Adapt "pixel-level-decorrelation" methods to sinusoidally varying stars

[gully]

Description

The EPIC Variability Extraction and Removal for Exoplanet Science Targets (EVEREST) pipeline "de-trends K2 light curves with pixel level decorrelation and Gaussian processes". These methods assume that the stellar source varies non-parametrically in time. In some cases, we can better predict stellar variability with explicit linear models. Sinusoidally varying light curves from rotationally-induced starspot photometric modulation stand to benefit from such a treatment, both for improved fidelity of stellar variability estimation, and for improved planet search methods. The first step for a given star would be to derive a period of sinusoidal variability (e.g. Lomb-Scargle), then build in additional columns in a design matrix, with a fixed period (keeping the problem linear), but sine and cosine amplitudes set through EVEREST. (See Equation 10.23 in Statistics, Data Mining, and Machine Learning for proof that fitting sine waves is linear-- "never fit phase!").

Benefits

• Should improve EVEREST-produced lightcurves for stars with large peak-to-valley sinusoidal amplitude (young, spotted stars).

Costs

• Have to understand the linear algebra related to regression
• Have to understand EVEREST at a level that allows modifying the code

[JeffLCoughlin]

Might be worth trying PyKE keppca to some of these stars and seeing how well it does - in theory it should not be robust against the stellar variability regardless of timescale or shape. (Just as long as a component corresponding to the target variability isn't subtracted - if the stellar variability is significant compared to the K2 systematics then just need to be careful it isn't among the first few principal components.)