Rosemary A. Mardling

Pavan Vynatheya, Adrian S. Hamers, Rosemary A. Mardling et al.

We present two approaches to determine the dynamical stability of a hierarchical triple-star system. The first is an improvement on the Mardling-Aarseth stability formula from 2001, where we introduce a dependence on inner orbital eccentricity and improve the dependence on mutual orbital inclination. The second involves a machine learning approach, where we use a multilayer perceptron (MLP) to classify triple-star systems as `stable' and `unstable'. To achieve this, we generate a large training data set of 10^6 hierarchical triples using the N-body code MSTAR. Both our approaches perform better than previous stability criteria, with the MLP model performing the best. The improved stability formula and the machine learning model have overall classification accuracies of 93 % and 95 % respectively. Our MLP model, which accurately predicts the stability of any hierarchical triple-star system within the parameter ranges studied with almost no computation required, is publicly available on Github in the form of an easy-to-use Python script.

Pavan Vynatheya, Rosemary A. Mardling, Adrian S. Hamers

The dynamical stability of quadruple-star systems has traditionally been treated as a problem involving two `nested' triples which constitute a quadruple. In this novel study, we employed a machine learning algorithm, the multi-layer perceptron (MLP), to directly classify 2+2 and 3+1 quadruples based on their stability (or long-term boundedness). The training data sets for the classification, comprised of $5\times10^5$ quadruples each, were integrated using the highly accurate direct $N$-body code MSTAR. We also carried out a limited parameter space study of zero-inclination systems to directly compare quadruples to triples. We found that both our quadruple MLP models perform better than a `nested' triple MLP approach, which is especially significant for 3+1 quadruples. The classification accuracies for the 2+2 MLP and 3+1 MLP models are 94% and 93% respectively, while the scores for the `nested' triple approach are 88% and 66% respectively. This is a crucial implication for quadruple population synthesis studies. Our MLP models, which are very simple and almost instantaneous to implement, are available on GitHub, along with Python3 scripts to access them.

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.