Analytic Estimates of the Achievable Precision of the Properties of Transiting Exoplanets

The structure and composition of low-mass exoplanets play a fundamental role in their capacity to harbor life as we know it. However, unambiguous determination of the structure of such small planets remain a challenge both because of their immense compositional diversity and because detailed characterization of their masses through Doppler spectroscopy is difficult, and resources are limited. Although the planet’s mass and radius are perhaps the most important parameters in determining its habitability, surface gravity is also a key parameter. The surface gravity dictates the atmospheric scale height and the ability of a planet to retain a secondary atmosphere. Moreover, surface gravity may drive or hinder plate tectonics, the latter which helps regulate the planet’s climate as well as certain geological processes, at least on Earth. It is therefore vital to understand the achievable precision with which the surface gravity and other fundamental properties will be measured, and which observable parameters contribute the most to the uncertainty in those properties. We show that if we express a planet’s mass, density, radius and surface gravity in terms of only radial velocity and transit observable parameters (such as the transit depth, orbital period, transit duration, and radial velocity semi-amplitude), along with an external measurement of the host star radius from its spectral energy distribution and a precise parallax, there is a hierarchy in the precision with which each parameter can be measured for a given system. Namely, the surface gravity is generally better constrained than the density, which is in turn better constrained than the mass. The surface gravity is generally better constrained than density or mass because it does not explicitly depend on an external constraint on the host star’s radius. In addition, we demonstrate that the planet’s surface gravity and radius may be a better proxy for the core/mantle fraction of a terrestrial planet than mean density as calculated from mass and radius. The core mass fraction (CMF) is strongly linked to a planet’s internal structure and bulk composition, both critical factors for habitability at the surface. Furthermore, a more precise constraint on a planet’s CMF relative to the CMF as predicted by the chemical composition of its host star yields insights into planetary formation processes, and evolution. Potential explanations for planets that have a core that is smaller than predicted by the composition of the host star include the oxidation of a planet’s iron, and extensive incorporation of oxygen and water into a planet’s interior. These both control the nature of gasses that form a planet’s secondary atmosphere, including the development of water worlds and planets with substantial volatile envelopes.