Measuring the Mass of Kepler-78b Using a Gaussian Process Model
Samuel K. Grunblatt, Andrew W. Howard, R. D. Haywood · arXiv (Cornell University) · 2015
Kepler-78b is a transiting planet that is 1.2 times the size of Earth and orbits a young K dwarf every 8 hours. Two teams independently reported the mass of Kepler-78b based on radial velocity measurements using the HIRES and HARPS-N spectrographs. We modeled these datasets using a nonparametric Gaussian process (GP) regression. We considered three kernel functions for our GP models to account for the quasi-periodic activity from the young host star. All three kernel functions gave consistent Doppler amplitudes. Based on a likelihood analysis, we selected a quasi-periodic kernel that gives a Doppler amplitude of 1.86 0.25 m s 1 . The mass of 1.87 +0:27 0:26 M is more precise than can be measured with either data set (a 2.5- improvement on the HIRES data). Reanalyzing only the HIRES data with a GP model, we reach a Doppler signal uncertainty equivalent with the previous study using slightly more than half of the HIRES measurements. Our GP model is the rst analysis of the RVs for this active star that accounts for continuously varying, quasi-periodic stellar activity signal. Based on our mass and the radius measurement from transit photometry, Kepler78b has a bulk density of 6.0 +1:9 1:4 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.