The HARPS search for southern extra-solar planets. XXXVI. Eight HARPS multi-planet systems hosting 20 super-Earth and Neptune-mass companions

We present radial-velocity measurement of eight stars observed with the HARPS Echelle spectrograph mounted on the 3.6-m telescope in La Silla (ESO, Chile). Data span more than ten years and highlight the long-term stability of the instrument. We search for potential planets orbiting HD20003, HD20781, HD21693, HD31527, HD45184, HD51608, HD134060 and HD136352 to increase the number of known planetary systems and thus better constrain exoplanet statistics. After a preliminary phase looking for signals using generalized Lomb-Scargle periodograms, we perform a careful analysis of all signals to separate \emph{bona-fide} planets from spurious signals induced by stellar activity and instrumental systematics. We finally secure the detection of all planets using the efficient MCMC available on the Data and Analysis Center for Exoplanets (DACE web-platform), using model comparison whenever necessary. In total, we report the detection of twenty new super-Earth to Neptune-mass planets, with minimum masses ranging from 2 to 30 M$_{\rm Earth}$, and periods ranging from 3 to 1300 days. By including CORALIE and HARPS measurements of HD20782 to the already published data, we also improve the characterization of the extremely eccentric Jupiter orbiting this host.