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\cite{1998ApJ...498L..51B} used the results from \cite{Baliunas_1995} to show that the difference between stars of intermediate age and stars of solar age or older give rise to a discontinuous dependence of the ratio of the cycle to rotation frequency $\omega_{\rm cyc}/\Omega$ as a function of the Rossby number Ro (which is defined as ...). In this way stars of intermediate age generally showed a $\omega_{\rm cyc} \propto {\rm Ro}^{-0.7}$ relationship, whereas the ratio $\omega_{\rm cyc}/\Omega$ increased by a factor of 6 for stars of solar age or older. This led them to suggest that the dynamo $\alpha$-parameter increases with magnetic field strength, contrary to the conventional idea of $\alpha$-quenching. \cite{1998ApJ...498L..51B} names the two groups of stars active and inactive branch stars. A naming that is still being used today.  \cite{1999ApJ...524..295S} extended the analysis of \cite{1998ApJ...498L..51B} to also include so-called RS Canum Venaticorum variables ( binary (binary  stars with shows very high activity levels) and less certain cycles and evolved stars from \cite{Baliunas_1995}. This study not only confirmed the result by \cite{1999ApJ...524..295S} it also showed that the most active stars with rotation period below 3 days occupied a third branch call the superactive branch and that the intermediate age and the solar age and older stars could in fact have cycles on both the active and the inactive branch, where the intermediate age stars tend to have their primarily cycle on the active branch and the solar age and older stars tend to have their primarily cycle on the inactive branch. The analysis was redone by \cite{2007ApJ...657..486B}, who compared the cycle periods to the rotation period in what is now known as the B{\"o}hm-Vitense diagram, which show the active and inactive branches very clearly. What is very peculiarly about the B{\"o}hm-Vitense diagram falls right between the active and the inactive branches. \cite{2007ApJ...657..486B} suggested that cycles on the different branches are driven by different kind of dynamos and thus that the discontinuous break between for stars around the age of the Sun is caused by a change in the dynamo action which she suggest is due to abruptly increased deep mixing. The idea behind the B{\"o}hm-Vitense diagram was taken up by \cite{Karoff_2009} and \cite{Karoff_2013} in their {\it sounding stellar cycles with Kepler} project, who rely on the fact the asteroseismic observations from the {\it Kepler} mission could be used to test the hypothesis that the discontinuous break between for stars around the age of the Sun is caused by a change in the dynamo action which she suggest is due to abruptly increased deep mixing. This is possible as asteroseismology can be used to measure both ages, differential rotation and ages of the stars. Unfortunally, {\it Kepler} was only fully operational for four years, which appears to be to short to allow any firm detection of stellar cycles using {\it Kepler} observations alone. The project does however continue using ground-based facilities to measure activity cycles. 
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THe theoretical description of how stars loss angular momentum to stellar winds was formulated by \cite{1984LNP...193...49M} and tested on stellar models by \cite{1988ApJ...333..236K}. This analysis suggested that though stars are form with a verity of different initial angular momentum, but the time the stars reach an age of 80 million years, then have also spun so much down that their rotation rate is independent of the initial angular momentum. This explains the strong relation between rotation rate and age seen by \cite{Skumanich_1972}, but the general picture is still that the angular momentum is distributed evenly over the convection zones of the stars. This was changes with the model by \cite{1990ApJS...74..501P} who used a set of coupled diffusion equations to describe the internal transport of angular momentum throughout the convection zone. These calculation show that F and G type stars losses angular momentum more efficient than K and M type stars. As the F and G type stars have thiner convective zone and larger radiative zones than K and M stars, F and G type stars will build up a stronger tachocline. THis will lead to a coupling between the radiative interior and the outer convection zone. In the K and M type stars there will be no such coupling and the angular momentum can therefore only be lost from the (thick) convective zone, which will lead to a relative faster spin-down rate.  \cite{2003ApJ...586..464B, \citet{2003ApJ...586..464B,  2007ApJ...669.1167B} combined these studies into the term he call {\it gyrochronology} -- i.e. how to relate stellar rotation periods to stellar ages. The idea is that FGKM stars separate into three different sequences: the I sequence, the C sequence and the R sequence. I stand for {\it interface} and represents stars that have a coupling between the radiative interior and the convective envelope. C stands for {\it convective} and represents stars with deep convective zones, where the radiative interior is decoupled from the convective envelope and where a $\alpha\Omega$ and an $\alpha^2\Omega$ dynamo have not yet set in. R stands for {\it radiative} and represents early F-type stars with very thin convective zones that are thus dominated by the radiative interior. A note of caution here. The I, C and R sequences by \citet{2003ApJ...586..464B} have nothing to do with the active and inactive branches by \cite{1998ApJ...498L..51B}. Stars on both the active and the inactive branch are likely to have an $\alpha\Omega$ or an $\alpha^2\Omega$ dynamo, where as stars on the C sequence are likely to have an $\alpha^2$ dynamo. Though dynamos in the stars on the R sequence are likely to be $\alpha^2\Omega$ dynamos (ref), they are also likely to have a rather different nature than the dynamos on the I sequence. The stars on the I sequence, however, can belong both to the active and the inactive branch.  [figure]