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tokens: of the solar-like stars for which rotational periods could not be determined exhibit near-solar photometric variability, R var . Here, we have provided one possible explanation for a decreased detection fraction for these stars. We investigated the compensation of the facular and spot contributions to the rotational signal in stellar photometric light curves. This compensation hampers the detection of stellar rotational periods, and contributes to a decreased detection rate for solar-like stars. Our results show that the detectability of rotational periods in stars with solar-like photometric variability crucially depends on metallicity. Hence, metallicity is one additional important parameter to consider when investigating solar-like stars, and more accurate measurements of metallicity are needed. Appendix A: Kepler rotation periods Fig. A.1. Period detection for the star KIC 10797342. Top panel : part of the full 4 yr light curve showing photometric variability. Middle panel : Lomb-Scargle periodogram showing several peaks above the 5 σ threshold (blue line). Bottom panel : auto-correlation function showing one pronounced peak indicated by the red asterisk. Table A.1. Stellar fundamental parameters and rotation periods of the 97 periodic stars in our sample. Notes. In the last two columns the apparent Kepler magnitude Kp and the absolute Gaia magnitude M G are given. We analysed stars from Table 2 in McQuillan et al. (2014) satisfying our selection criteria (i.e. the non-periodic sample) to search for potentially undetected rotation periods. The Kepler data used in this study were reduced with the Presearch Data Conditioning (PDC) pipeline (version 8.0-9.2). We appended all available Kepler quarters by dividing each light curve by its median and subtracting unity. Then we rebinned the data from 30-minute to 6-hour cadences, and analysed the full 4-year time series using Lomb-Scargle periodograms and auto-correlation functions. The Lomb-Scargle periodogram return peaks of different power on a period grid. The peak height is equivalent to the goodness of sine fit to the data, i.e. the more sinusoidal the signal, the higher the peak at this period. At the same time, the auto-correlation function (ACF) searches for self-similarity of the light curve signal, independently of the shape of the signal, and returns a peak at the best time lag (i.e. the ACF period). Since the time series of these slowly rotating solar-like stars are usually non-sinusoidal, we use the ACF period as initial period guess. For both the periodogram and the ACF, we searched for cases where both methods returned consistent peaks, with periods of up to 50 days. The term “consistent” covers different cases. In case a) the periodogram and the ACF both show a pronounced peak at roughly the same period (i.e. the periods may differ by up to five days). This case is considered the easiest one, and we do not show an example here. In case b) the ACF shows a pronounced peak and the