The democratic detrender: Ensemble-Based Removal of the Nuisance Signal in Stellar Time-Series Photometry

Abstract

Accurate, precise, and computationally efficient removal of unwanted activity that exists as a combination of periodic, quasi-periodic, and non-periodic systematic trends in time-series photometric data is a critical step in exoplanet transit analysis. Throughout the years, many different modeling methods have been used for this process, often called "detrending." However, there is no community-wide consensus regarding the favored approach. In order to mitigate model dependency, we present an ensemble-based approach to detrending via community-of-models and the democratic detrender: a modular and scalable open-source coding package that implements ensemble detrending. The democratic detrender allows users to select from a number of packaged detrending methods (including cosine filtering, Gaussian processes, and polynomial fits) or provide their own set of detrended light curves via methods of their choosing. It then combines the individually detrended light curves into a single method marginalized light curve. Additionally, the democratic detrender inflates each data point's uncertainty based on the scatter between detrenders, thereby propagating model-selection uncertainty into the final light curve. This ensemble strategy does not guarantee improvement over the single best-performing detrending method, but it substantially reduces the risk of selecting a detrending solution that is poorly calibrated or overfit to noise.

Figures (8)

• Figure 1: The four primary contributions to space-based stellar time-series photometric data are (1) detector noise, (2) stellar activity, (3) spacecraft motion, telescope, & instrumental induced variations, and (4) eclipses or transits. Detrending is the process of removing as much of the stellar activity and spacecraft, telescope, & instrument noise (i.e., "nuisance signal") as possible without adding additional non-physical features.
• Figure 2: An example of ensemble detrending in practice. Here we've taken the simulated light curve (LC), presented in Figure \ref{['fig: light curve']} and fit the non-transit data with four different detrending methods. Detrending model $\#$4 failed to accurately fit the data, and thus would fail the tests of Gaussianity and be removed before the ensemble step. In the top right one can see that detrending with each of the three individual detrended methods can result in noticeably different predictions for the transit shape. In the ensemble detrended light curve in the bottom right, we take the median detrended solution for each data point, as described in Equation \ref{['eq: ensemble median']}. Additionally, we inflate the error bars, as shown by the shaded region in the ensemble detrended LC, by adding in quadrature the reported errors with the median absolute deviation between the different detrending methods, as described in Equation \ref{['eq: ensemble errors']}. In total, the ensemble step is thus described by Equation \ref{['eq: ensemble function']}.
• Figure 3: Flow chart depicting required and optional user inputs, built-in functions, and output data products for the democratic detrender. As long as the user passes in the requisite inputs and data products, the democratic detrender can be initiated at any of the intermediate functions. This flow chart thus displays the modularity and customizability of the democratic detrender.
• Figure 4: Raw (not detrendend) SAP [left] and PDCSAP [right] light curves for Kepler-1519 b. Red data points are those that were deemed outliers via moving median rejection and thus removed from subsequent modeling. The grey dotted lines show the different Kepler quarters in the data.
• Figure 5: The top row is Kepler-1519 b's 2$^\textrm{nd}$ quarter of SAP data. In the 2$^\textrm{nd}$ quarter we can see that there are 3 time discontinuities, but as these time gaps don't coincide with a flux intensity discontinuity as well, we wouldn't want to remove any of the data from our detrending. The bottom row is Kepler-1519 b's 15$^\textrm{th}$ quarter of SAP data. In the 15$^\textrm{th}$ quarter, we can see that there are 2 flux intensity discontinuities that coincide with time discontinuities. In this case, we would want to label the closest flux discontinuity to the transit (KBJD $\sim$ 1527). Once we label this problem time, the democratic detrender will clip the data here, and remove all data from earlier in the quarter, before fitting the detrending models.