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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 obtainedi  ′   =  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.

Follow‐up observations of the binary system γ Cep