A Pair of Warm Giant Planets near the 2:1 Mean Motion Resonance around the K-dwarf Star TOI-2202*

TOI-2202 b is a transiting warm Jovian-mass planet with an orbital period of P = 11.91 days identified from the Full Frame Images data of five different sectors of the TESS mission. Ten TESS transits of TOI-2202 b combined with three follow-up light curves obtained with the CHAT robotic telescope show strong transit timing variations (TTVs) with an amplitude of about 1.2 hr. Radial velocity follow-up with FEROS, HARPS, and PFS confirms the planetary nature of the transiting candidate (a b = 0.096 ± 0.001 au, m b = 0.98 ± 0.06 M Jup), and a dynamical analysis of RVs, transit data, and TTVs points to an outer Saturn-mass companion (a c = 0.155 ± 0.002 au, m c = 0.37 ± 0.10 M Jup) near the 2:1 mean motion resonance. Our stellar modeling indicates that TOI-2202 is an early K-type star with a mass of 0.82 M ⊙, a radius of 0.79 R ⊙, and solar-like metallicity. The TOI-2202 system is very interesting because of the two warm Jovian-mass planets near the 2:1 mean motion resonance, which is a rare configuration, and their formation and dynamical evolution are still not well understood.

Revisiting The Averaged Problem in The Case of Mean-Motion Resonances of The Restricted Three-Body Problem. Global Rigorous Treatment and Application To The Co-Orbital Motion.

A classical approach to the restricted three-body problem is to analyze the dynamics of the massless body in the synodic reference frame. A different approach is represented by the perturbative treatment: in particular the averaged problem of a mean-motion resonance allows to investigate the long-term behavior of the solutions through a suitable approximation that focuses on a particular region of the phase space. In this paper, we intend to bridge a gap between the two approaches in the specific case of mean-motion resonant dynamics, establish the limit of validity of the averaged problem, and take advantage of its results in order to compute trajectories in the synodic reference frame. After the description of each approach, we develop a rigorous treatment of the averaging process, estimate the size of the transformation and prove that the averaged problem is a suitable approximation of the restricted three-body problem as long as the solutions are located outside the Hill's sphere of the secondary. In such a case, a rigorous theorem of stability over finite but large timescales can be proven. We establish that a solution of the averaged problem provides an accurate approximation of the trajectories on the synodic reference frame within a finite time that depend on the minimal distance to the Hill's sphere of the secondary. The last part of this work is devoted to the co-orbital motion (i.e., the dynamics in 1:1 mean-motion resonance) in the circular-planar case. In this case, an interpretation of the solutions of the averaged problem in the synodic reference frame is detailed and a method that allows to compute co-orbital trajectories is displayed.

On a possibility of transfer of asteroids from the 2:1 mean motion resonance with Jupiter to the Centaur zone

ABSTRACT The paper analyses possible transfers of bodies from the main asteroid belt (MBA) to the Centaur region. The orbits of asteroids in the 2:1 mean motion resonance (MMR) with Jupiter are analysed. We selected the asteroids that are in resonant orbits with e > 0.3 whose absolute magnitudes H do not exceed 16 m. The total number of the orbits amounts to 152. Numerical calculations were performed to evaluate the evolution of the orbits over 100,000-year time interval with projects for the future. Six bodies are found to have moved from the 2:1 commensurability zone to the Centaur population. The transfer time of these bodies to the Centaur zone ranges from 4,600 to 70,000 yr. Such transfers occur after orbits leave the resonance and the bodies approach Jupiter Where after reaching sufficient orbital eccentricities bodies approach a terrestrial planet, their orbits go out of the MMR. Accuracy estimations are carried out to confirm the possible asteroid transfers to the Centaur region.

Artificial neural network classification of asteroids in the M1:2 mean-motion resonance with Mars

ABSTRACT Artificial neural networks (ANNs) have been successfully used in the last years to identify patterns in astronomical images. The use of ANN in the field of asteroid dynamics has been, however, so far somewhat limited. In this work, we used for the first time ANN for the purpose of automatically identifying the behaviour of asteroid orbits affected by the M1:2 mean-motion resonance with Mars. Our model was able to perform well above 85 per cent levels for identifying images of asteroid resonant arguments in term of standard metrics like accuracy, precision, and recall, allowing to identify the orbital type of all numbered asteroids in the region. Using supervised machine learning methods, optimized through the use of genetic algorithms, we also predicted the orbital status of all multi-opposition asteroids in the area. We confirm that the M1:2 resonance mainly affects the orbits of the Massalia, Nysa, and Vesta asteroid families.

Fomalhaut b could be massive and sculpting the narrow, eccentric debris disc, if in mean-motion resonance with it

ABSTRACT The star Fomalhaut hosts a narrow, eccentric debris disc, plus a highly eccentric companion Fomalhaut b. It is often argued that Fomalhaut b cannot have significant mass, otherwise it would quickly perturb the disc. We show that material in internal mean-motion resonances with a massive, coplanar Fomalhaut b would actually be long-term stable, and occupy orbits similar to the observed debris. Furthermore, millimetre dust released in collisions between resonant bodies could reproduce the width, shape, and orientation of the observed disc. We first re-examine the possible orbits of Fomalhaut b, assuming that it moves under gravity alone. If Fomalhaut b orbits close to the disc mid-plane then its orbit crosses the disc, and the two are apsidally aligned. This alignment may hint at an ongoing dynamical interaction. Using the observationally allowed orbits, we then model the interaction between a massive Fomalhaut b and debris. While most debris is unstable in such an extreme configuration, we identify several resonant populations that remain stable for the stellar lifetime, despite crossing the orbit of Fomalhaut b. This debris occupies low-eccentricity orbits similar to the observed debris ring. These resonant bodies would have a clumpy distribution, but dust released in collisions between them would form a narrow, relatively smooth ring similar to observations. We show that if Fomalhaut b has a mass between those of Earth and Jupiter then, far from removing the observed debris, it could actually be sculpting it through resonant interactions.

Exploring the Origin and Evolution of the Kepler 36 System

We examine the origins of the Kepler 36 planetary system, which features two very different planets: Kepler 36b, ($\rm \rho = 7.46$ $\rm g$ $\rm cm^{-3}$) and Kepler 36c ($\rm \rho = 0.89$ $\rm g$ $\rm cm^{-3}$). The planets lie extremely close to one another, separated by just 0.01 AU, and they orbit just a tenth of an AU from the host star. In our origin scenario, Kepler 36b starts with far less mass than Kepler 36c, a gaseous giant planet that forms outside the ice line and quickly migrates inward, capturing its neighbour into its 2:1 mean-motion resonance while continuing to move inward through a swarm of planetesimals and protoplanets. Subsequent collisions with these smaller bodies knock Kepler 36b out of resonance and raise its mass and density (via self-compression). We find that our scenario can yield planets whose period ratio matches that of Kepler 36b and c, although these successes are rare, occurring in just 1.2 per cent of cases. However, since systems like Kepler 36 are themselves rare, this is not necessarily a drawback.

Hiding resonant planets behind a big friend

<p class="western" align="justify">The characterization of the interplay between the inner and outer parts of planetary systems has long been impractical due to the separated detection ranges of the corresponding observation techniques. However, this gap is closing thanks to the technical improvements of the instruments and the longer observational baselines, and statistical insights are already within reach on the impact of cold Jupiters on super Earths. In this talk, I would like to present a theoretical study on the influence of an external giant planet misaligned with inner resonant planets, within the circular restricted problem. The behavior of the system depends on the relative strength between the coupling of the planets and the perturbations from the outer body. We demonstrated that mean-motion resonance strengthens the inner coupling and is very resilient to the perturbation, surviving periodic relative inclination increases of tens of degrees between the inner planets. This study has applications for the indirect detection of exoplanets, as well as the understanding of their formation and evolution, in particular the role of mean-motion resonance and relative inclinations.</p>