  The detectability of exoplanets and the determination of their projected mass
in radial velocity are affected by stellar magnetic activity and photospheric
dynamics. The effect of granulation, and even more so of supergranulation, has
been shown to be significant in the solar case. Our study is aimed at
quantifying the impact of these flows for other stars and estimating how such
contributions affect their performance. We analysed a broad array of extended
synthetic time series that model these processes for main sequence stars with
spectral types from F6 to K4, focusing on Earth-mass planets orbiting within
the habitable zone around those stars. We estimated the expected detection
rates and detection limits, and performed blind tests. We find that both
granulation and supergranulation on these stars significantly affect planet
mass characterisation in radial velocity when performing a follow-up of a
transit detection, with uncertainties sometimes below 20% for a 1 MEarth, but
much larger for supergranulation. For granulation and low levels of
supergranulation, the detection rates are good for K and late G stars (if the
number of points is large), but poor for more massive stars. The highest level
of supergranulation leads to a very poor performance, even for K stars; this is
both due to low detection rates and to high levels of false positives, even for
a very dense temporal sampling over ten years. False positive levels estimated
from standard false alarm probabilities sometimes significantly overestimate or
underestimate the true level, depending on the number of points. We conclude
that granulation and supergranulation significantly affect the performance of
exoplanet detectability. Future works will focus on improving the following
aspects: decreasing the number of false positives, increasing detection rates,
and improving the false alarm probability estimations from observations.
