KeplerPresearch Data Conditioning II - A Bayesian Approach to Systematic Error Correction

Abstract

ABSTRACT. With the unprecedented photometric precision of the Kepler spacecraft, significant systematic and stochastic errors on transit signal levels are observable in the Kepler photometric data. These errors, which include discontinuities, outliers, systematic trends, and other instrumental signatures, obscure astrophysical signals. The presearch data conditioning (PDC) module of the Kepler data analysis pipeline tries to remove these errors while preserving planet transits and other astrophysically interesting signals. The completely new noise and stellar variability regime observed in Kepler data poses a significant problem to standard cotrending methods. Variable stars are often of particular astrophysical interest, so the preservation of their signals is of significant importance to the astrophysical community. We present a Bayesian maximum a posteriori (MAP) approach, where a subset of highly correlated and quiet stars is used to generate a cotrending basis vector set, which is in turn used to establish a range of "reasonable" robust fit parameters. These robust fit parameters are then used to generate a Bayesian prior and a Bayesian posterior probability distribution function (PDF) which, when maximized, finds the best fit that simultaneously removes systematic effects while reducing the signal distortion and noise injection that commonly afflicts simple least-squares (LS) fitting. A numerical and empirical approach is taken where the Bayesian prior PDFs are generated from fits to the light-curve distributions themselves.Online material: color figures AN OVERVIEW OF THE KEPLER DATA PIPELINEKepler's primary science objective is to determine the frequency of Earth-size planets transiting their Sun-like host stars in the habitable zone. 6 This daunting task demands an instrument capable of measuring the light output from each of over 100,000 stars simultaneously with an unprecedented photometric precision of 20 parts per million (ppm) at 6.5-hr intervals. The large number of stars is required because the probability of the geometrical alignment of planetary orbits that permit observation of transits is the ratio of the size of the star to the size of the planetary orbit. For Earth-like planets in 1 AU orbits about Sun-like stars, only ∼0:5% will exhibit transits. By observing such a large number of stars, Kepler is guaranteed to produce a robust result in the happy event that many Earth-size planets are detected in or near the habitable zone.The Kepler data pipeline is divided into several components in order to allow for efficient management and parallel processing of data (Jenkins 2010a). Raw pixel data downlinked from the Kepler photometer are calibrated by the calibration module (CAL) to produce calibrated target and background pixels (Quintana 2010) and their associated uncertainties (Clarke 2010). The calibrated pixels are then processed by the photometric analysis module (PA) to fit and remove sky background and extract simple aperture photometry from the backgroundcorrected, calibrated target pixel...

Rotation and differential rotation of activeKeplerstars

“…Hence, in many cases true stellar variability has been removed. The next reduction pipeline PDC-MAP 2 Smith et al 2012) removes the so-called co-trending basis vectors from the data. This pipeline removes the most common trends but keeps the stellar variability.…”

Rotation, differential rotation, and gyrochronology of activeKeplerstars

“…This pipeline was changed to the so-called PDC-MAP (Maximum A Posteriori) pipeline Smith et al 2012) because the PDC pipeline coarsely removed stellar variability signals. Recently, all Kepler data has been reprocessed by the PDC-msMAP (multiscale MAP) pipeline (Stumpe et al 2014).…”

An independent planet search in theKeplerdataset

“…Also, the very long LCs are naturally divided in to single-quarter lengths, so they are SARS-processed by quarter and channel and no division in to smaller blocks is required. Batalha et al (2013) presented two major improvements to the Kepler pipeline: improved systematic errors correction (called PDC-MAP, Smith et al 2012), and an ability to use multiple quarters in the detrending and transit search modules (Jenkins et al 2010;Tenenbaum et al 2012). These upgrades were the most significant factors in the near-doubling of the number of KOIs reported in B12.…”