Kepler Data Analysis: NonGaussian Noise and Fourier Gaussian Process Analysis of Stellar Variability
Abstract
We develop a statistical analysis model of Kepler stellar flux data in the presence of planet transits, nonGaussian noise, and stellar variability. We first develop a model for the Kepler noise probability distribution in the presence of outliers, which make the noise probability distribution nonGaussian. We develop a signal likelihood analysis based on this probability distribution, in which we model the signal as a sum of the star variability and planetary transits. We argue that these components need to be modeled together if optimal signal is to be extracted from the data. For the stellar variability model we develop an optimal Gaussian process analysis using a Fourierbased Wiener filter approach, where the power spectrum is nonparametric and learned from the data. We develop high dimensional optimization of the objective function, where we jointly optimize all the model parameters, including thousands of star variability modes, and planet transit parameters. We apply the method to Kepler90 data and show that it gives a better match to the stellar variability than the existing methods, and robustly handles noise outliers. As a consequence, the planet radii have a higher value than what the existing methods give, including splines and celerite.
 Publication:

The Astronomical Journal
 Pub Date:
 May 2020
 DOI:
 10.3847/15383881/ab8460
 arXiv:
 arXiv:1910.01167
 Bibcode:
 2020AJ....159..224R
 Keywords:

 Exoplanet detection methods;
 NonGaussianity;
 Astronomy data modeling;
 Exoplanet astronomy;
 Astronomy data analysis;
 489;
 1116;
 1859;
 486;
 1858;
 Astrophysics  Earth and Planetary Astrophysics
 EPrint:
 doi:10.3847/15383881/ab8460