  Convective motions at the stellar surface generate a stochastic colored noise
source in the radial velocity (RV) data. This noise impedes the detection of
small exoplanets. Moreover, the unknown statistics (amplitude, distribution)
related to this noise make it difficult to estimate the false alarm probability
(FAP) for exoplanet detection tests. In this paper, we investigate the
possibility of using 3D magneto-hydrodynamical simulations (MHD) of stellar
convection to design detection methods that can provide both a reliable
estimate of the FAP and a high detection power. We tested the realism of 3D
simulations in producing solar RV by comparing them with the observed disk
integrated velocities taken by the GOLF instrument on board the SOHO
spacecraft. We presented a new detection method based on periodograms
standardized by these simulated time series, applying several detection tests
to these standarized periodograms. The power spectral density of the 3D
synthetic convective noise is consistent with solar RV observations for short
periods. For regularly sampled observations, the analytic expressions of FAP
derived for several statistical tests applied to the periodogram standardized
by 3D simulation noise are accurate. The adaptive tests considered in this work
(Higher-Criticism, Berk-Jones), which are new in the exoplanet field, may offer
better detection performance than classical tests (based on the highest
periodogram value) in the case of multi-planetary systems and planets with
eccentric orbits. 3D MHD simulations are now mature enough to produce reliable
synthetic time series of the convective noise affecting RV data. These series
can be used to access to the statistics of this noise and derive accurate FAP
of tests that are a critical element in the detection of exoplanets down to the
cm/s level.
