Activity time series of old stars from late F to early K IV. Diagnosis from photometry

High-precision time series have recently become available for many stars as a result of data from CoRoT, Kepler, and TESS and have been widely used to study stellar activity. They provide information integrated over the stellar disk, hence many degeneracies between spots and plages or sizes and contrasts. Our aim is to understand how to relate photometric variability to physical parameters in order to help the interpretation of these observations. We computed a large number of synthetic time series of brightness variations for old MS stars within the F6-K4 range, using consistent modeling for radial velocity, astrometry, and LogR'HK. We analyzed these time series to study the effect of the star spectral type on brightness variability, the relationship between brightness variability and LogR'HK, the interpretation of brightness variability as a function of spot and plage properties, and the spot-dominated or plage-dominated regimes. Within our range of activity levels, the brightness variability increases toward low-mass stars, as suggested by Kepler results. Brightness variability roughly correlates to LogR'HK level, but with a large dispersion, caused by spot contrast and inclination. It is also directly related to the number of structures, and we show that it cannot be interpreted solely in terms of spot sizes. In the activity range of old main-sequence stars, we can obtain both spot or plage dominated regimes, as in observation. The same star can be observed in both regimes depending on inclination. Only strong correlations between LogR'HK and brightness variability are significant. Our realistic time series proves to be extremely useful when interpreting observations and understanding their limitations, most notably in terms of activity interpretation. Inclination is crucial and affects many properties, such as amplitudes and the respective role of spots and plages.