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tokens: Pillet et al. (1993) , Baumann Solanki (2005) , Lagrange et al. (2010) , and Meunier et al. (2010a) . Faculae properties. The faculae properties were similar to those used in Borgniet et al. (2015) , which included the ratio distribution between plage and spot sizes, and decay rates (here we considered the plages that were produced each time we generated a spot). Network properties. Network properties were similar to those used in Borgniet et al. (2015) , which include the diffusion coeficient from Schrijver (2001) , the fraction of plage flux that was used to build the network, and the decay rate. The diffusion coefficient was scaled with the amplitude of the convective blueshift, as discussed in Sect. 2.7 . 3 From structures to observables 3.1 Filling factor and photometric and radial velocity time series Because of the huge number of simulations, it is not possible to compute the observables as done in our previous work ( Lagrange et al. 2010 ; Meunier et al. 2010a ; Borgniet et al. 2015 ), in which we computed maps, then spectra, and finally RVs (and other observables) in the same way as for stellar observations. We therefore simplified the computations as follows: we directly summed the contribution from each structure to the RV, photometry, and astrometry. The filling factors were also computed. This implies that we assumed that the structures are point-like, which means that we did not need to check for superimpositions. This is different to what was done in Borgniet et al. (2015) . This also means that we neglected any geometrical effect that would be due to a large area covered by a structure, which is a good assumption because we modeled relatively quiet stars with moderate structure sizes. The assumption is very good for spots because the maximum size of a spot would correspond to a radius of about 3° (which would be a very rare case; typical spots are much smaller, see Table E.1 ). Plages may cover a larger area, which is expected to add a second-order distortion to an ideal time series: in most cases, the extreme sections of a structure (east and west) are expected to produce a signal that is very similar to the central part of the structures on average; in addition, we considered at each time step an irregular decay of the structures that has a random amplitude, so that the distortion produced by the assumption would not be identifiable given this other source of irregularity. The same structures were used for all stellar inclinations. The formulae are provided in Appendix C . We recall that we chose to study different laws for several of our parameters (as summarized in Fig. 1 ), so that several time series of spots, plages, and network features were produced for each of the 141 points of the 2D grid in ( B – V , Log ), each corresponding to a different parameter set ( Table E.1 ). This leads to 11 421 time series, or 22 842 when the two levels for Tspot are considered for each inclination and observable, hence a total of 228