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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 orbiting the primary star at 13 au, and a low-mass debris disk around the primary star with possible cold and warm components inferred from the spectral energy distribution. Aims. We aim to better constrain the orbital parameters of the known giant planet. Methods. We monitored the system over three years from 2015 to 2018 with the Spectro-Polarimetric High-contrast Exoplanet REsearch (SPHERE) instrument at the Very Large Telescope (VET). Results. We measure an orbital motion for the planet of similar to 130 mas with a slightly decreasing separation (similar to 10 mas) and find a hint of curvature. This potential curvature is further supported at 3 sigma significance when including literature Gemini Planet Imager (GPI) astrometry corrected for calibration systematics. Fits of the SPHERE and GPI data using three complementary approaches provide broadly similar results. The data suggest an orbital period of 32(-9)(+17) yr (i.e., 12(-2)(+4), au in semi-major axis), an inclination of 133(-7)(+1)(4) deg, an eccentricity of 0.45(-0.15)(+0.10), and an argument of periastron passage of 87(-30)(+34) deg [mod 180 degrees]. The time at periastron passage and the longitude of node exhibit bimodal distributions because we do not yet detect whether the planet is accelerating or decelerating along its orbit. Given the inclinations of the orbit and of the stellar rotation axis (134-144 degrees), we infer alignment or misalignment within 18 degrees for the star-planet spin-orbit. Further astrometric monitoring in the next 3-4 yr is required to confirm at a higher significance the curvature in the motion of the planet, determine if the planet is accelerating or decelerating on its orbit, and further constrain its orbital parameters and the star-planet spin-orbit.

The nearby Herbig Be star HD 100546 is known to be a laboratory for the study of protoplanets and their relation with the circum stellar disk, which is carved by at least two gaps. We observed the HD 100546 environment with high-contrast imaging exploiting several different observing modes of SPHERE, including data sets with and without coronagraphs, dual band imaging, integral field spectroscopy and polarimetry. The picture emerging from these different data sets is complex. Flux-conservative algorithm images clearly show the disk up to 200 au. More aggressive algorithms reveal several rings and warped arms that are seen overlapping the main disk. Some of these structures are found to lie at considerable height over the disk mid-plane at about 30 au. Our images demon-strate that the brightest wings close to the star in the near side of the disk are a unique structure, corresponding to the outer edge of the intermediate disk at similar to 40 au. Modeling of the scattered light from the disk with a geometrical algorithm reveals that a moderately thin structure (H/r = 0.18 at 40 au) can well reproduce the light distribution in the flux-conservative images. We suggest that the gap between 44 and 113 au spans between the 1:2 and 3:2 resonance orbits of a massive body located at similar to 70 au, which might coincide with the candidate planet HD 100546b detected with previous thermal infrared (IR) observations. In this picture, the two wings can be the near side of a ring formed by disk material brought out of the disk at the 1:2 resonance with the same massive object. While we find no clear evidence confirming detection of the planet candidate HD 100546c in our data, we find a diffuse emission close to the expected position of HD 100546b. This source can be described as an extremely reddened substellar object surrounded by a dust cloud or its circumplanetary disk. Its astrometry is broadly consistent with a circular orbital motion on the disk plane, a result that could