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 (MHD) simulations 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⁻¹ level.