K2SC: Flexible systematics correction and detrending of K2 light curves using Gaussian Process regression

Suzanne Aigrain; Hannu Parviainen; Benjamin Pope

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K2SC: Flexible systematics correction and detrending of K2 light curves using Gaussian Process regression

Suzanne Aigrain, Hannu Parviainen, Benjamin Pope

arXiv:1603.09167v1Mar 30, 2016astro-ph.SRastro-ph.EPastro-ph.IM

TL;DR

K2 light curves contain pointing-induced systematics that can limit photometric precision and transit searches. K2SC uses Gaussian-process components for detector position, time-dependent variability, and noise, and achieves near-Kepler precision while improving transit-search sensitivity. Its performance is constrained for some large-amplitude roll-angle systematics and rapidly varying eclipsing-binary signals.

Problem
K2 light curves retain significant residual systematics, limiting the adequacy of standard PDC correction for these data.
Method
K2SC models each light curve with additive Gaussian processes for position-dependent systematics, time-dependent astrophysical variability, and white noise.
Results
K2SC achieves 6-hour CDPP within a factor 1.5 of original Kepler precision for bright stars and demonstrates better than 50% transit sensitivity down to k = 0.03 at P = 5 d.
Takeaways & Limitations
The methodology is readily applicable to other datasets, including future transit missions such as TESS and PLATO, with possible changes to the systematics inputs.
Takeaways & Limitations
K2SC may function less effectively with large-amplitude roll-angle systematics, and its time component can struggle with eclipses when similar-timescale variability is present.

Abstract

from arXiv · show

We present K2SC (K2 Systematics Correction), a Python pipeline to model instrumental systematics and astrophysical variability in light curves from the K2 mission. K2SC uses Gaussian process regression to model position-dependent systematics and time-dependent variability simultaneously, enabling the user to remove both (e.g., for transit searches) or to remove systematics while preserving variability (for variability studies). For periodic variables, K2SC automatically computes estimates of the period, amplitude and evolution timescale of the variability. We apply K2SC to publicly available K2 data from campaigns 3--5, showing that we obtain photometric precision approaching that of the original Kepler mission. We compare our results to other publicly available K2 pipelines, showing that we obtain similar or better results, on average. We use transit injection and recovery tests to evaluate the impact of K2SC on planetary transit searches in K2 PDC (Pre-search Data Conditioning) data, for planet-to-star radius ratios down Rp/Rstar = 0.01 and periods up to P = 40 d, and show that K2SC significantly improves the ability to distinguish between correct and false detections, particularly for small planets. K2SC can be run automatically on many light curves, or manually tailored for specific objects such as pulsating stars or large amplitude eclipsing binaries. It can be run on ASCII and FITS light curve files, regardless of their origin. Both the code and the processed light curves are publicly available, and we provide instructions for downloading and using them. The methodology used by K2SC will be applicable to future transit search missions such as TESS and PLATO.

1 INTRODUCTION

K2 offers valuable observations but suffers reduced photometric precision from pointing variations and residual systematics. K2SC addresses this by modeling position-dependent systematics and time-dependent variability with Gaussian processes, while extending the method beyond earlier approaches.

Motivation: K2 provides observations of bright Sun-like stars, low-mass stars, and open clusters, but reduced pointing accuracy lowers photometric precision.The mission surveys fields near the Ecliptic plane after Kepler’s reaction-wheel failure.
Motivation: Existing K2 pipelines extract light curves and correct pointing-induced flux variations using aperture photometry or PSF fitting.Their systematics corrections generally model each star’s flux as a function of position.
Problem: K2 PDC light curves often retain significant residual systematics, motivating an improved standalone star-by-star correction method.The paper contrasts this with Kepler’s use of co-trending basis vectors constructed from many light curves.
Method: K2SC models flux with three additive Gaussian-process components for position-dependent systematics, time-dependent variability, and white noise.Subtracting the position component preserves intrinsic variability while correcting pointing-dependent effects.
Contributions: The method models two-dimensional stellar position instead of roll angle alone, introduces GP parameter priors, and supports quasi-periodic variability kernels.These changes target positional drift, field-dependent sensitivity variations, and spotted or pulsating stars.
Evaluation: The pipeline is evaluated using transit-timescale scatter and simulated transit injection-and-recovery tests, with code and Campaigns 3–5 data publicly available.These evaluations use a proxy for Combined Differential Photometric Precision and transit-recovery performance.

2 METHOD

K2SC models instrumental systematics, stellar variability, and white noise jointly with Gaussian processes, separating position-dependent effects from time-dependent signals. The pipeline uses two-dimensional stellar positions, component-wise prediction, outlier handling, and specialized treatment for periodic variables.

GP model: Gaussian-process regression models position-dependent systematics, intrinsic variability, and white noise as additive components.The covariance function combines position, time, and white-noise terms, allowing the model contributions to be separated.
Position-dependent systematics: The position input uses each star’s two-dimensional x and y coordinates rather than a single satellite roll-angle coordinate.Separate x- and y-direction length scales allow the model to represent two-dimensional position dependence.
Systematics correction: The position component can be subtracted from the raw light curve while preserving intrinsic variability and providing uncertainty estimates for corrected points.The predictive variance of the position component supplies a robust uncertainty estimate for the corrected light curve.
Variable stars: For strong variables, the standard model can absorb both systematics and intrinsic variability into white noise, limiting correction quality.The authors report this limitation for classical pulsators and active, rapidly rotating stars, while moderate variability on timescales longer than about 6 hours is handled better.
Variable stars: A quasi-periodic covariance model improves results for spotted and pulsating stars with periods of a day or more and yields period and evolutionary-timescale estimates.The model initializes the period from a periodogram peak and refines the covariance parameters through the same optimization procedure.
Hyperparameter behavior: Hyperparameter distributions are broadly consistent across Campaigns 3–6, although systematics parameters depend somewhat on distance from the satellite boresight.The latter dependence suggests that location-informed initial guesses could improve detrending in future work.

3 PHOTOMETRIC PERFORMANCE FOR K2 DATA

K2SC improves photometric precision in K2 Campaign 5 light curves by removing position-dependent systematics, with performance approaching original Kepler levels for many dwarf stars. Its performance varies for giant stars and relative to other pipelines.

Evaluation: The CDPP proxy compares photometric precision on transit timescales, with 6-hour estimates evaluated against Kepler pipeline values and multiple K2SC processing stages.The study uses a proxy because the authors lack access to the KSOC transit-search pipeline.
Giant stars: Red giants form a distinct reduced-proper-motion population and show excess few-hour variability from stochastically excited pulsations.Their short-timescale variability complicates comparisons between K2SC proxy CDPP values and filtered transit-search estimates.
K2SC performance: CDPP proxy values for systematics-corrected data are considerably lower and tighter with Kepler magnitude than raw-light-curve values, using either SAP or PDC inputs.PDC light curves yield slightly lower CDPP values; removing the time component mainly reduces variable-star outliers.
K2SC performance: 38 ppm median CDPP for 11.5 ≤ Kp ≤ 12.5 is 50% higher than the 25 ppm median for the same magnitude range in original Kepler data.For dwarf stars with Kp ≤14.5, the lower envelope ranges from <20 ppm near Kp∼10 to about 70 ppm near Kp∼14.
Giant stars: For giant stars, short-period time-component fits can absorb white noise, while some oscillations remain unmodelled when the quasi-periodic-GP criterion is not met.Improved pulsating-star performance would require object-by-object modelling of individual oscillation frequencies, beyond this study’s scope.
Comparison to other pipelines: Figure 10 compares relative CDPP differences between k2sff and K2SC-corrected PDC light curves for Campaign 4, with red-giant points clustered near zero.The comparison uses author-computed proxy CDPP estimates because the k2sff CDPP procedure differs slightly.
Comparison to other pipelines: K2SC light curves are systematically less noisy than k2varcat outputs in the reported Campaign 4 examples, although k2varcat can sometimes have lower raw noise and fewer obvious systematics.The comparison includes both variable and quiet stars; one k2varcat example contains a discontinuity absent from the K2SC version.

4 TRANSIT INJECTION TESTS

The authors inject simulated transits into Campaign 5 PDC light curves and compare BLS recovery before and after K2SC detrending. K2SC improves correct identification, especially for small planets when applying an SDE threshold.

Injection and recovery setup: 7000 randomly selected Campaign 5 stars were tested with injected PyTransit signals and BLS searches on original and K2SC-detrended PDC light curves.The injected signals were also searched in the original PDC data for comparison.
Injection and recovery setup: An injected transit was correctly identified when the recovered period was within 2% of the injected period.The search used 5000 frequencies spanning periods from 0.75 to 40 days, and recorded the signal with the highest SDE.
Recovery classification: Unidentified signals are false alarms because they recover a signal other than the injected transit.The distinction is applied to light curves containing injected signals without strong pre-injection BLS detections.
Results: Figures 11 and 12 compare BLS SDE distributions for correctly identified and unidentified signals across original and K2SC-detrended PDC data.Figure 12 additionally shows the comparison as a function of injected orbital period.

5 PUBLICLY AVAILABLE CODE AND DATA

K2SC is distributed as open-source Python software for detrending light curves from multiple sources, with both command-line and lower-level interfaces. Processed Campaigns 3–5 light curves are publicly available through MAST.

Code: The k2sc package provides an executable and Python modules for detrending light curves from several sources.The executable supports automatic MPI parallelization, while the modules support custom photometry pipelines and formats.
Code: K2SC is open source under a GPLv3 license and is available through GitHub and PyPI.The package is designed to support extension with new GP kernels and data importers.
Performance: A typical light curve requires approximately 2 minutes of detrending time on a modern computer.Runtime is dominated by differential-evolution iterations and local hyperparameter optimization.
Data: K2SC-processed long-cadence light curves from Campaigns 3–5 are available from MAST as a K2 High-Level Science Product.The paper provides instructions for searching, downloading, and using these products.

6 CONCLUSIONS AND FUTURE WORK

K2SC models position-dependent systematics and time-dependent variability with separate Gaussian processes, achieving near-Kepler photometric precision and improving transit-search identification. The authors also identify input-data and systematics-related boundaries and describe extensions to other datasets.

Method: K2SC separates position-dependent instrumental systematics from time-dependent astrophysical variability using additive Gaussian processes.The method can remove both components or preserve variability while correcting position-dependent systematics.
Photometric performance: For bright stars with V ∼12, 6-hour CDPP is within a factor 1.5 of the original Kepler mission.The result is based on proxy CDPP measurements of detrended K2 light curves.
Pipeline comparison: Compared with other pipelines, K2SC light curves are less noisy than k2varcat and have precision broadly similar to k2sff.k2sff is slightly better for bright stars, while K2SC is slightly better for fainter stars; K2SC is also more robust to strong astrophysical variability.
Transit searches: Transit injection tests show better than 50% sensitivity down to radius ratio k = 0.03 at P = 5 d and k = 0.05 at P = 40 d.The authors state that these results imply sensitivity to warm Neptunes and hot super-Earths around Sun-like stars, and some Earth-sized planets around habitable-zone M dwarfs.
Limitations and future work: Photometric performance might improve with different input light curves or more optimal apertures.The pipeline can accept light curves containing time, flux, and two-dimensional position information.
Future applications: The methodology could extend to NGTS, TESS, and PLATO, although their different systematics may require modified model inputs.Suggested additional variables include detector temperature, seeing, and airmass.