The GAPS programme with HARPS-N at TNG XI. Pr~0211 in M~44: the first multi-planet system in an open cluster

Open cluster (OC) stars share the same age and metallicity, and, in general, their age and mass can be estimated with higher precision than for field stars. For this reason, OCs are considered an important laboratory to study the relation between the physical properties of the planets and those of their host stars, and the evolution of planetary systems. We started an observational campaign within the GAPS collaboration to search for and characterize planets in OCs We monitored the Praesepe member Pr0211 to improve the eccentricity of the Hot-Jupiter (HJ) already known to orbit this star and search for additional planets. An eccentric orbit for the HJ would support a planet-planet scattering process after its formation. From 2012 to 2015, we collected 70 radial velocity (RV) measurements with HARPS-N and 36 with TRES of Pr0211. Simultaneous photometric observations were carried out with the robotic STELLA telescope in order to characterize the stellar activity. We discovered a long-term trend in the RV residuals that we show to be due to the presence of a second, massive, outer planet. Orbital parameters for the two planets are derived by simultaneously fitting RVs and photometric light curves, with the activity signal modelled as a series of sinusoids at the rotational period of the star and its harmonics. We confirm that Pr0211b has a nearly circular orbit ($e = 0.02 \pm 0.01$), with an improvement of a factor two with respect to the previous determination of its eccentricity, and estimate that Pr0211c has a mass $M_p\sin i = 7.9 \pm 0.2 M_J$, a period $P>$3500 days and a very eccentric orbit ($e>$0.60). Such peculiar systems may be typical of open clusters if the planet-planet scattering phase leading to the formation of HJs is caused by stellar encounters rather than unstable primordial orbits. Pr0211 is the first multi-planet system discovered around an OC star. (abridged)