The HARPS search for southern extra-solar planets. XXXI. Magnetic activity cycles in solar-type stars: statistics and impact on precise radial velocities

Context. Searching for extrasolar planets through radial velocity measurements relies on the stability of stellar photospheres. Aims. We aim at characterizing the statistical properties of magnetic activity cycles, and studying their impact on spectroscopic measurements such as radial velocities, line bisectors and line shapes. Methods. We use data from the HARPS high-precision planet-search sample comprising 304 FGK stars followed over about 7 years. We obtain high-precision Ca II H&K chromospheric activity measurements and convert them to R'HK indices using an updated calibration taking into account stellar metallicity. We study R'HK variability as a function of time and search for possible correlations with radial velocities and line shape parameters. Results. We classify stars according to the magnitude and timescale of the Ca II H&K variability, and identify activity cycles whenever possible. We find that 39+/-8% of old solar-type stars in the solar neighborhood do not show any activity cycles (or only very weak ones), while 61+/-8% do have one. Non-cycling stars are almost only found among G dwarfs and at mean activity levels log R'HK < -4.95. Magnetic cycle amplitude generally decreases with decreasing activity level. A significant fraction of stars exhibit small variations in radial velocities and line shape parameters that are correlated with activity cycles. The sensitivity of radial velocities to magnetic cycles increases towards hotter stars, while late K dwarfs are almost insensitive. Conclusions. Activity cycles do induce long-period, low-amplitude radial velocity variations, at levels up to ~25 m/s. Caution is therefore mandatory when searching for long-period exoplanets. However, these effects can be corrected to high precision by detrending the radial velocity data using simultaneous measurements of Ca II H&K flux and line shape parameters. (Abridged)