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$\epsilon$~Eridani is a young planetary system hosting a complex multi-beltdebris disk and a confirmed Jupiter-like planet orbiting at 3.48 AU from itshost star. Its age and architecture are thus reminiscent of the early SolarSystem. The most recent study of Mawet et al. 2019, which combined radialvelocity (RV) data and Ms-band direct imaging upper limits, started toconstrain the planet's orbital parameters and mass, but are still affected bylarge error bars and degeneracies. Here we make use of the most recent datacompilation from three different techniques to further refine$\epsilon$~Eridani~b's properties: RVs, absolute astrometry measurements fromthe Hipparcos~and Gaia~missions, and new Keck/NIRC2 Ms-band vortex coronagraphimages. We combine this data in a Bayesian framework. We find a new mass, $M_b$= $0.66_{-0.09}^{+0.12}$~M$_{Jup}$, and inclination, $i$ =$77.95_{-21.06}^{\circ+28.50}$, with at least a factor 2 improvement overprevious uncertainties. We also report updated constraints on the longitude ofthe ascending node, the argument of the periastron, and the time of periastronpassage. With these updated parameters, we can better predict the position ofthe planet at any past and future epoch, which can greatly help define thestrategy and planning of future observations and with subsequent data analysis.In particular, these results can assist the search for a direct detection withJWST and the Nancy Grace Roman Space Telescope's coronagraph instrument (CGI).

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Constraining the Orbit and Mass of epsilon Eridani b with Radial  Velocities, Hipparcos IAD-Gaia DR2 Astrometry, and Multi-epoch Vortex  Coronagraphy Upper Limits