4. Summary and conclusions
We have demonstrated that for slowly rotating () lower main-sequence stars with well-defined periodic chromospheric activity the cycle period can be parametrised according to , with and . The existence of such a relation points to a common dynamo mechanism for slowly rotating stars. Cycle periods of rapidly rotating stars () do not match this relation.
We used linear mean-field dynamo theory to explain the cycle periods of slowly rotating lower main-sequence stars, assuming that the geometry of the dynamo in all these stars, including the Sun, is that of Parker's surface-wave model (Parker 1993). We assumed that the differential rotation and the -coefficient depend on the rotation rate according to and . The other parameters were taken to be independent of . In estimating we assumed that the activity belts extend over of latitude on either side of the equator. This is probably a reasonable assumption for slowly rotating stars, since model calculations have shown that starspot activity occurs near the poles only for rapidly rotating stars (for a star of one solar mass if , Schüssler et al. 1996).
The observed correlation between , and is reproduced if and . The positive sign of p suggests that differential rotation decreases with increasing rotation rate. Such a trend is supported by calculations of Kitchatinov & Rüdiger (1995), who found a similar dependence on rotation, with . The negative value of q indicates that the -coefficient increases if Ro decreases, in accordance with the common assumption that increases with increasing rotation rate. Our result also implies that for constant , increases with increasing , i.e. with increasing (Eq. 15). This is due to the fact that convective cells with longer turnover times are more strongly influenced by rotation.
© European Southern Observatory (ESO) 1997
Online publication: June 5, 1998