Context. Magnetic activity and surface flows at different scales pertub radial velocity measurements. This affects the detectability of low-mass exoplanets. Aims. In these flows, the effect of supergranulation is not as well characterized as the other flows, and we wish to estimate its effect on the detection of Earth-like planets in the habitable zone of Sun-like stars. Methods. We produced time series of radial velocities due to oscillations, granulation, and supergranulation, and estimated the detection limit for a G2 star and a period of 300 days. We also studied in detail the behavior of the power when the signal of a 1 MEarth planet was superposed on the signal from the stellar flows. Results. We find that the detection rate does not reach 100% except for the supergranulation level we assume, which is still optimistic, and for an excellent sampling. Conclusions. We conclude that with current knowledge, it is a very challenging task to find Earth twins around Sun-like stars with our current capabilities.
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