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We present follow‐up imaging and spectroscopic observations of the exoplanet host star γ Cep A, and of its low‐mass stellar companion γ Cep B. We used the lucky‐imager AstraLux at the Calar Alto observatory to follow the orbital motion of the companion around its primary, whose radial velocity (RV) was determined with spectra of the star, taken with the Échelle spectrograph FLECHAS at the University Observatory Jena. We measured the astrometry of the companion relative to the exoplanet host star in all AstraLux images and determined its apparent SDSS i′‐band photometry, for which we obtained i′=9.84±0.17 mag. Using stellar evolutionary models and the Gaia parallax of the exoplanet host star, we derived the mass of γ Cep B to be 0.39 ± 0.03 M⊙. This is in good agreement with the mass of the companion that we derived from its near‐infrared photometry given in the literature. With the detection limit reached in our AstraLux images, we explored the detection space of potential additional companions in the γ Cep binary system. In the background limited region at angular separations larger than 5 arcsec (or 69 au of projected separation) companions down to 0.11 M⊙ are detectable around the bright exoplanet host star. The radial field of view, fully covered by our AstraLux observations, exhibits a radius of 11.2 arcsec. This allows the detection of companions with projected separations up to 155 au. However, except for γ Cep B, no additional companions could be imaged with AstraLux around the exoplanet host star. We redetermined the orbital solution of the γ Cep binary system with the new AstraLux astrometry of γ Cep B and the additional radial velocities of γ Cep A, obtained from our FLECHAS spectroscopy of the star, combined with astrometric and RV data from the literature. The determined Keplerian orbital elements were used to derive the system parameters and to calculate specific future ephemeris for this intriguing exoplanet host binary star system. [ABSTRACT FROM AUTHOR]

Dark spots on the surface of active stars produce changes in the shapes of the spectral lines that mimic spurious Doppler shifts, compromising the detection of small planets by means of the radial velocity (RV) technique. Modeling the spot‐driven RV variability (known as "jitter") and how it affects the RV data sets is therefore crucial to design efficient activity‐filtering techniques and inform observing strategies. Here, we characterize starspots and simulate the RV curves induced by them to determine typical jitter amplitudes for a representative sample of 15 known host stars spanning between F and M spectral types. We collect information on the logRHK′ activity index from the literature for 205 stars and, due to a lack of data in the temperature range 4,000–4,500 K, we measure it for 10 stars using archival data. Additional stellar parameters required for the simulations are collected from the literature or constrained by observational data in order to derive realistic estimates. Our results can be used as reference to determine typical peak‐to‐peak spot‐induced RV jitter in the visible domain that can be expected when targeting host stars with different properties. [ABSTRACT FROM AUTHOR]