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Kepler Presearch Data Conditioning I - Architecture and Algorithms for Error Correction in Kepler Light Curves
Martin C. Stumpe, Jeffrey C. Smith, Jeffrey E. Van Cleve, Joseph D. Twicken, Thomas S. Barclay, Michael N. Fanelli, Forrest R. Girouard, Jon M. Jenkins, Jeffery J. Kolodziejczak, Sean D. McCauliff, Robert L. Morris
TL;DR
Kepler light curves contain instrumental errors that can obscure tiny planet transits and other astrophysical signals. The paper presents a completely rewritten PDC module using Bayesian MAP cotrending and associated correction algorithms. The new PDC-MAP significantly improves correction while preserving stellar variability and astrophysical features, though direct application to short-cadence data remains constrained.
Problem
Kepler light curves contain varied systematic and stochastic errors that can obscure small planet transits and astrophysical signals, while earlier least-squares correction could remove stellar variability.
Method
The new PDC-MAP combines Bayesian Maximum A Posteriori fitting against same-channel light-curve ensembles with corrections for discontinuities, harmonics, outliers, and systematic trends.
Results
PDC-MAP significantly improves correction performance, particularly by removing systematic trends and correcting flux discontinuities while preserving stellar variability and astrophysical signals.
Takeaways & Limitations
The rewritten PDC module provides corrected Kepler light curves better suited to detecting planet transits and analyzing stellar variability.
Takeaways & Limitations
PDC-MAP cannot be applied directly as-is to short-cadence data because short-cadence data lack conditions needed to generate proper MAP priors.
Abstract
from arXiv · showhide
Kepler provides light curves of 156,000 stars with unprecedented precision. However, the raw data as they come from the spacecraft contain significant systematic and stochastic errors. These errors, which include discontinuities, systematic trends, and outliers, obscure the astrophysical signals in the light curves. To correct these errors is the task of the Presearch Data Conditioning (PDC) module of the Kepler data analysis pipeline. The original version of PDC in Kepler did not meet the extremely high performance requirements for the detection of miniscule planet transits or highly accurate analysis of stellar activity and rotation. One particular deficiency was that astrophysical features were often removed as a side-effect to removal of errors. In this paper we introduce the completely new and significantly improved version of PDC which was implemented in Kepler SOC 8.0. This new PDC version, which utilizes a Bayesian approach for removal of systematics, reliably corrects errors in the light curves while at the same time preserving planet transits and other astrophysically interesting signals. We describe the architecture and the algorithms of this new PDC module, show typical errors encountered in Kepler data, and illustrate the corrections using real light curve examples.
1. Introduction
Kepler’s high-precision, large-scale observations support Earth-size planet searches, but instrumental and local errors can obscure transits and other astrophysical signals. The new PDC module in SOC 8.0 was rewritten to correct these varied errors while preserving scientifically important light-curve features.
- 1.1. The Kepler Mission: Kepler continuously observes about 156,000 targets using 29.4-minute Long Cadence integrations to support transit detection.The spacecraft uses 42 CCDs organized into 84 module output channels.
- 1.1. The Kepler Mission: 20 ppm photometric precision is required to detect Earth-like transits, while systematic errors can occlude transit signatures and other astrophysical signals.Major error sources include focus changes, differential velocity aberration, pointing errors, vibrations, and electrical interference.
- 1.2. Kepler Science Processing Pipeline: Cotrending is part of the processing pipeline that prepares calibrated Kepler photometry for transit extraction and asteroseismological analysis.The pipeline passes data through calibration, aperture definition, photometric analysis, and subsequent processing stages.
- 1.2. Kepler Science Processing Pipeline: The SOC 8.0 PDC module completely replaces the previous version and introduces PDC-MAP, based on Bayesian Maximum A Posteriori cotrending.The paper describes its architecture, algorithms, comparisons with PDC-LS, and real light-curve examples.
- 1.3. Errors in the Light Curves: Tasks of PDC: PDC must identify and correct systematic trends, outliers, discontinuities, Argabrightenings, gaps, and flux-amplitude errors while preserving transits and astrophysical signals.These errors arise across a wide range of frequencies and amplitudes.
2.1. Cotrending of Systematic Errors in PDC
PDC-MAP replaces the older least-squares cotrending approach with Bayesian fitting against neighboring light curves, aiming to remove systematic errors while preserving stellar variability. The section describes typical error types, limitations of PDC-LS, and the architecture of the improved correction method.
- Typical errors: Typical PA light-curve errors include long trends, thermal recoveries, fast oscillations, outliers, and SPSD discontinuities.These arise from effects including differential velocity aberration, spacecraft events, reaction-wheel desaturation, and energetic-particle impacts.
- PDC-LS deficiencies: PDC-LS overfitted systematic trends and removed stellar variability, leaving many corrected light curves overly flat and featureless.The failure arose because coincidental correlations between engineering data and stellar variability were mistaken for systematic errors.
- PDC-LS deficiencies: PDC-LS could also inject high-frequency noise as an unwanted side effect of reducing bulk root-mean-square deviation.Its self-check therefore returned partially corrected light curves when noise injection was excessive.
- PDC-LS deficiencies: 15.6% of 162,926 quarter-7 targets were not cotrended because PDC-LS rejected corrections that injected too much noise.The per-channel fraction ranged from 7.7% to 25.4%.
- PDC-MAP approach: PDC-MAP uses Bayesian maximum a posteriori cotrending against correlated light curves on the same channel instead of PDC-LS fitting to ancillary engineering data.Neighborhood information constrains fit coefficients and is intended to prevent overfitting.
- PDC-MAP approach: PDC-MAP constructs basis vectors from correlated same-channel light curves and uses neighborhood-derived priors to constrain their fit coefficients.The basis vectors are obtained using singular value decomposition, while the number of vectors is an input parameter with eight as the default.
2.2. Inputs to PDC
PDC processes calibrated, uncorrected flux time series from Photometric Analysis for each CCD module output over a three-month quarter.
- PDC takes calibrated, uncorrected flux time series measured in photoelectrons as prepared by Photometric Analysis.
- Each processing unit is one CCD module output, or channel, spanning three months with 29.4-minute sampling.
- Each channel typically contains 1000–3500 targets, with about 4500 cadences per target.
- Target data include flux uncertainties, gap indicators, flux fraction, crowding metric, and bookkeeping information such as Kepler ID and KIC data.
2.3. Overview and Data Flow
PDC-MAP applies a sequential workflow that prepares Kepler light curves, temporarily corrects trends and anomalies, and then restores or refines corrections for export and downstream analysis.
- PDC-MAP’s data flow is organized as sequential operations illustrated by the architecture and processed light-curve examples.
- I. Gap Data Anomalies: The pipeline flags unusable anomalous cadences, including target-specific and channel-wide events, and records their anomaly types.
- II. Gap Filling: Gaps are linearly filled internally because some operations require contiguous time series, then refilled more sophisticatedly before export to TPS.
- III. Coarse Cotrending: A temporary coarse Bayesian MAP cotrending removes trends to facilitate discontinuity correction and outlier removal before being removed for the proper MAP correction.
2.3.4. IV. Sudden Pixel Sensitivity Dropoff (SPSD) Correction
SPSD correction addresses downward sensitivity steps that are common in Kepler light curves, while the broader anomaly workflow balances correction accuracy with preservation of astrophysical variability.
- Approximately 3 % of light curves contain one or more noticeable downward step discontinuities per quarter, typically caused by cosmic rays or solar energetic particles.
- SPSDs are not correlated systematics, so PDC-MAP detects and corrects them with a dedicated module rather than the MAP algorithm.
- In Quarter 9, SPSDs were detected in 5252 of 167404 targets (3.1 %).
- V. Harmonics Removal: Harmonics removal is optional because MAP fitting is robust to uncorrelated target-specific harmonics, and it can preserve or restore harmonic content in exported light curves.
- VI. Outlier Correction: Outlier correction replaces only isolated single-cadence threshold excursions with linear interpolations to avoid flagging planet transits or stellar flares.
- Iteration: SPSD correction, harmonics removal, and outlier correction are non-orthogonal and are normally performed once, with iteration available as an input option.
2.3.8. VII. Bayesian MAP approach for cotrending to remove systematic errors
The main systematic-trend correction uses Bayesian MAP cotrending against ensembles of light curves, with cleaned inputs and improved gap treatment supporting downstream transit searches.
- The main cotrending step removes correlated systematic trends using a Bayesian Maximum A Posteriori approach applied against an ensemble of light curves.
- Only clean targets without detected discontinuities generate the basis vectors for the final cotrending fit.
- Discontinuities, optional harmonics, and outliers are removed before fitting, improving the quality of the systematic-trend correction.
- A sophisticated gap-filling algorithm refills corrected light curves before export because TPS requires contiguous data and statistically continuous wavelet-coefficient variances.
- If harmonics were removed, they are added back after MAP cotrending, while harmonic-free corrected curves are also exported.
2.3.11. X. Crowding Metric and Flux Fraction Correction
PDC corrects aperture-related photometric biases using the crowding metric and flux fraction, with robust median-based normalization.
- Nearby light sources can dilute apparent transit depths, causing systematic underestimation of planet radii if excess aperture flux is not removed.The crowding metric records the fraction of optimal-aperture flux attributable to the target.
- PDC uses the crowding metric to correct excess flux and the flux fraction to account for target light missing from the optimal aperture.The two corrections are applied together to normalize the flux.
- The correction uses the median rather than the mean, making normalization robust against mathematical outliers such as planetary transits and eclipsing-binary events.
2.3.12. XI. Goodness Metric
The Goodness Metric numerically evaluates cotrending by combining residual systematic correlation, introduced noise, and preservation of stellar variability into a normalized score.
- The Goodness Metric reduces subjective review by numerically assessing systematic-trend removal, introduced noise, and preservation of stellar variability.Human inspection can miss subtle cotrending problems.
- Residual systematic trends are evaluated through target-to-target Pearson correlations, with stronger correlations receiving greater emphasis through cubing.
- Introduced noise is estimated from increases in the noise-floor power spectral density, focusing on regions where power increases by more than one.The noise floor is defined using first differences between adjacent flux values.
- Stellar-variability preservation is estimated from changes in a mid-frequency band after filtering high- and low-frequency components.Earth-point recovery regions are masked because they can be unusually strong.
- Each component worsens as performance deteriorates, is inverted to range from 0 to 1, and contributes to a total goodness computed as their geometric mean.
- The weighting parameters αC = 12.0, αN = 1.0E −4, and αV = 1.0E4 were empirically tuned to match observed cotrending performance.
- The experimentally developed metric supports data-product review and user assessment, while future work plans to incorporate it into the MAP posterior and iteratively improve fitting.
2.4. Outputs of PDC
PDC outputs corrected light curves together with optional harmonic-free products and diagnostic information describing processing decisions and identified artifacts.
- PDC outputs corrected light curves and, when Harmonics Removal is performed, a second set without harmonic content.
- Additional outputs include identified SPSD target and cadence indices, outlier locations, and Bayesian prior-weighting diagnostics for each target.
2.5. Processing Times
PDC processes one channel for one quarter as its unit of work, with computational cost concentrated in MAP fitting and final gap filling.
- A typical long-cadence work unit contains 1000–3500 targets and approximately 4500 data points per target.
- MAP fitting and final gap filling are the computationally most expensive PDC operations.
3. Summary and Conclusions
The SOC 8.0 PDC-MAP corrects diverse Kepler light-curve errors while preserving stellar variability. Its applicability remains limited for short-cadence data, and several algorithmic improvements are planned.
- 3. Summary and Conclusions: PDC-MAP uses a Bayesian Maximum A Posteriori approach to remove correlated trends while preserving stellar variability.It replaces the previous PDC-LS least-squares approach using ancillary engineering data.
- 3. Summary and Conclusions: PDC corrects systematic trends, flux discontinuities, outliers, and scalar corrections for targets’ finite point-spread functions.The corrected trends commonly result from velocity aberration, temperature drift, and pointing errors due to vibrations; discontinuities can result from cosmic rays or solar energetic particles.
- 3. Summary and Conclusions: The new PDC-MAP has significantly improved performance over the previous PDC-LS implementation.PDC-LS used a least-squares fitting approach with ancillary engineering data.
- 3. Summary and Conclusions: Potential improvements include band-splitting, automatic parameter selection, and time-dependent flux-fraction and crowding-metric corrections.The current version uses input parameters such as the number of basis vectors and approximates these corrections as scalar values for each quarter.
- 3. Summary and Conclusions: PDC-MAP currently processes only Kepler long-cadence light curves, while PDC-LS remains in use for short-cadence data.Interpolated basis vectors from long-cadence processing are suggested as one way to extend PDC-MAP to short-cadence data.