| Summary: | 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/sec, 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.
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