Detection of Four Cold Jupiters through Combined Analyses of Radial Velocity and Astrometry Data*

Abstract Cold Jupiters play a crucial role in planet formation and dynamical evolution. Since their initial discovery around 47 UMa, they have attracted significant interest; however, their formation mechanisms remain uncertain, underscoring the need to expand the known population. In this work, we combine radial velocity (RV) data with Gaia astrometry using Hipparcos–Gaia proper-motion anomalies over a 25 yr baseline. By jointly modeling both data sets with the Markov Chain Monte Carlo 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 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msubsup> <mml:mrow> <mml:mn>7832</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>323</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>+</mml:mo> <mml:mn>463</mml:mn> </mml:mrow> </mml:msubsup> </mml:math> days and 5681 ± 42 days and dynamical masses of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msubsup> <mml:mrow> <mml:mn>5.16</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>0.47</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>+</mml:mo> <mml:mn>0.53</mml:mn> </mml:mrow> </mml:msubsup> </mml:math> M Jup and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msubsup> <mml:mrow> <mml:mn>1.2</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>0.18</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>+</mml:mo> <mml:mn>0.30</mml:mn> </mml:mrow> </mml:msubsup> </mml:math> M Jup , respectively. In multiplanet systems, HD 48265 c has a period of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msubsup> <mml:mrow> <mml:mn>10,418</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>1400</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>+</mml:mo> <mml:mn>2400</mml:mn> </mml:mrow> </mml:msubsup> </mml:math> days and a mass of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msubsup> <mml:mrow> <mml:mn>3.71</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>0.43</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>+</mml:mo> <mml:mn>0.68</mml:mn> </mml:mrow> </mml:msubsup> </mml:math> M Jup , while HD 114386 c orbits at <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msubsup> <mml:mrow> <mml:mn>444.00</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>0.88</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>+</mml:mo> <mml:mn>0.93</mml:mn> </mml:mrow> </mml:msubsup> </mml:math> days with a minimum mass of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msubsup> <mml:mrow> <mml:mn>0.37</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>0.03</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>+</mml:mo> <mml:mn>0.03</mml:mn> </mml:mrow> </mml:msubsup> </mml:math> M 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 the Extremely Large Telescope’s Mid-infrared ELT Imager and Spectrograph. We identified a Jupiter analog with the longest known orbital period among planets with masses between 0.5 and 2 M 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 RV and astrometry in exoplanet research.