbital period due to tidal dissipation. Here we show that planet-planet perturbations can drive the spin of these planets into non-synchronous or even chaotic states. In particular, we show that the transit timing variation (TTV) is a very good probe to study the spin dynamics, since both are dominated by the perturbations of the mean longitude of the planet. We apply our model to KOI-227 b and Kepler-88 b, which are both observed undergoing strong TTVs. We also perform numerical simulations of the spin evolution of these two planets. We show that for KOI-227 b non-synchronous rotation is possible, while for Kepler-88 b the rotation can be chaotic. © ESO, 2017.

The detection of Earth-like planets, exocomets or Kuiper belts show that the different components found in the solar system should also be present in other planetary systems. Trojans are one of these components and can be considered fossils of the first stages in the life of planetary systems. Their detection in extrasolar systems would open a new scientific window to investigate formation and migration processes. In this context, the main goal of the TROY project is to detect exotrojans for the first time and to measure their occurrence rate (eta-Trojan). In this first paper, we describe the goals and methodology of the project. Additionally, we used archival radial velocity data of 46 planetary systems to place upper limits on the mass of possible trojans and investigate the presence of co-orbital planets down to several tens of Earth masses. We used archival radial velocity data of 46 close-in (P<5 days) transiting planets (without detected companions) with information from high-precision radial velocity instruments. We took advantage of the time of mid-transit and secondary eclipses (when available) to constrain the possible presence of additional objects co-orbiting the star along with the planet. This, together with a good phase coverage, breaks the degeneracy between a trojan planet signature and signals coming from additional planets or underestimated eccentricity. We identify nine systems for which the archival data provide 1-sigma evidence for a mass imbalance between L4 and L5. Two of these systems provide 2-sigma detection, but no significant detection is found among our sample. We also report upper limits to the masses at L4/L5 in all studied systems and discuss the results in the context of previous findings.

Co-orbital bodies are the byproduct of planet formation and evolution, as we know from the solar system. Although planet-size co-orbitals do not exists in our planetary system, dynamical studies show that they can remain stable for long periods of time in the gravitational well of massive planets. Should they exist, their detection is feasible with the current instrumentation. Aims. In this paper, we present new ground-based observations searching for these bodies co-orbiting with nine close-in (P < 5 days) planets, using various observing techniques. The combination of all of these techniques allows us to restrict the parameter space of any possible trojan in the system. Methods. We used multi-Technique observations, comprised of radial velocity, precision photometry, and transit timing variations, both newly acquired in the context of the TROY project and publicly available, to constrain the presence of planet-size trojans in the Lagrangian points of nine known exoplanets. Results. We find no clear evidence of trojans in these nine systems through any of the techniques used down to the precision of the observations. However, this allows us to constrain the presence of any potential trojan in the system, especially in the trojan mass or radius vs. libration amplitude plane. In particular, we can set upper mass limits in the super-Earth mass regime for six of the studied systems