The relation between stellar rotation rate and activity cycle periods

Abstract

The empirical relation between rotation period, spectral type, and cycle activity period in 13 slowly rotating main-sequence stars is investigated, on the basis of available spectrometric data. It is shown that for slowly rotating stars with similar spectral types, the cycle period P(cyc), and rotation period P(rot) were related such that P(cyc) varies as P(rot) to the nth, where n equals 1.25. In a group of stars with individual spectral types from G2 to K7, the cycle periods were consistent with the relation P(cyc) is approximately equal to (P rot/tauc) exp n, where tauc is the convective turnover time near the bottom of the convection zone. On the basis of the above relations, it is suggested that an increase of P(cyc) with increasing P(rot) does not agree with conventional estimates from nonlinear dynamo models, and is limited by two factors: the quenching of the alpha effect; and differential rotation.