The GAPS Programme at TNG LVIII. Two multi-planet systems with long-period substellar companions around metal-rich stars

Context. Due to observational biases, a large fraction of known exoplanets are short-period objects. However, the search for planets began more than 20 yr ago, and so it is already possible - with the use of a suitable dataset - to begin exploring a wider range of the parameter space, such as that encompassing long-period planets. Aims. The aim of this paper is to investigate the presence of long-period giant companions in two systems where one or more planets are already known and for which a long-term trend in the radial velocities (RVs) was noted in previous works. Methods. Over the last 11 yr, we have collected 122 spectra of HD 75898 and 72 spectra of HD 11506 with the High Accuracy Radial velocity Planet Searcher for the Northern hemisphere (HARPS-N) in the framework of the Global Architecture of Planetary Systems (GAPS) project, from which we derived precise RV and activity indicator measurements. Additional RV data from the High-Resolution Echelle Spectrometer (HIRES) are also used here to increase the total time span. For our RV analysis, we used PyORBIT, an advanced Python tool for the simultaneous Bayesian analysis of RVs and stellar activity indicators. In addition, we used astrometric (Gaia DR3) and imaging archive data to complete our analysis. In particular, we combined RVs and astrometry to better constrain the mass and period of the new long-period companions. Results. We find evidence for one additional long-period companion (gas giant planet or brown dwarf) in both systems considered. The new candidate for HD 75898 has a period of roughly 18 yr and a true mass of around 8.5 M-j. For HD 11506, we confirm the new object (planet d) recently announced using HIRES data but we find that the period and true mass are both almost double the values based on HIRES results (P-d similar to 72 yr, M-d similar to 13 Mj). In addition, for HD 75898, we also find evidence of an activity cycle affecting RVs with a period of one order of magnitude lower than found in the literature.