STARSPOT EVOLUTION, DIFFERENTIAL ROTATION, AND MAGNETIC CYCLES IN THE CHROMOSPHERICALLY ACTIVE BINARIES LAMBDA-ANDROMEDAE, SIGMA-GEMINORUM, II-PEGASI, AND V711-TAURI

We have analyzed 15-19 yr of photoelectric photometry, obtained manually and with automated telescopes, of the chromospherically active binaries lambda And, sigma Gem, II Peg, and V711 Tau. These observations let us identify individual dark starspots on the stellar surfaces from periodic dimming of the starlight, follow the evolution of these spots, and search for long-term cyclic changes in the properties of these starspots that might reveal magnetic cycles analogous to the Sun's 11 yr sunspot cycle. We developed a computer code to fit a simple two-spot model to our observed light curves that allows us to extract the most easily determinable and most reliable spot parameters from the light curves, i.e., spot longitudes and radii. We then used these measured properties to identify individual spots and to chart their life histories by constructing migration and amplitude curves. We identified and followed II spots in lambda And, 16 in sigma Gem, 12 in II Peg, and 15 in V711 Tau. Lifetimes of individual spots ranged from a few months to longer than 6 yr. Differential rotation coefficients, estimated from the observed range of spot rotation periods for each star and defined by equation(2), were 0.04 for lambda And, 0.038 for sigma Gem, 0.005 for II Peg, and 0.006 for V711 Tau, versus 0.19 for the Sun. We searched for cyclic changes in mean brightness, B - V color index, and spot rotation period as evidence for long-term cycles. Of these, long-term variability in mean brightness appears to offer the best evidence for such cycles in these four stars. Cycles of 11.1 yr for lambda And, 8.5 yr for sigma Gem, 11 yr for II Peg, and 16 yr for V711 Tau are implied by these mean brightness changes. Cyclic changes in spot rotation period were found in lambda And and possibly II Peg. Errors in B - V were too large for any long-term changes to be detectable. We discuss the results of our analyses of these four binary systems in the context of what we now know about chromospherically active stars in general. We argue that the cool, magnetic spot model continues to offer the best explanation for the observed properties of these stars. We show that the Rossby numbers of our four stars successfully predict their enhanced starspot activity and that the differential rotation coefficients determined for these stars are consistent with a trend toward solid-body rotation in rapid rotators. We show that the results for our four stars are consistent with the picture that starspot lifetimes are roughly predictable from their sizes and that the largest spots have lifetimes limited by the shear forces of differential rotation. We review the evidence for rigid structure in surface activity as implied by active quadrants and preferred longitudes for starspot formation. Finally, we find increasing evidence for long-term cycles, possibly magnetic, in a growing number of chromospherically active stars, primarily from long-term changes in mean brightness, but also from latitude drift and orbital period changes.