New ephemerides and detection of transit-timing variations in the K2-138 system using high-precision CHEOPS photometry

Multi-planet systems are a perfect laboratory for constraining planetary formation models. A few of these systems present planets that come very close to mean motion resonance, potentially leading to significant transit-timing variations (TTVs) due to their gravitational interactions. Of these systems, K2-138 represents a excellent laboratory for studying the dynamics of its six small planets (with radii ranging between $\sim1.5$ -- $3.3 R_\oplus$), as the five innermost planets are in a near 3:2 resonant chain. In this work, we aim to constrain the orbital properties of the six planets in the K2-138 system by monitoring their transits with CHaracterising ExOPlanets Satellite (CHEOPS). We also seek to use this new data to lead a TTV study on this system. We obtained twelve light curves of the system with transits of planets $d$, $e$, $f,$ and $g$. With these data, we were able to update the ephemerides of the transits for these planets and search for timing transit variations. With our measurements, we reduced the uncertainties in the orbital periods of the studied planets, typically by an order of magnitude. This allowed us to correct for large deviations, on the order of hours, in the transit times predicted by previous studies. This is key to enabling future reliable observations of the planetary transits in the system. We also highlight the presence of potential TTVs ranging from 10 minutes to as many as 60 minutes for planet $d$.