What is Kepler Really Telling Us about Starspots?

The signature of starspots in Kepler data is obvious and pervasive. There have been many papers discussing aspects of these light curves, including rotation period detection, dependence of amplitude on rotation, differential rotation signatures, and activity cycles. There are some subtleties of interpretation, however, that have received much less attention (but are relevant to these analyses). 1) as the light curves change, how much of that is due to differential rotation (spots changing phase with respect to each other) and how much is due to spot evolution (spots growing and decaying in various locations)? 2) given that Kepler only provides differential photometry, how can we properly convert light deficits to actual spot areas (what does the unspotted star look like)? 3) how much information is actually in the light curves, given that there are generally only one or two dips in intensity per rotation? I discuss progress on these questions, utilizing a large search of parameter space with spot models. I also present a new rotation-activity relation: there is a strong correlation between a) the ratio of of the time spent by a light curve in single dip mode to that spent in double dip mode, and b) the rotation period of that star. I give a tentative interpretation of this new result. Most of the contents of this presentation have been published in 2018 in ApJ: v. 863, p. 190 and v. 865, p. 142.