Title: Closeby Habitable Exoplanet Survey (CHES). I. Astrometric Noise and Planetary Detection Efficiency due to Stellar Spots and Faculae

Abstract: The Closeby Habitable Exoplanet Survey (CHES) is dedicated to the astrometric exploration for habitable-zone Earth-like planets orbiting solar-type stars in close proximity, achieving unprecedented micro-arcsecond precision. Given the elevated precision, thorough consideration of photocenter jitters induced by stellar activity becomes imperative. This study endeavors to model the stellar activity of solar-type stars, compute astrometric noise, and delineate the detection limits of habitable planets within the astrometric domain. Simulations were conducted for identified primary targets of CHES, involving the generation of simulated observed data for astrometry and photometry, accounting for the impact of stellar activity. Estimation of activity levels in our samples was achieved through chromospheric activity indices, revealing that over 90% of stars exhibited photocenter jitters below 1 $\mu\mathrm{as}$. Notably, certain proximate stars, such as $\alpha$ Cen A and B, displayed more discernible noise arising from stellar activity. Subsequent tests were performed to evaluate detection performance, unveiling that stellar activity tends to have a less pronounced impact on planetary detectability for the majority of stars. Approximately 95% of targets demonstrated a detection efficiency exceeding 80%. However, for several cold stars, e.g., HD 32450 and HD 21531, with the habitable zones close to the stars, a reduction in detection efficiency was observed. These findings offer invaluable insights into the intricate interplay between stellar activity and astrometric precision, significantly advancing our understanding in the search for habitable planets.