Hint of curvature in the orbital motion of the exoplanet 51 Eridani b using 3 years of VLT/SPHERE monitoring

Context. The 51 Eridani system harbors a complex architecture with its primary star forming a hierarchical system with the binary GJ 3305AB at a projected separation of 2000 au, a giant planet orbitingthe primary star at 13 au, and a low-mass debris diskaround the primary star with possibly a cold component and a warm component inferred from the spectral energy distribution. Aims. We aim to better constrain the orbitalparameters of the known giant planet. Methods. We monitored the system over three years from 2015 to 2018 with the VLT/SPHERE exoplanetimaging instrument. Results. We measure an orbital motionfor the planetof ~130 mas with a slightly decreasing separation (~10 mas) and find a hint of curvature. This potential curvature is further supported at 3$\sigma$ significance when including literature GPI astrometrycorrected for calibration systematics. Fits of the SPHERE and GPI data using three complementary approaches provide broadly similar results. The data suggest an orbital periodof 32$^{+17}_{-9}$ yr (i.e. 12$^{+4}_{-2}$ au in semi-major axis), an inclination of 133$^{+14}_{-7}$ deg, an eccentricity of 0.45$^{+0.10}_{-0.15}$, and an argument of periastron passage of 87$^{+34}_{-30}$ deg [mod 180 deg]. The time at periastron passage and the longitude of node exhibit bimodal distributions because we do not detect yet if the planetis accelerating or decelerating along its orbit. Given the inclinations of the planet's orbitand of the stellar rotationaxis (134-144 deg), we infer alignment or misalignment within 18 deg for the star- planetspin- orbit. Further astrometric monitoring in the next 3-4 years is required to confirm at a higher significance the curvature in the planet's motion, determine if the planetis accelerating or decelerating on its orbit, and further constrain its orbitalparameters and the star- planetspin- orbit.