True masses using radial velocity data with Hipparcos and Gaia astrometry

Long-period companions are detected and characterised thanks to long-baseline radial velocity surveys. By combining Doppler time series with astrometry, and in particular with the proper motion anomalies technique, it is possible to put strong constraints on their orbital inclination and true mass. This work aims to present a model that combines Hipparcos and Gaia astrometric data with radial velocity measurements to constrain the orbital inclinations and true masses of long-period companions. Additionally, we re-analyse a small sample of targets that have not yet been studied using this combined approach. This research leverages the simultaneous modelling of proper motion anomalies and radial velocities in conjunction with an analysis of the sensitivity curve. This approach serves not only as a verification of the parameters but also as a means to acquire valuable insights into planetary systems. The new analyses reveal that some of the targets classified as brown dwarfs or small-mass stars have a planetary nature. HD 5388 b and HD 6718 b are likely planets with masses of 3. 2_ -0. 2 ^ +0. 3 mathrm M_ Jup and 2. 4_ -0. 2 ^ +0. 3 mathrm M_ Jup, respectively. HD 141937 b is likely a planet, but the current dataset does not allow us to firmly constrain its true mass. HD 16760 b belongs to the brown dwarf regime, and it has a probable second companion. From the analysis of 30 Ari B b, we found that it falls within the stellar regime, but the presence of an additional stellar companion could compromise the reliability of the final results. For HD 148427 b, HD 96127 b, and HIP 65891 b, we determined a range for the orbital inclinations.