Time evolution of the magnetic activity cycle period. II. Results for an expanded stellar sample

We further explore nondimensional relationships between the magnetic dynamo cycle period P-eye, the rotational period P-rot, the activity level (as observed in Ca II HK), and other stellar properties by expanding the stellar sample studied in the first paper in this series. We do this by adding photometric and other cycles seen in active stars and the secondaries of CV systems and by selectively adding less certain cycles from the Mount Wilson HK survey; evolved stars, long-term HK trends and secondary P-eye are also considered. We confirm that most stars with age t greater than or similar to 0.1 Gyr occupy two roughly parallel branches, separated by a factor of similar to 6 in P-eye, with the ratio of cycle and rotational frequencies omega(eye)/Omega proportional to Ro(-0.5), where Ro is the Rossby number. Using the model of the first paper in this series, this result implies that the alpha effect increases with mean magnetic field (contrary to the traditional alpha-quenching concept) and that alpha and omega(eye) decrease with t. Stars are not strictly segregated onto one or the other branch by activity level, though the high-omega(eye)/Omega branch is primarily composed of inactive stars. The expanded data set suggests that for t greater than or similar to 1 Gyr, stars can have cycles on one or both branches, though among older stars, those with higher (lower) mass tend to have their primary P-eye on the lower (upper) omega(eye)/Omega branch. The Sun's similar to 80 yr Gleissberg cycle agrees with this scenario, suggesting that longterm activity "trends" in many stars may be segments of long (P-eye similar to 50-100 yr) cycles not yet resolved by the data. Most very active stars (P-rot < 3 days) appear to occupy a new, third branch with omega(eye)/Omega proportional to Ro(0.4). Many RS CVn variables lie in a transition region between the two most active branches. We compare our results with various models, discuss their implications for dynamo theory and evolution, and use them to predict P-eye for three groups: stars with long-term HK trends, stars in young open clusters, and stars that may be in Maunder-like magnetic minima.