k-Means Aperture Optimization Applied to Kepler K2 Time Series Photometry of Titan

Abstract: Motivated by the Kepler K2 time series of Titan, we present an aperture optimization technique for extracting photometry of saturated moving targets with high temporally- and spatially-varying backgrounds. Our approach uses $k$-means clustering to identify interleaved families of images with similar Point-Spread Function and saturation properties, optimizes apertures for each family independently, then merges the time series through a normalization procedure. By applying $k$-means aperture optimization to the K2 Titan data, we achieve $\leq$0.33% photometric scatter in spite of background levels varying from 15% to 60% of the target's flux. We find no compelling evidence for signals attributable to atmospheric variation on the timescales sampled by these observations. We explore other potential applications of the $k$-means aperture optimization technique, including testing its performance on a saturated K2 eclipsing binary star. We conclude with a discussion of the potential for future continuous high-precision photometry campaigns for revealing the dynamical properties of Titan's atmosphere.