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

TL;DR

This paper introduces a comprehensive statistical model for Kepler star flux data that accounts for non-Gaussian noise, star variability, and planetary transits, improving signal extraction and parameter estimation.

Contribution

It develops a joint modeling approach combining non-Gaussian noise distribution, Gaussian process star variability analysis, and joint optimization of all parameters for Kepler data.

Findings

Better match to star variability than spline methods

Robust handling of noise outliers

More accurate planet radius estimates

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.