& Brandenburg 2002) of stellar-cycle variability in $R'_{\rm HK}$ were then used to fix the amplitudes, $\Delta R'_{\rm HK}$, and the periods of the stellar cycles. Cycle amplitudes $\Delta R'_{\rm HK}$ were then converted to equivalent p-mode parameter shifts (e.g., in frequency, power and damping) in the manner described in Chaplin et al. (2007a). There is also the provision to include effects of acoustic asphericity, from the non-homogeneous distribution of the simulated near-surface activity (again, see Chaplin et al. 2007a).

Mode visibilities were calculated according to Christensen-Dalsgaard & Gough (1982). We also allowed for limb darkening, and used the limb-darkening laws of van Hamme (1993) to describe variation of the limb-darkening properties from one star to another. These laws use the effective temperature, $T_{\rm eff}$, and the surface gravity to fix the coefficients describing the limb-darkening.

To estimate the standard deviation and timescale of the granulation, we have used scaling laws, and scaled against solar values (see also Stello et al. 2007b; Kjeldsen & Bedding, in preparation). The solar values were estimated from analysis of a multi-year timeseries of solar intensity observations made by the VIRGO/PMO6 instrument on board the *ESA/NASA* SOHO spacecraft. We have assumed that the standard deviation 