  The HArps-n red Dwarf Exoplanet Survey is providing a major contribution to
the widening of the current statistics of low-mass planets, through the
in-depth analysis of precise radial velocity measurements in a narrow range of
spectral sub-types. As part of that program, we obtained radial velocity
measurements of Gl 686, an M1 dwarf at d = 8.2 pc. The analysis of data
obtained within an intensive observing campaign demonstrates that the excess
dispersion is due to a coherent signal, with a period of 15.53 d. Almost
simultaneous photometric observations were carried out within the APACHE and
EXORAP programs to characterize the stellar activity and to distinguish
periodic variations related to activity from signals due to the presence of
planetary companions, complemented also with ASAS photometric data. We took
advantage of the available radial velocity measurements for this target from
other observing campaigns. The analysis of the radial velocity composite time
series from the HIRES, HARPS and HARPS-N spectrographs, consisting of 198
measurements taken over 20 years, enabled us to address the nature of periodic
signals and also to characterize stellar physical parameters (mass,
temperature, and rotation). We report the discovery of a super-Earth orbiting
at a distance of 0.092 AU from the host star Gl 686. Gl 686 b has a minimum
mass of 7.1 +/- 0.9 MEarth and an orbital period of 15.532 +/- 0.002 d. The
analysis of the activity indexes, correlated noise through a Gaussian process
framework and photometry, provides an estimate of the stellar rotation period
at 37 d, and highlights the variability of the spot configuration during the
long timespan covering 20 yrs. The observed periodicities around 2000 d likely
point to the existence of an activity cycle.
