Planets around stars in young nearby associations. Radial velocity searches: a feasibility study and first results

International audienceContext. Stars in young nearby associations are the only targets that allow giant planet searches in the near future, at all separations by coupling indirect techniques, such as radial velocity (RV) and deep imaging. These stars are first priority targets for the forthcoming planet imagers on eight- to ten-metre class telescopes. Young stars rotate more rapidly and are more active than their older counterparts. Both effects can limit the ability to detect planets using RV. Aims: We wish to explore the planet detection abilities of a representative sample of stars in close and young associations with RV data and to explore the complementarity between this technique and direct imaging. Methods: We observed 26 such targets with spectral types from A to K and ages from 8 to 300 Myr with HARPS. We computed the detection limits with two methods, in particular, a method we have recently developed that takes the frequency distribution of the RV variations into account. We also attempted to improve the detection limits in a few cases by correcting for the stellar activity. Results: Our A-type stars RV show high-frequency variations due to pulsations, while our F-K stars clearly show activity with more or less complex patterns. For F-K stars, the RV jitter and vsini rapidly decrease with star age. The data allow us to search for planets with periods typically ranging from 1 day to 100 days, and up to more than 500 days in a few cases. Within the present detection limits, no planet was found in our sample. For the bulk of our F-K stars, the detection limits fall to sub-Jupiter masses. We show that these limits can be significantly improved by correcting even partially for stellar activity, down to a few Neptune masses for the least active stars. The detection limits on A-type stars can be significantly improved, down to a few Jupiter-mass planets, provided an appropriate observing strategy. We finally show the tremendous potential of coupling RV and adaptive-optics deep imaging results. Conclusions: The RV technique allows the detection of planets lighter than Jupiter, reaching a few Neptune masses around young stars aged typically 30 Myr or more. Detection limits increase at younger ages, but (sub-)Jupiter mass planets are still detectable. In the next few years, using complementary techniques will allow a full exploration of the Jupiter-mass planets' content of many of these stars. Based on observations made with the ESO3.6m/Harps spectrograph at La Silla.083.C-0794(ABCD); 084.C-1039(A); 084.C-1024(A).Appendices A and B are available in electronic form at http://www.aanda.orgTables of radial velocities are only available at the CDS via anonymous ftp to http://cdsarc.u-strasbg.fr (ftp://130.79.128.5) or via http://cdsarc.u-strasbg.fr/viz-bin/qcat?J/A+A/559/A83