Planetary detection limits taking into account stellar noise II. Effect of stellar spot groups on radial-velocities

Context. The detection of small mass planets with the radial-velocity technique is now confronted with the interference of stellar noise. HARPS can now reach a precision below the meter-per-second, which corresponds to the amplitudes of different stellar perturbations, such as oscillation, granulation, and activity. Aims. Solar spot groups induced by activity produce a radial-velocity noise of a few meter-per-second. The aim of this paper is to simulate this activity and calculate detection limits according to different observational strategies. Methods. Based on Sun observations, we reproduce the evolution of spot groups on the surface of a rotating star. We then calculate the radial-velocity effect induced by these spot groups as a function of time. Taking into account oscillation, granulation, activity, and a HARPS instrumental error of 80 cm s(-1), we simulate the effect of different observational strategies in order to efficiently reduce all sources of noise. Results. Applying three measurements per night of 10 min every three days, 10 nights a month seems the best tested strategy. Depending on the level of activity considered, from log R-HK' = -5 to -4.75, this strategy would allow us to find planets of 2.5 to 3.5 M-circle plus in the habitable zone of a K1V dwarf. Using Bern's model of planetary formation, we estimate that for the same range of activity level, 15 to 35% of the planets between 1 and 5 M-circle plus and with a period between 100 and 200 days should be found with HARPS. A comparison between the performance of HARPS and ESPRESSO is also emphasized by our simulations. Using the same optimized strategy, ESPRESSO could find 1.3 M-circle plus planets in the habitable zone of K dwarfs. In addition, 80% of planets with mass between 1 and 5 M-circle plus and with a period between 100 and 200 days could be detected.