The Information Content in Analytic Spot Models of Broadband Precision Light Curves. II. Spot Distributions and Lifetimes and Global and Differential Rotation

With the advent of space-based precision photometry missions, the quantity and quality of starspot light curves has greatly increased. This paper presents a large number of starspot models and their resulting light curves to (1) better determine light-curve metrics and methods that convey useful physical information and (2) understand how the underlying degeneracies of the translation from physical starspot distributions to the resulting light curves obscure that information. We explore models of relatively active stars at several inclinations while varying the number of (dark) spots, random spot distributions in position and time, timescales of growth and decay, and differential rotation. We examine the behavior of absolute and differential variations of individual intensity dips and overall light curves and demonstrate how complex spot distributions and behaviors result in light curves that typically exhibit only one or two dips per rotation. Unfortunately, simplistic "one- or two-spot" or "active longitude" descriptions or modeling of light curves can often be highly misleading. We also show that short "activity cycles" can easily be simply due to random processes. It turns out to be quite difficult to disentangle the competing effects of spot lifetime and differential rotation, but under most circumstances, spot lifetime is the more influential of the two. Many of the techniques tried to date only work when spots live for many rotations. These include autocorrelation degradation for spot lifetimes and periodograms for both global and differential rotation. Differential rotation may be nearly impossible to accurately infer from light curves alone unless spots live for many rotations. The Sun and solar-type stars its age or older are unfortunately the most difficult type of case. Further work is needed to have increased confidence in light-curve inferences.