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Published August 1, 2015 | Published + Submitted
Journal Article Open

Determining the Mass of Kepler-78b With Nonparametric Gaussian Process Estimation

Abstract

Kepler-78b is a transiting planet that is 1.2 times the radius of Earth and orbits a young, active K dwarf every 8 hr. The mass of Kepler-78b has been independently reported by two teams based on radial velocity (RV) measurements using the HIRES and HARPS-N spectrographs. Due to the active nature of the host star, a stellar activity model is required to distinguish and isolate the planetary signal in RV data. Whereas previous studies tested parametric stellar activity models, we modeled this system using nonparametric Gaussian process (GP) regression. We produced a GP regression of relevant Kepler photometry. We then use the posterior parameter distribution for our photometric fit as a prior for our simultaneous GP + Keplerian orbit models of the RV data sets. We tested three simple kernel functions for our GP regressions. Based on a Bayesian likelihood analysis, we selected a quasi-periodic kernel model with GP hyperparameters coupled between the two RV data sets, giving a Doppler amplitude of 1.86 ± 0.25 m s^(−1) and supporting our belief that the correlated noise we are modeling is astrophysical. The corresponding mass of 1.87_(-0.26)^(+0.27) M_⨁ is consistent with that measured in previous studies, and more robust due to our nonparametric signal estimation. Based on our mass and the radius measurement from transit photometry, Kepler-78b has a bulk density of 6.0_(-1.4)^(+1.9) g cm^(−3). We estimate that Kepler-78b is 32% ± 26% iron using a two-component rock-iron model. This is consistent with an Earth-like composition, with uncertainty spanning Moon-like to Mercury-like compositions.

Additional Information

© 2015 American Astronomical Society. Received 2014 December 19. Accepted 2015 June 16. Published 2015 July 27. We thank the anonymous referee for suggestions. We also thank Suzanne Aigrain, B. J. Fulton, Conor McPartland, and Maxwell Service for helpful discussions. A.W.H. acknowledges NASA grant NNX12AJ23G. We gratefully acknowledge the efforts and dedication of the Keck Observatory staff and extend special thanks to those of Hawaiian ancestry on whose sacred mountain of Mauna Kea we are privileged to be guests. Without their generous hospitality, the Keck observations presented herein would not have been possible.

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Published - Grunblatt_2015_ApJ_808_127.pdf

Submitted - 1501.00369.pdf

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