CORALIE radial velocity search for companions around evolved stars (CASCADES). II. Seismic masses for three red giants orbited by long-period massive planets
Context. The advent of asteroseismology as the golden path to precisely
characterize single stars naturally led to synergies with the
field of exoplanetology. Today, the precise determination of
stellar masses, radii and ages for exoplanet-host stars is a
driving force in the development of dedicated software and
techniques to achieve this goal. However, as various approaches
exist, it is clear that they all have advantages and
inconveniences and that there is a trade-off between accuracy,
efficiency, and robustness of the techniques. \Aims: We aim to compare and discuss various modelling techniques
for exoplanet-host red giant stars for which TESS data are
available. The results of the seismic modelling are then used to
study the dynamical evolution and atmospheric evaporation of the
planetary systems. \Methods: We study, in detail,
the robustness, accuracy and precision of various seismic
modelling techniques when applied to four exoplanet-host red
giants observed by TESS. We discuss the use of global seismic
indexes, the use of individual radial frequencies and that of
non-radial oscillations. In each case, we discuss the advantages
and inconveniences of the modelling technique. \Results: We determine precise and accurate masses of exoplanet-
host red giant stars orbited by long-period Jupiter-like planets
using various modelling techniques. For each target, we also
provide a model-independent estimate of the mass from a mean
density inversion combined with radii values from Gaia and
spectroscopic data. We show that no engulfment or migration is
observed for these targets, even if their evolution is extended
beyond their estimated seismic ages up the red giant branch.
\on observations collected with
the CORALIE echelle spectrograph on the 1.2 m Euler Swiss
telescope at La Silla Observatory, ESO, Chile.