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While the mission’s primary goal was focused on exoplanet detection and characterization, Kepler made and continues to make extraordinary advances in stellar physics. Stellar rotation and magnetic activity are no exceptions. Kepler allowed for these properties to be determined for tens of thousands of stars from the main sequence up to the red giant branch. From photometry, this can be achieved by investigating the brightness fluctuations due to active regions, which cause surface inhomogeneities, or through asteroseismology as oscillation modes are sensitive to rotation and magnetic fields. This review summarizes the rotation and magnetic activity properties of the single main-sequence solar-like stars within the Kepler field. We contextualize the Kepler sample by comparing it to known transitions in the stellar rotation and magnetic-activity evolution, such as the convergence to the rotation sequence (from the saturated to the unsaturated regime of magnetic activity) and the Vaughan-Preston gap. While reviewing the publicly available data, we also uncover one interesting finding related to the intermediate-rotation gap seen in Kepler and other surveys. We find evidence for this rotation gap in previous ground-based data for the X-ray luminosity. Understanding the complex evolution and interplay between rotation and magnetic activity in solar-like stars is crucial, as it sheds light on fundamental processes governing stellar evolution, including the evolution of our own Sun.

Over 2,000 stars were observed for 1 month with a high enough cadence in order to look for acoustic modes during the survey phase of the Kepler mission. Solar-like oscillations have been detected in about 540 stars. The question of why no oscillations were detected in the remaining stars is still open. Previous works explained the non-detection of modes with the high level of magnetic activity of the stars. However, the sample of stars studied contained some classical pulsators and red giants that could have biased the results. In this work, we revisit this analysis on a cleaner sample of main-sequence solar-like stars that consists of 1,014 stars. First we compute the predicted amplitude of the modes of that sample and for the stars with detected oscillation and compare it to the noise at high frequency in the power spectrum. We find that the stars with detected modes have an amplitude to noise ratio larger than 0.94. We measure reliable rotation periods and the associated photometric magnetic index for 684 stars out of the full sample and in particular for 323 stars where the amplitude of the modes is predicted to be high enough to be detected. We find that among these 323 stars 32% of them have a level of magnetic activity larger than the Sun during its maximum activity, explaining the non-detection of acoustic modes. Interestingly, magnetic activity cannot be the primary reason responsible for the absence of detectable modes in the remaining 68% of the stars without acoustic modes detected and with reliable rotation periods. Thus, we investigate metallicity, inclination angle of the rotation axis, and binarity as possible causes of low mode amplitudes. Using spectroscopic observations for a subsample, we find that a low metallicity could be the reason for suppressed modes. No clear correlation with binarity nor inclination is found. We also derive the lower limit for our photometric activity index (of 20–30 ppm) below which rotation and magnetic activity are not detected. Finally, with our analysis we conclude that stars with a photometric activity index larger than 2,000 ppm have 98.3% probability of not having oscillations detected.

Magnetic activity changes the gravito-acoustic modes of solar-like stars and in particular their frequencies. There is an angular-degree dependence that is believed to be caused by the non-spherical nature of the magnetic activity in the stellar convective envelope. These changes in the mode frequencies could modify the small separation of low-degree modes (i.e., frequency difference between consecutive quadrupole and radial modes), which is sensitive to the core structure and hence to the evolutionary stage of the star. Determining global stellar parameters such as the age using mode frequencies at a given moment of the magnetic activity cycle could lead to biased results. Our estimations show that in general these errors are lower than other systematic uncertainties, but in some circumstances they can be as high as 10% in age and of a few percent in mass and radius. In addition, the frequency shifts caused by the magnetic activity are also frequency dependent. In the solar case this is a smooth function that will mostly be masked by the filtering of the so-called surface effects. However, the observations of other stars suggest that there is an oscillatory component with a period close to the one corresponding to the acoustic depth of the He II zone. This could give rise to a misdetermination of some global stellar parameters, such as the helium abundance. Our computations show that the uncertainties introduced by this effect are lower than the 3% level.