The magnetic activity of the Sun and other stars causes their brightness to vary. We investigated how typical the Sun’s variability is compared with other solar-like stars, i.e., those with near-solar effective temperatures and rotation periods. By combining 4 years of photometric observations from the Kepler space telescope with astrometric data from the Gaia spacecraft, we were able to measure photometric variabilities of 369 solar-like stars. Most of those with well-determined rotation periods showed higher variability than the Sun and are therefore considerably more active. These stars appear nearly identical to the Sun except for their higher variability. Therefore, we speculate that the Sun could potentially also go through epochs of such high variability.

Context. Considerable effort has been put into using light curves observed by space telescopes such as CoRoT, Kepler and TESS for determining stellar rotation periods. While rotation periods of active stars can be reliably determined, the light curves of many older and less active stars (e.g. stars similar to the Sun) are quite irregular, which hampers determination of their periods. Aims. We examine the factors causing the irregularities in stellar brightness variations and develop a method for determining rotation periods of low activity stars with irregular light curves. Methods. We extend the Spectral And Total Irradiance Reconstruction (SATIRE) approach for modelling solar brightness variations to Sun-like stars. We calculate the power spectra of stellar brightness variations for various combinations of parameters defining the surface configuration and evolution of stellar magnetic features. Results. The short lifetime of spots in comparison to the stellar rotation period as well as the interplay between spot and facular contributions to brightness variations of stars with near solar activity cause irregularities in their light curves. The power spectra of such stars often lack a peak associated with the rotation period. Nevertheless, the rotation period can still be determined by measuring the period where the concavity of the power spectrum plotted in the log-log scale changes sign, i.e. by identifying the position of the inflection point. Conclusions. The inflection point of the (log-log) power spectrum is found to be a new diagnostic for stellar rotation periods that is shown to work even in cases where the power spectrum shows no peak at the rotation rate.

Context. Characterizing the relation between stellar photometric variability and radial velocity (RV) jitter can help us to better understand the physics behind these phenomena. The current and upcoming high precision photometric surveys such as TESS, CHEOPS, and PLATO will provide the community with thousands of new exoplanet candidates. As a consequence, the presence of such a correlation is crucial in selecting the targets with the lowest RV jitter for efficient RV follow-up of exoplanetary candidates. Studies of this type are also crucial to design optimized observational strategies to mitigate RV jitter when searching for Earth-mass exoplanets. Aims. Our goal is to assess the correlation between high-precision photometric variability measurements and high-precision RV jitter over different time scales. Methods. We analyze 171 G, K, and M stars with available TESS high precision photometric time-series and HARPS precise RVs. We derived the stellar parameters for the stars in our sample and measured the RV jitter and photometric variability. We also estimated chromospheric Ca II H & K activity indicator log(RHK′), v sin i, and the stellar rotational period. Finally, we evaluate how different stellar parameters and an RV sampling subset can have an impact on the potential correlations. Results. We find a varying correlation between the photometric variability and RV jitter as function of time intervals between the TESS photometric observation and HARPS RV. As the time intervals of the observations considered for the analysis increases, the correlation value and significance becomes smaller and weaker, to the point that it becomes negligible. We also find that for stars with a photometric variability above 6.5 ppt the correlation is significantly stronger. We show that such a result can be due to the transition between the spot-dominated and the faculae-dominated regime. We quantified the correlations and updated the relationship between chromospheric Ca II H & K activity indicator log(RHK′) and RV jitter.