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

Context. A number of high-precision time series have recently become available for many stars as a result of data from CoRoT, Kepler , and TESS. These data have been widely used to study stellar activity. Photometry provides information that is integrated over the stellar disk. Therefore, there are many degeneracies between spots and plages or sizes and contrasts. In addition, it is important to relate activity indicators, derived from photometric light curves, to other indicators (Log R ′ HK and radial velocities). Aims. Our aim is to understand how to relate photometric variability to physical parameters in order to help the interpretation of these observations. Methods. We used a large number of synthetic time series of brightness variations for old main sequence stars within the F6-K4 range. Simultaneously, we computed using consistent modeling for radial velocity, astrometry, and chromospheric emission. We analyzed these time series to study the effect of the star spectral type on brightness variability, the relationship between brightness variability and chromospheric emission, and the interpretation of brightness variability as a function of spot and plage properties. We then studied spot-dominated or plage-dominated regimes. Results. We find that within our range of activity levels, the brightness variability increases toward low-mass stars, as suggested by Kepler results. However, many elements can create an interpretation bias. Brightness variability roughly correlates to Log R ′ HK level. There is, however, a large dispersion in this relationship, mostly caused by spot contrast and inclination. It is also directly related to the number of structures, and we show that it can not be interpreted solely in terms of spot sizes. Finally, a detailed analysis of its relation with Log R ′ HK shows that in the activity range of old main-sequence stars, we can obtain both spot or plage dominated regimes, as was shown by observations in previous works. The same star can also be observed in both regimes depending on inclination. Furthermore, only strong correlations between chromospheric emission and brightness variability are significant. Conclusions. 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.