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Astron. Astrophys. 323, 151-157 (1997)

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1. Introduction

The flux that is emitted in the Ca II H and K lines serves as a diagnostic of stellar magnetic activity (Wilson  1978, Saar & Baliunas  1992, Baliunas et al.  1995). These emission lines are formed in the chromosphere by non-thermal heating related to magnetic fields. Direct confirmation of the magnetic nature of Ca II H and K emission is observed on the Sun, where the strength of these lines is correlated with the magnitude of, and the area covered by magnetic fields (Schrijver et al.  1989). On the main sequence, chromospheric activity is observed for [FORMULA], a limit which roughly coincides with the onset of a convective envelope. This suggests that stellar magnetic fields are produced by dynamos and raises the question whether various features of stellar magnetic activity can be parametrized by quantities related to dynamo theory.

The overall chromospheric activity level of lower main-sequence stars is well parametrized by an empirical Rossby number, [FORMULA] (Noyes et al.  1984a, Stepie  1994). Here [FORMULA] is the stellar rotation period and [FORMULA] is the empirical convective turnover time, whose functional dependence on [FORMULA] is determined from the data themselves by minimizing the scatter in the relation between activity and [FORMULA]. The resulting parametrization indicates that stellar activity increases with decreasing [FORMULA] (more rapid rotation). For [FORMULA] the empirical [FORMULA] closely resembles [FORMULA], the theoretical turnover time near the base of the convection zone, (Gilman  1980, Gilliland  1985, Kim & Demarque  1996). For [FORMULA], however, the activity level depends only on [FORMULA] and not, or only mildly, on [FORMULA] (Stepie  1989). Hence the empirical turnover time [FORMULA] is essentially constant for [FORMULA]. This is not in disagreement with the results of Gilman, since his calculations did not extend beyond [FORMULA], but the calculations by Gilliland and Kim & Demarque reveal a further increase of [FORMULA] with [FORMULA]. It follows that for [FORMULA] the Rossby number is not a useful indicator of the chromospheric activity level.

Four main categories of chromospheric activity are identified by Baliunas et al.  1995), namely stars with a constant activity level (13%), long-term variations (13%), irregular variations (24%) and periodic variations (50%). Here the percentages indicate the fraction of stars within each category, as estimated by Baliunas et al. In this paper we focus on stars with periodic variations. The assignment of a star to this category rather than to that of the irregular variations or long-term trends depends on the confidence level at which one requires the periods to be determined. In fact, the percentage of stars that have well-defined cyclic variations, i.e. those with periods rated good or excellent by Baliunas et al., is 15%. Furthermore, it is hard to distinguish between stars with cyclic variations on timescales longer than about 20 years and stars with long-term variations or a constant activity level within the time interval (about 25 years), spanned by the observations. Only continued observations can resolve these issues by increasing the reliability of the period determinations and by allowing longer periods to be detected.

As a result, the search for possible trends in the cycle length [FORMULA] has yielded mixed results. Noyes et al. (1984b) found a correlation between [FORMULA] and [FORMULA] for a small sample of stars with clear periodic variations. In the mean time, the sample of stars with periodic activity variations has grown, and it has been claimed that there is no longer any evidence of a correlation between cycle length and rotation period or Rossby number for the extended sample (Soderblom  1988, Saar & Baliunas  1992).

However, a trend may be concealed by a large spurious scatter that is caused by stars with ill-defined cycle periods. Several further arguments can be given to justify a renewed investigation of possible trends in the cycle length. First, we now have at our disposal estimates of the convective turnover time for lower main-sequence stars up to [FORMULA] (Kim & Demarque  1996). Most of the stars studied by Noyes et al. (1984b) are in the range [FORMULA], for which no estimates of [FORMULA] - apart from the empirical [FORMULA] - were available at that time. Second, the accuracy of the measured cycle periods has increased due to the longer span of observations. Third, for several stars new measurements of the rotation periods are available, that differ from previous values, or replace values that were predicted by means of the observed correlation between the Ca II flux and [FORMULA].

In Sect. 2 we examine the available cycle periods and look for trends in terms of dynamo parameters. In Sect. 3 we compare the observed trends with a simple linear mean-field dynamo model. Sect. 4 contains our conclusions.

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© European Southern Observatory (ESO) 1997

Online publication: June 5, 1998