  Predicting how a young planet shapes the gas and dust emission of its parent
disc is key to constraining the presence of unseen planets in protoplanetary
disc observations. We investigate the case of a 2 Jupiter mass planet that
becomes eccentric after migrating into a low-density gas cavity in its parent
disc. Two-dimensional hydrodynamical simulations are performed and
post-processed by three-dimensional radiative transfer calculations. In our
disc model, the planet eccentricity reaches ~0.25, which induces strong
asymmetries in the gas density inside the cavity. These asymmetries are
enhanced by photodissociation and form large-scale asymmetries in 12CO J=3-2
integrated intensity maps. They are shown to be detectable for an angular
resolution and a noise level similar to those achieved in ALMA observations.
Furthermore, the planet eccentricity renders the gas inside the cavity
eccentric, which manifests as a narrowing, stretching and twisting of
iso-velocity contours in velocity maps of 12CO J=3-2. The planet eccentricity
does not, however, give rise to detectable signatures in 13CO and C18O J=3-2
inside the cavity because of low column densities. Outside the cavity, the gas
maintains near-circular orbits, and the vertically extended optically thick CO
emission displays a four-lobed pattern in integrated intensity maps for disc
inclinations > 30 degrees. The lack of large and small dust inside the cavity
in our model further implies that synthetic images of the continuum emission in
the sub-millimetre, and of polarized scattered light in the near-infrared, do
not show significant differences when the planet is eccentric or still circular
inside the cavity.
