AI method: Development of an upgraded version of our DNN-based interior structure model. The full code is available on GitHub.
Paper Abstract: Multiplanetary systems spanning the radius valley are ideal testing grounds for exploring the different proposed explanations for the observed bimodality in the radius distribution of close-in exoplanets. One such system is HIP 29442 (TOI-469), an evolved K0V star hosting two super-Earths and one sub-Neptune. We observed HIP 29442 with CHEOPS for a total of 9.6 days, which we modelled jointly with two sectors of TESS data to derive planetary radii of 3.410 ± 0.046, 1.551 ± 0.045, and 1.538 ± 0.049 R⊕ for planets b, c, and d, which orbit HIP 29442 with periods of 13.6, 3.5, and 6.4 days, respectively. For planet d this value deviates by more than 3σ from the median value reported in the discovery paper, leading us to conclude that caution is required when using TESS photometry to determine the radii of small planets with low per-transit signal-to-noise ratios and large gaps between observations. Given the high precision of these new radii, combining them with published RVs from ESPRESSO and HIRES provides us with ideal conditions to investigate the internal structure and formation pathways of the planets in the system. We introduced the publicly available code plaNETic, a fast and robust neural network-based Bayesian internal structure modelling framework. We then applied hydrodynamic models to explore the upper atmospheric properties of these inferred structures. Finally, we identified planetary system analogues in a synthetic population generated with the Bern model for planet formation and evolution. Based on this analysis, we find that the planets likely formed on opposing sides of the water iceline from a protoplanetary disk with an intermediate solid mass. We finally report that the observed parameters of the HIP 29442 system are compatible with a scenario where the second peak in the bimodal radius distribution corresponds to sub-Neptunes with a pure H/He envelope and with a scenario with water-rich sub-Neptunes.
Posterior distributions of the most important internal structure parameters for HIP 29442 b. The top row shows the posteriors assuming a prior consistent with the planet forming outside the iceline, while the middle row uses a prior that is consistent with the planet forming inside the iceline. The bottom row shows the posterior distributions of the mass fractions of an inner core, mantle, condensed water layer and separately modelled H/He envelope with respect to the total planet mass when applying the previously used version of the model assuming stellar Si/Mg/Fe ratios. Adapted from Egger et al. (2024). Astronomy &Astrophysics, 688, A223 (2024).
doi:10.1051/0004-6361/202450472
AI method: A new Deep Neural Network based model is used to compute the interior structure of planets observed by transit (CHEOPS) and radial velocity instruments (ESPRESSO).
Paper Abstract: 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 the possible presence of a near 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 1.02−0.23+0.28 to 0.177−0.061+0.055 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 (H = 8.76 mag, J = 9.37 mag, V = 11.95 mag) 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.
Internal structure's parameter posterior distribution as computed by our model, for one of the planets (Planet c) of the TOI-178 resonant chain.
Adapted from Leleu et al. (2021), Astronomy & Astrophysics, Volume 649, id.A26. doi:10.1051/0004-6361/202039767
AI method: This project was developed as part of the NCCR PlanetS, in collaboration with Disaitek , under the lead of Prof. Adrien Leleu (University of Geneva). The paper presents a new technique to detect extrasolar planets in resonant pairs, using CNN and semantic segmentation models.
Paper Abstract (abridged): Transit timing variations (TTVs) can provide useful information for systems observed by transit, as they allow us to put constraints on the masses and eccentricities of the observed planets, or even to constrain the existence of non-transiting companions. However, TTVs can also act as a detection bias that can prevent the detection of small planets in transit surveys that would otherwise be detected by standard algorithms such as the Boxed Least Square algorithm (BLS) if their orbit was not perturbed. This bias is especially present for surveys with a long baseline, such as Kepler, some of the TESS sectors, and the upcoming PLATO mission. Here we introduce a detection method that is robust to large TTVs, and illustrate its use by recovering and confirming a pair of resonant super-Earths with ten-hour TTVs around Kepler-1705 (prev. KOI-4772). The method is based on a neural network trained to recover the tracks of low-signal-to-noise-ratio(S/N) perturbed planets in river diagrams. We recover the transit parameters of these candidates by fitting the light curve. The individual transit S/N of Kepler-1705b and c are about three times lower than all the previously known planets with TTVs of 3 hours or more, pushing the boundaries in the recovery of these small, dynamically active planets.
River diagram of Kepler-36 at the period 13.848d: the bottom row displays the first 13.848 days of data for Kepler-36, with the colour code representing the normalised flux. Each subsequent row displays a new set of 13.848 days of data. The flux has been clipped at 3σ for visibility, and missing data have been replaced by a flux of 1.
Adapted from Leleu et al. (2021), Astronomy & Astrophysics, Volume 655, id.A66, doi:10.1051/0004-6361/202141471
AI method: This paper is the first ever paper using Invertible Neural Networks to compute the interior structure of planets observed in transit.
Paper Abstract: The characterization of the interior of an exoplanet is an inverse problem. The solution requires statistical methods such as Bayesian inference. Current methods employ Markov chain Monte Carlo (MCMC) sampling to infer the posterior probability of the planetary structure parameters for a given exoplanet. These methods are time-consuming because they require the evaluation of a planetary structure model ~105 times. To speed up the inference process when characterizing an exoplanet, we propose to use conditional invertible neural networks to calculate the posterior probability of the planetary structure parameters.
Conditional invertible neural networks (cINNs) are a special type of neural network that excels at solving inverse problems. We constructed a cINN following the framework for easily invertible architectures (FreIA). This neural network was then trained on a database of 5.6 × 106 internal structure models to recover the inverse mapping between internal structure parameters and observable features (i.e., planetary mass, planetary radius, and elemental composition of the host star). We also show how observational uncertainties can be accounted for.
The cINN method was compared to a commonly used Metropolis-Hastings MCMC. To do this, we repeated the characterization of the exoplanet K2-111 b, using both the MCMC method and the trained cINN. We show that the inferred posterior probability distributions of the internal structure parameters from both methods are very similar; the largest differences are seen in the exoplanet water content. Thus, cINNs are a possible alternative to the standard time-consuming sampling methods. cINNs allow infering the composition of an exoplanet that is orders of magnitude faster than what is possible using an MCMC method. The computation of a large database of internal structures to train the neural network is still required, however. Because this database is only computed once, we found that using an invertible neural network is more efficient than an MCMC when more than ten exoplanets are characterized using the same neural network.
Comparison of the cINN and an MCMC method when applied to K2-111 b. The data in the lower triangle of each subfigure (blue points) was generated with the cINN method, while the data in the upper triangle (black points) was generated with the MCMC sampler. Adapted from Haldemann et al., (2023), Astronomy & Astrophysics; A&A 672, A180.
doi:10.1051/0004-6361/202243230.