Kepler data analysis: non-Gaussian noise and Fourier Gaussian process analysis of star variability

Abstract

We develop a statistical analysis model of Kepler star flux data in the presence of planet transits, non-Gaussian noise, and star variability. We first develop a model for Kepler noise probability distribution in the presence of outliers, which make the noise probability distribution non-Gaussian. 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 these components need to be modeled together if optimal signal is to be extracted from the data. For the star variability model we develop an optimal Gaussian process analysis using a Fourier based Wiener filter approach, where the power spectrum is non-parametric 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 Kepler-90 data and show that it gives a better match to the star variability than the standard spline method, and robustly handles noise outliers. As a consequence, the planet radii have a higher value than the standard spline method.

References in corpus (14)

• SciPy 1.0--Fundamental Algorithms for Scientific Computing in Python
• Analytic Lightcurves for Planetary Transit Searches
• Fast and scalable Gaussian process modeling with applications to astronomical time series
• Efficient, uninformative sampling of limb darkening coefficients for two-parameter laws
• A Technique for Extracting Highly Precise Photometry for the Two-Wheeled Kepler Mission
• Planetary Candidates Observed by Kepler. VIII. A Fully Automated Catalog With Measured Completeness and Reliability Based on Data Release 25
• Identifying Exoplanets with Deep Learning: A Five Planet Resonant Chain around Kepler-80 and an Eighth Planet around Kepler-90
• EVEREST: Pixel Level Decorrelation of K2 Light curves
• PyTransit: Fast and Easy Exoplanet Transit Modelling in Python
• Characterizing the Cool KOIs III. KOI-961: A Small Star with Large Proper Motion and Three Small Planets
• A uniform asteroseismic analysis of 22 solar-type stars observed by Kepler
• K2SC: Flexible systematics correction and detrending of K2 light curves using Gaussian Process regression
• Photometric Variability in Kepler Target Stars: The Sun Among Stars -- A First Look
• Aldebaran b's temperate past uncovered in planet search data

Cited by in corpus (7)

• Kepler-90: Giant transit-timing variations reveal a super-puff
• Matched filtering with non-Gaussian noise for planet transit detections
• fBLS -- a fast-folding BLS algorithm
• Self-Calibrating the Look-Elsewhere Effect: Fast Evaluation of the Statistical Significance Using Peak Heights
• Statistical significance testing for mixed priors: a combined Bayesian and frequentist analysis
• An Independent Search for Small Long-period Planets in Kepler Data I: Detection Pipeline
• Exoplanet transit search at the detection limit: detection and false alarm vetting pipeline