DETERMINING THE MASS OF KEPLER-78b WITH NONPARAMETRIC GAUSSIAN PROCESS ESTIMATION

By S. Grunblatt, Andrew W. Howard, R. Haywood. 2015

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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.

Subfields: Astronomy and Astrophysics, Instrumentation

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Citations in the corpus

STELLAR AND PLANETARY PROPERTIES OF K2 CAMPAIGN 1 CANDIDATES AND VALIDATION OF 17 PLANETS, INCLUDING A PLANET RECEIVING EARTH-LIKE INSOLATION (2015, methodology): “A better strategy is to simultaneously fit both the signal and the systematics, as is common practice in cosmology and, increasingly, in radial velocity searches for planetary systems (e.g., Ferreira & Jaffe 2000; Boisse et al. 2011; Haywood et al. 2014; Grunblatt et al. 2015).”
Limits on Planetary Companions from Doppler Surveys of Nearby Stars (2016, methodology): “…groups are developing techniques to suppress stellar activity including modeling magnetic activity with time-series methods (Haywood et al. 2014; Grunblatt et al. 2015), identification and removal of photospheric signals (Hébrard et al. 2014), and Bayesian methods to identify noise by its…”