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An apparently eccentric orbit of the exoplanet WASP-12 b as a radial velocity signature of planetary-induced tides in the host star

Massive exoplanets on extremely tight orbits, such as WASP-12 b, induce equilibrium tides in their host stars. Following the orbital motion of the planet, the tidal fluid flow in the star can be detected with the radial velocity method. Its signature manifests as the second harmonics of the orbital frequency that mimics a non-zero orbital eccentricity. Using the new radial velocity measurements acquired with the HARPS-N spectrograph at the Telescopio Nazionale Galileo and combining them with the literature data, we show that the apparent eccentricity of WASP-12 b's orbit is non-zero at a 5.8 sigma level, and the longitude of periastron of this apparently eccentric orbit is close to 270 degrees. This orbital configuration is compatible with a model composed of a circular orbit and a signature of tides raised in the host star. The radial velocity amplitude of those tides was found to be consistent with the equilibrium tide approximation. The tidal deformation is predicted to produce a flux modulation with an amplitude of 80 ppm which could be detected using space-born facilities.