We have collected transit times for the TRAPPIST-1 system with the Spitzer Space Telescope over four years. We add to these ground-based, HST, and K2 transit-time measurements, and revisit an N-body dynamical analysis of the seven-planet system using our complete set of times from which we refine the mass ratios of the planets to the star. We next carry out a photodynamical analysis of the Spitzer light curves to derive the density of the host star and the planet densities. We find that all seven planets’ densities may be described with a single rocky mass–radius relation which is depleted in iron relative to Earth, with Fe 21 wt% versus 32 wt% for Earth, and otherwise Earth-like in composition. Alternatively, the planets may have an Earth-like composition but enhanced in light elements, such as a surface water layer or a core-free structure with oxidized iron in the mantle. We measure planet masses to a precision of 3%–5%, equivalent to a radial-velocity (RV) precision of 2.5 cm s−1, or two orders of magnitude more precise than current RV capabilities. We find the eccentricities of the planets are very small, the orbits are extremely coplanar, and the system is stable on 10 Myr timescales. We find evidence of infrequent timing outliers, which we cannot explain with an eighth planet; we instead account for the outliers using a robust likelihood function. We forecast JWST timing observations and speculate on possible implications of the planet densities for the formation, migration, and evolution of the planet system.

The existence of a radius valley in the Kepler size distribution stands as one of the most important observational constraints to understand the origin and composition of exoplanets with radii between those of Earth and Neptune. In this work we provide insights into the existence of the radius valley, first from a pure formation point of view and then from a combined formation-evolution model. We run global planet formation simulations including the evolution of dust by coagulation, drift, and fragmentation, and the evolution of the gaseous disc by viscous accretion and photoevaporation. A planet grows from a moon-mass embryo by either silicate or icy pebble accretion, depending on its position with respect to the water ice line. We include gas accretion, type I–II migration, and photoevaporation driven mass-loss after formation. We perform an extensive parameter study evaluating a wide range of disc properties and initial locations of the embryo. We find that due to the change in dust properties at the water ice line, rocky cores form typically with ∼3 M⊕ and have a maximum mass of ∼5 M⊕, while icy cores peak at ∼10 M⊕, with masses lower than 5 M⊕ being scarce. When neglecting the gaseous envelope, the formed rocky and icy cores account naturally for the two peaks of the Kepler size distribution. The presence of massive envelopes yields planets more massive than ∼10 M⊕ with radii above 4 R⊕. While the first peak of the Kepler size distribution is undoubtedly populated by bare rocky cores, as shown extensively in the past, the second peak can host half-rock–half-water planets with thin or non-existent H-He atmospheres, as suggested by a few previous studies. Some additional mechanisms inhibiting gas accretion or promoting envelope mass-loss should operate at short orbital periods to explain the presence of ∼10–40 M⊕ planets falling in the second peak of the size distribution.

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.

Context. Water is one of the key chemical elements in planetary structure modelling. Due to its complex phase diagram, equations of state often only cover parts of the pressure-temperature space needed in planetary modelling. Aims. We aim to construct an equation of state of H2O spanning a very wide range, from 0.1 Pa to 400 TPa and 150 to 105 K, which can be used to model the interior of planets. Methods. We combined equations of state valid in localised regions to form a continuous equation of state spanning over the above-mentioned pressure and temperature range. Results. We provide tabulated values for the most important thermodynamic quantities: the density, adiabatic temperature gradient, entropy, internal energy, and bulk speed of sound of water over this pressure and temperature range. For better usability we also calculated density-temperature and density-internal energy grids. We discuss further the impact of this equation of state on the mass radius relation of planets compared to other popular equations of state like ANEOS and QEOS. Conclusions. AQUA is a combination of existing equations of state useful for planetary models. We show that, in most regions, AQUA is a thermodynamic consistent description of water. At pressures above 10 GPa, AQUA predicts systematic larger densities than ANEOS or QEOS. This is a feature that was already present in a previously proposed equation of state, which is the main underlying equation of this work. We show that the choice of the equation of state can have a large impact on the mass-radius relation, which highlights the importance of future developments in the field of equations of state and regarding experimental data of water at high pressures.

Parameters Values Star ν 2 Lupi Effective temperature, T eff (K) 5664 ± 61 Log surface gravity, log g (cgs) 4.39 ± 0.11 Microturbulence, ξ t (km/s) 0.85 ± 0.02 Metallicity, [M/H] (dex) −0.24 ± 0.05 Radius, R (R ) 1.058 ± 0.019 Mass, M (M ) 0.87 ± 0.04 Density, ρ (ρ ) 0.734 ± 0.053 Age (Gyr) 12.3 +1.2 −2.9 Rotation period, a P rot (days) 23.8 ± 3.1 Luminosity, L (L ) 1.038 ± 0.059 Planets b c d Orbital period, P (days) 11.57797 +0.00008 −0.00013 27.59221 ± 0.00011 107.245 ± 0.050 Mid-transit time, T 0 (BJD TDB − 2, 450, 000) 8944.3726 +0.