  Astrometry is less sensitive to stellar activity than the radial velocity
technique when attempting to detect Earth mass planets in the habitable zone of
solar-type stars. This is due to a smaller number of physical processes
affecting the signal, and a larger ratio of the amplitude of the planetary
signal to the stellar signal. A few high-precision astrometric missions have
therefore been proposed over the past two decades. We aim to re-estimate the
detection limits in astrometry for the nearby stars which are the main targets
proposed for the THEIA astrometric mission, the most elaborate mission to
search for planets, and to characterise its performance. This analysis is
performed for the 55 F-G-K stars in the THEIA sample. We used realistic
simulations of stellar activity and selected those that correspond best to each
star in terms of spectral type and average activity level. Then, we performed
blind tests to estimate the performance. We find worse detection limits
compared to those previously obtained for that sample based on a careful
analysis of the false positive rate, with values in the Earth-mass regime for
most stars of the sample. The difference is attributed to the fact that we
analysed full time series, adapted to each star in the sample, rather than
using the expected solar jitter only. Although these detection limits have a
relatively low signal-to-noise ratio, the fitted parameters have small
uncertainties. We confirm the low impact of stellar activity on exoplanet
detectability for solar-type stars, although it plays a significant role for
the closest stars such as alpha Cen A and B. However, for the few stars in the
sample with a habitable zone corresponding to long periods, namely subgiants,
the THEIA observational strategy is not well adapted and should prevent the
detection of planets in the habitable zone, unless a longer mission can be
proposed.
