Y. Alibert

Yann Alibert, Jeanne Davoult, Sara Marques

Numerical calculations of planetary system formation are very demanding in terms of computing power. These synthetic planetary systems can however provide access to correlations, as predicted in a given numerical framework, between the properties of planets in the same system. Such correlations can, in return, be used in order to guide and prioritize observational campaigns aiming at discovering some types of planets, as Earth-like planets. Our goal is to develop a generative model which is capable of capturing correlations and statistical relationships between planets in the same system. Such a model, trained on the Bern model, offers the possibility to generate large number of synthetic planetary systems with little computational cost, that can be used, for example, to guide observational campaigns. Our generative model is based on the transformer architecture which is well-known to efficiently capture correlations in sequences and is at the basis of all modern Large Language Models. To assess the validity of the generative model, we perform visual and statistical comparisons, as well as a machine learning driven tests. Finally, as a use case example, we consider the TOI-469 system, in which we aim at predicting the possible properties of planets c and d, based on the properties of planet b (the first that has been detected). We show using different comparison methods that the properties of systems generated by our model are very similar to the ones of the systems computed directly by the Bern model. We also show in the case of the TOI-469 system, that using the generative model allows to predict the properties of planets not yet observed, based on the properties of the already observed planet. We provide our model to the community on our website www.ai4exoplanets.com.

Jeanne Davoult, Romain Eltschinger, Yann Alibert

Searching for planets analogous to Earth in terms of mass and equilibrium temperature is currently the first step in the quest for habitable conditions outside our Solar System and, ultimately, the search for life in the universe. Future missions such as PLATO or LIFE will begin to detect and characterise these small, cold planets, dedicating significant observation time to them. The aim of this work is to predict which stars are most likely to host an Earth-like planet (ELP) to avoid blind searches, minimises detection times, and thus maximises the number of detections. Using a previous study on correlations between the presence of an ELP and the properties of its system, we trained a Random Forest to recognise and classify systems as 'hosting an ELP' or 'not hosting an ELP'. The Random Forest was trained and tested on populations of synthetic planetary systems derived from the Bern model, and then applied to real observed systems. The tests conducted on the machine learning (ML) model yield precision scores of up to 0.99, indicating that 99% of the systems identified by the model as having ELPs possess at least one. Among the few real observed systems that have been tested, 44 have been selected as having a high probability of hosting an ELP, and a quick study of the stability of these systems confirms that the presence of an Earth-like planet within them would leave them stable. The excellent results obtained from the tests conducted on the ML model demonstrate its ability to recognise the typical architectures of systems with or without ELPs within populations derived from the Bern model. If we assume that the Bern model adequately describes the architecture of real systems, then such a tool can prove indispensable in the search for Earth-like planets. A similar approach could be applied to other planetary system formation models to validate those predictions.

Jonas Haldemann, Victor Ksoll, Daniel Walter et al.

The characterization of an exoplanet's interior is an inverse problem, which requires statistical methods such as Bayesian inference in order to be solved. Current methods employ Markov Chain Monte Carlo (MCMC) sampling to infer the posterior probability of planetary structure parameters for a given exoplanet. These methods are time consuming since they require the calculation of a large number of planetary structure models. To speed up the inference process when characterizing an exoplanet, we propose to use conditional invertible neural networks (cINNs) to calculate the posterior probability of the internal structure parameters. cINNs are a special type of neural network which excel in solving inverse problems. We constructed a cINN using FrEIA, which was then trained on a database of $5.6\cdot 10^6$ internal structure models to recover the inverse mapping between internal structure parameters and observable features (i.e., planetary mass, planetary radius and composition of the host star). The cINN method was compared to a Metropolis-Hastings MCMC. For that 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 of the internal structure parameters from both methods are very similar, with the biggest differences seen in the exoplanet's water content. Thus cINNs are a possible alternative to the standard time-consuming sampling methods. Indeed, using cINNs allows for orders of magnitude faster inference of an exoplanet's composition than what is possible using an MCMC method, however, it still requires the computation of a large database of internal structures to train the cINN. Since this database is only computed once, we found that using a cINN is more efficient than an MCMC, when more than 10 exoplanets are characterized using the same cINN.

A. Leleu, J. -B. Delisle, R. Mardling et al.

Transit Timing Variations (TTVs) can provide useful information for systems observed by transit, by putting constraints on the masses and eccentricities of the observed planets, or even constrain the existence of non-transiting companions. However, TTVs can also prevent the detection of small planets in transit surveys, or bias the recovered planetary and transit parameters. Here we show that Kepler-1972 c, initially the "not transit-like" false positive KOI-3184.02, is an Earth-sized planet whose orbit is perturbed by Kepler-1972 b (initially KOI-3184.01). The pair is locked in a 3:2 Mean-motion resonance, each planet displaying TTVs of more than 6h hours of amplitude over the duration of the Kepler mission. The two planets have similar masses $m_b/m_c =0.956_{-0.051}^{+0.056}$ and radii $R_b=0.802_{-0.041}^{+0.042}R_{Earth}$, $R_c=0.868_{-0.050}^{+0.051}R_{Earth}$, and the whole system, including the inner candidate KOI-3184.03, appear to be coplanar. Despite the faintness of the signals (SNR of 1.35 for each transit of Kepler-1972 b and 1.10 for Kepler-1972 c), we recovered the transits of the planets using the RIVERS method, based on the recognition of the tracks of planets in river diagrams using machine learning, and a photo-dynamic fit of the lightcurve. Recovering the correct ephemerides of the planets is essential to have a complete picture of the observed planetary systems. In particular, we show that in Kepler-1972, not taking into account planet-planet interactions yields an error of $\sim 30\%$ on the radii of planets b and c, in addition to generating in-transit scatter, which leads to mistake KOI3184.02 for a false positive. Alleviating this bias is essential for an unbiased view of Kepler systems, some of the TESS stars, and the upcoming PLATO mission.

A. Leleu, G. Chatel, S. Udry et al.

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. 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. Recovering this type of object is essential for obtaining a complete picture of the observed planetary systems, and solving for a bias not often taken into account in statistical studies of exoplanet populations. In addition, TTVs are a means of obtaining mass estimates which can be essential for studying the internal structure of planets discovered by transit surveys. Finally, we show that due to the strong orbital perturbations, it is possible that the spin of the outer resonant planet of Kepler-1705 is trapped in a sub- or super-synchronous spin-orbit resonance.