Searching for the near-infrared counterpart of Proxima c using multi-epoch high-contrast SPHERE data at VLT

Context. Proxima Centauri is the closest star to the Sun and it is known to host an Earth-like planet in its habitable zone; very recently a second candidate planet was proposed based on radial velocities. At quadrature, the expected projected separation of this new candidate is larger than 1 arcsec, making it a potentially interesting target for direct imaging. Aims. While identification of the optical counterpart of this planet is expected to be very difficult, successful identification would allow for a detailed characterization of the closest planetary system. Methods. We searched for a counterpart in SPHERE images acquired over four years through the SHINE survey. In order to account for the expected large orbital motion of the planet, we used a method that assumes the circular orbit obtained from radial velocities and exploits the sequence of observations acquired close to quadrature in the orbit. We checked this with a more general approach that considers Keplerian motion, calle...