Activity-Rotation Relations for Lower Main Sequence Stars.

It has been known for some time that stellar rotation and activity are related, both for chromospheric activity (e.g., Noyes et al. 1984) and coronal activity (e.g., Pallavicini et al. 1981; Maggio et al. 1987). Younger, more rapidly rotating stars of a given spectral type generally show higher levels of activity than do older, more slowly rotating stars. On the Sun activity is distinctly related to magnetic fields. This leads to the suggestion that activity, at least in solar-type stars, is traceable to a magnetic dynamo which results from the interaction of rotation and differential rotation with convection. The more efficient the coriolis forces are at introducing helicity into convective motions, the more the magnetic field will be amplified and the more activity we may expect to see. The precise nature of the relationship between magnetic fields, rotation, and activity remains to be well -defined. It is our purpose here to examine the relationship between activity (both chromospheric and coronal) and rotation in order to better define and express such a relation (or relations). To meet this goal, a comprehensive sample of stars has been collected from the published literature having two or more of the following: chromospheric Ca II H & K emission indices, coronal soft x-ray luminosities, rotation rates, and, where possible, ages. It will be seen that the use of normalized activity units and the Rossby number generally improves the correlation between activity and rotation. This allows one to define one functional relationship between the activity index being used (either chromospheric or coronal) and the rotation parameter. These single functions vary smoothly from young, highly active objects to very inactive ones. No discontinuities in physical or functional behavior are needed to explain the distribution of data points. The use of the convective turnover time further permits a possible explanation for the distribution of stars in an activity-color diagram, accounting for the existence of the Vaughan-Preston gap. Finally, a large and homogeneous data set permit better definition of previously examined functional dependences such as the time decay of activity and the relationship between chromospheric and coronal activity indicators.