Reiners & Schmidt 2003). (The $B-V$ colour was derived from the effective temperature, $T_{\rm eff}$, and metallicity of the model, using the empirical relations of Alonso, Arribas & Martínez-Roger 1996.) Rotation kernels calculated from the stellar models, together with simple internal rotation laws, were then used to determine the rotational frequency splittings. We note that the rotational frequency splittings of the models used in Exercise\#1 were fixed deliberately at Sun-like, twice Sun-like and three-times Sun-like values (see Section \[sec:data\] below).

Stellar-cycle effects were not included in the artificial timeseries data described in this paper. However, the asteroFLAG simulator can include these effects. The outline implementation is as follows. A commonly used indicator of surface activity on stars is the Ca II H & K index. This index is usually expressed as $R'_{\rm HK}$: the average fraction of the star’s total luminosity that is emitted in the H & K line cores (having been corrected for the photospheric component). We use scaling relations due to Noyes (1983) and Noyes et al. (1984), which require $B-V$ and the surface rate of rotation, to estimate $R'_{\rm HK}$ for our artificial stars. Scaling laws, based on fits to observations (Radick et al. 1995; Saar 