The true masses of radial-velocity exoplanets constrained by stability

Abstract

Exoplanets discovered with the radial velocity method suffer from a mass-inclination degeneracy: only the minimum mass $M_{\rm min} = M \sin i$ is measured. An exoplanet with an Earth-sized minimum mass could actually therefore be a sub-Neptune, or even a gas giant. However, for compact multi-planet systems, the inclination angle cannot be too low, as this would imply masses so large that the system would be dynamically unstable on time-scales shorter than the age of the system. We present CINEMAS, a Bayesian framework to constrain the inclinations - and hence true masses - of radial-velocity exoplanets in flat multi-planet systems, by accounting for dynamical stability. Applying this framework to five compact exoplanetary systems, we cut upper limits on the true masses of their planets by as much as 45%. As two examples, the masses of the four Barnard's Star planets are constrained to all be below $0.6~M_{\oplus}$ to at least 95% confidence; and the three gas giants orbiting HD 184010 are found to be intermediate in mass between Saturn and Jupiter. With only ~1% of planetary systems being inclined enough to transit, methods of studying non-transiting systems are vital for constraining the properties of nearby exoplanets.