  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.
