Photo-dynamical characterisation of the TOI-178 resonant chain. Exploring the robustness of transit-timing variations and radial velocity mass characterisations

The TOI-178 system consists of a nearby, late-K-dwarf with six transiting planets in the super-Earth to mini-Neptune regime, with radii ranging from sim 1.1 to 2.9 $R_ oplus $ and orbital periods between 1.9 and 20.7 days. All the planets, but the innermost one, form a chain of Laplace resonances. The fine-tuning and fragility of such orbital configurations ensure that no significant scattering or collision event has taken place since the formation and migration of the planets in the protoplanetary disc, thereby providing important anchors for planet formation models. We aim to improve the characterisation of the architecture of this key system and, in particular, the masses and radii of its planets. In addition, since this system is one of the few resonant chains that can be characterised by both photometry and radial velocities, we propose to use it as a test bench for the robustness of the planetary mass determination with each technique. We performed a global analysis of all the available photometry from CHEOPS, TESS and NGTS, and radial velocity from ESPRESSO, using a photo-dynamical modelling of the light curve. We also tried different sets of priors on the masses and eccentricity, as well as different stellar activity models, to study their effects on the masses estimated by transit-timing variations (TTVs) and radial velocities (RVs). We demonstrate how stellar activity prevents a robust mass estimation for the three outer planets using radial velocity data alone. We also show that our joint photo-dynamical and radial velocity analysis has resulted in a robust mass determination for planets $c$ to $g$, with precision of $ 12$ for the mass of planet $c$, and better than $10$ for planets $d$ to $g$. The new precisions on the radii range from $2$ to $3$. The understanding of this synergy between photometric and radial velocity measurements will be valuable for the PLATO mission. We also show that TOI-178 is indeed currently locked in the resonant configuration, librating around an equilibrium of the chain.