Detection of four cold Jupiters through combined analyses of radial velocity and astrometry data

Cold Jupiters play a crucial role in planet formation and dynamical evolution. Since their initial discovery around 47 UMa, they have attracted significant interest, yet their formation mechanisms remain uncertain, underscoring the need to expand the known population. In this work, we combine RV data with Gaia astrometry using Hipparcos-Gaia proper-motion anomalies over a 25-year baseline. By jointly modeling both datasets with the MCMC framework, we constrain planetary masses, orbital inclinations, and three-dimensional orbital architectures. This reduces RV degeneracies and improves mass determinations. Four cold Jupiters are reported: HD 68475 b and HD 100508 b are each the first confirmed planet in their systems, with orbital periods $7832_{-323}^{+463}$ d and $5681\pm42$ d and dynamical masses of $5.16_{-0.47}^{+0.53} M_{\text{Jup}}$ and $1.2_{-0.18}^{+0.30} M_{\text{Jup}}$, respectively. In multi-planet systems, HD 48265 c has a period of $10418_{-1400}^{+2400}$ d and a mass of $3.71_{-0.43}^{+0.68} M_{\text{Jup}}$, while HD 114386 c orbits at $444.00_{-0.88}^{+0.93}$ d with a minimum mass of $0.37 \pm 0.03 M_{\text{Jup}}$. The two planets in the HD 48265 system may exhibit a significant mutual inclination, making it a target for testing the von-Zeipel-Kozai-Lidov mechanism. HD 68475 b is a promising candidate for future direct imaging with ELT/METIS. We identified a Jupiter analog with the longest known orbital period among planets with masses between 0.5 and 2 $M_{\text{Jup}}$, implying that a substantial population of cold Jupiters likely awaits discovery by Gaia. This study expands the sample of cold Jupiters with constrained orbits and dynamical masses, demonstrating the value of combining radial velocity and astrometry in exoplanet research.