Analytic estimates of the achievable precision on the physical properties of transiting planets using purely empirical measurements

Romy Rodríguez Martínez, Daniel J. Stevens, B. Scott Gaudi, Joseph G. Schulze, Wendy R. Panero, Jennifer A. Johnson, Ji Wang

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We present analytic estimates of the fractional uncertainties on the mass, radius, surface gravity, and density of a transiting planet, using only empirical or semi-empirical measurements. We first express these parameters in terms of transit photometry and radial velocity (RV) observables, as well as the stellar radius Rå, if required. In agreement with previous results, we find that, assuming a circular orbit, the surface gravity of the planet (gp) depends only on empirical transit and RV parameters, namely the planet period P, the transit depth δ, the RV semi-amplitude Kå, the transit duration T, and the ingress/egress duration τ. However, the planet mass and density depend on all these quantities, plus Rå. Thus, an inference about the planet mass, radius, and density must rely upon an external constraint such as the stellar radius. For bright stars, stellar radii can now be measured nearly empirically by using measurements of the stellar bolometric flux, the effective temperature, and the distance to the star via its parallax, with the extinction AV being the only free parameter. For any given system, there is a hierarchy of achievable precisions on the planetary parameters, such that the planetary surface gravity is more accurately measured than the density, which in turn is more accurately measured than the mass. We find that surface gravity provides a strong constraint on the core mass fraction of terrestrial planets. This is useful, given that the surface gravity may be one of the best measured properties of a terrestrial planet.

Original languageEnglish (US)
Article number84
JournalAstrophysical Journal
Issue number2
StatePublished - Apr 20 2021
Externally publishedYes

Bibliographical note

Funding Information:
We would like to thank Andrew Collier Cameron for his suggestion that the surface gravity of a transiting planet may be better constrained than its mass, radius, or density. We thank René Heller for useful discussions that improved this manuscript. We also thank the anonymous referee for careful review of this paper. R.R.M. and B.S.G. were supported by the Thomas Jefferson Chair for Space Exploration endowment from the Ohio State University. D.J.S. acknowledges funding support from the Eberly Research Fellowship from The Pennsylvania State University Eberly College of Science. The Center for Exoplanets and Habitable Worlds is supported by the Pennsylvania State University, the Eberly College of Science, and the Pennsylvania Space Grant Consortium. The results reported herein benefited from collaborations and/or information exchange within NASA’s Nexus for Exoplanet System Science (NExSS) research coordination network sponsored by NASA’s Science Mission Directorate. J.G.S. acknowledges the support of The Ohio State School of Earth Sciences through the Friends of Orton Hall research grant. W. R.P. was supported from the National Science Foundation under Grant No. EAR-1724693.

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© 2021. The American Astronomical Society. All rights reserved.


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