  TOI-216 hosts a pair of warm, large exoplanets discovered by the TESS
Mission. These planets were found to be in or near the 2:1 resonance, and both
of them exhibit transit timing variations (TTVs). Precise characterization of
the planets' masses and radii, orbital properties, and resonant behavior can
test theories for the origins of planets orbiting close to their stars.
Previous characterization of the system using the first six sectors of TESS
data suffered from a degeneracy between planet mass and orbital eccentricity.
Radial velocity measurements using HARPS, FEROS, and PFS break that degeneracy,
and an expanded TTV baseline from TESS and an ongoing ground-based transit
observing campaign increase the precision of the mass and eccentricity
measurements. We determine that TOI-216c is a warm Jupiter, TOI-216b is an
eccentric warm Neptune, and that they librate in the 2:1 resonance with a
moderate libration amplitude of 60 +/- 2 degrees; small but significant free
eccentricity of 0.0222 +0.0005/-0.0003 for TOI-216b; and small but significant
mutual inclination of 1.2-3.9 degrees (95% confidence interval). The libration
amplitude, free eccentricity, and mutual inclination imply a disturbance of
TOI-216b before or after resonance capture, perhaps by an undetected third
planet.
