  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.
