Calibration of Differential Light Curves for Physical Analysis of Starspots

This paper presents detailed consideration of methodologies to calibrate differential light curves for accurate physical starspot modeling. We use the Sun and starspot models as a testbed to highlight some factors in this calibration that that have not yet been treated with care. One unambiguously successful procedure for converting a differential light curve into a light deficit curve appears difficult to implement, but methodologies are presented that work in many cases. The years-long time coverage of Kepler provides a strong advantage, but unresolved issues concerning the competing and sometimes similar effects of surface differential rotation versus spot number and size evolution can prevent the confident recovery of correct spot covering fractions in certain cases. We also consider whether faculae are detected by Kepler and/or must be accounted for. We conclude their effects are such that absolute photometry is not required for spot deficit calibrations. To elucidate their signature, we re-examine correlations between absolute brightness, differential variability, and apparent spot coverage for hundreds of Kepler stars with absolute calibrations from Montet et al. The results are similar to theirs, but we draw somewhat different conclusions. Most of the stars in this active solar-type sample are spot-dominated as expected. Partly because of a dearth of longer period stars, the evidence for facular dominance in this sample is both sparse and relatively weak. The facular population exhibits a puzzling lack of dependence on rotation period, which raises questions about the apparent detection of a "facular" signal at short periods.