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

Grunblatt, Samuel K. and Howard, Andrew W. and Haywood, Raphaëlle D. (2015) Determining the Mass of Kepler-78b With Nonparametric Gaussian Process Estimation. Astrophysical Journal, 808 (2). Art. No. 127. ISSN 1538-4357.

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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.

Item Type:Article
Related URLs:
URLURL TypeDescription Paper
Grunblatt, Samuel K.0000-0003-4976-9980
Howard, Andrew W.0000-0001-8638-0320
Haywood, Raphaëlle D.0000-0001-9140-3574
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.
Funding AgencyGrant Number
Subject Keywords:methods: statistical; planets and satellites: detection; planets and satellites: individual (Kepler-78b) ; planets and satellites: terrestrial planets; stars: activity; starspots
Issue or Number:2
Record Number:CaltechAUTHORS:20170620-100013897
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Official Citation:Samuel K. Grunblatt et al 2015 ApJ 808 127
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:78372
Deposited By: Ruth Sustaita
Deposited On:21 Jun 2017 19:54
Last Modified:09 Mar 2020 13:18

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