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We present the discovery of four new long-period planets within the HARPShigh-precision sample: \object{HD137388}b ($M\sin{i}$ = 0.22 $M_J$),\object{HD204941}b ($M\sin{i}$ = 0.27 $M_J$), \object{HD7199}b ($M\sin{i}$ =0.29 $M_J$), \object{HD7449}b ($M\sin{i}$ = 1.04 $M_J$). A long-periodcompanion, probably a second planet, is also found orbiting HD7449. Planetsaround HD137388, HD204941, and HD7199 have rather low eccentricities (less than0.4) relative to the 0.82 eccentricity of HD7449b. {All these planets werediscovered even though their hosting stars have clear signs of activity.Solar-like magnetic cycles, characterized by long-term activity variations, canbe seen for HD137388, HD204941 and HD7199, whereas the measurements of HD7449reveal a short-term activity variation, most probably induced by magneticfeatures on the stellar surface. We confirm that magnetic cycles induce along-term radial velocity variation and propose a method to reduce considerablythe associated noise.} The procedure consists of fitting the activity index andapplying the same solution to the radial velocities because a linearcorrelation between the activity index and the radial velocity is found. Testedon HD137388, HD204941, and HD7199, this correction reduces considerably thestellar noise induced by magnetic cycles and allows us to derive precisely theorbital parameters of planetary companions.

astronomy and astrophysics

The HARPS search for southern extra-solar planets. XXX. Planetary  systems around stars with solar-like magnetic cycles and short-term activity  variation