  Stellar activity strongly affects and may prevent the detection of Earth-mass
planets in the habitable zone of solar-type stars with radial velocity
technics. Astrometry is in principle less sensitive to stellar activity because
the situation is more favourable: the stellar astrometric signal is expected to
be fainter than the planetary astrometric signal compared to radial velocities.
We quantify the effect of stellar activity on high-precision astrometry when
Earth-mass planets are searched for in the habitable zone around old
main-sequence solar-type stars. We used a very large set of magnetic activity
synthetic time series to characterise the properties of the stellar astrometric
signal. We then studied the detectability of exoplanets based on different
approaches: first based on the theoretical level of false positives derived
from the synthetic time series, and then with blind tests for old main-sequence
F6-K4 stars. The amplitude of the signal can be up to a few times the solar
value depending on the assumptions made for activity level, spectral type, and
spot contrast. The detection rates for 1 MEarth planets are very good, however,
with extremely low false-positive rates in the habitable zone for stars in the
F6-K4 range at 10 pc. The standard false-alarm probability using classical
bootstrapping on the time series strongly overestimates the false-positive
level. This affects the detection rates. We conclude that if technological
challenges can be overcome and very high precision is reached, astrometry is
much more suitable for detecting Earth-mass planets in the habitable zone
around nearby solar-type stars than radial velocity, and detection rates are
much higher for this range of planetary masses and periods when astrometric
techniques are used than with radial velocity techniques.
