Refining the Transit-timing and Photometric Analysis of TRAPPIST-1: Masses, Radii, Densities, Dynamics, and Ephemerides

Abstract

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.

Waterworlds Probably Do Not Experience Magmatic Outgassing

“…Results for Trappist-1e and Trappist-1h are similar and shown in Appendix B. These results are broadly consistent with those in Agol et al (2021) and we provide an explicit comparison in Appendix B. It was necessary to repeat these internal structure calculations to self-consistently calculate seafloor pressure as a function of iron and water mass fractions.…”

“…To explore the implications of these outgassing calculations for the Trappist-1 system, we estimated the implied ocean depth and seafloor pressures for the Trappist-1 planets using mass and radius constraints (Agol et al 2021) and a modified In the case of the CO 2 rich melt (a), a pressure overburden more than 0.7 GPa will inhibit outgassing of all volatiles, whereas in the case of a lower CO 2 content melt (b), this cutoff is around 0.1 GPa. Full details of outgassing calculations are provided in Wogan et al (2020).…”

“…Figure 3 shows the inferred pressure at the silicate-water interface based on mass and radius constraints in Agol et al (2021). Separate probability distributions are shown assuming iron core fractions of 10%-20%, 20%-30%, 30%-40%, and 40%-50%.…”

“…Inner Trappist-1 planets are not considered because they are within the runaway greenhouse limit, and any surface water would become an extended steam atmosphere. However, thick steam atmospheres are unlikely for the Trappist-1 inner planets based on current mass-radius constraints (Turbet et al 2019;Agol et al 2021).…”

“…Indeed, preliminary mass constraints of the Trappist-1 planets suggested that they may all be volatile-rich (Grimm et al 2018;Unterborn et al 2018). Updated mass constraints show volatiles may not be required to explain their relatively low densities if iron fractions are also low, but the volatile enrichment remains a possibility for the outer planets: 1e, 1f, 1g, and 1h (Agol et al 2021). Evaluating the capacity for volatile cycling between the atmosphere and interior will be crucial for interpreting future spectroscopic observations of waterworld atmospheres, and for interpreting any potential biosignature gases.…”