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The recent development of brand new observational techniques and theoreticalmodels have greatly advanced the exoplanet research field. Despite significantachievements, which have allowed the detection of thousands extrasolar systems,a comprehensive understanding of planetary formation and evolution mechanismsis still desired. One relevant limitation is given by the accuracy in themeasurements of planet-host star ages. The star GJ 504 has been found to host asubstellar companion whose nature is strongly debated. There has been a recentdifference of opinion in the literature owing to the uncertainty on the age ofthe system: a young age of $\sim$ 160 Myr would imply a giant planet as acompanion, but a recent revision pointing to a solar age ($\sim$ 4 Gyr) insteadsuggests a brown dwarf. With the aim of shedding light on this debated topic,we have carried out a high-resolution spectroscopic study of GJ 504 to derivestellar parameters, metallicity, and abundances of both light and heavyelements, providing a full chemical characterisation. The main objective is toinfer clues on the evolutionary stage (hence the age) of this system. Weperformed a strictly differential (line-by-line) analysis of GJ 504 withrespect to two reference stars, that is the planet-host dwarf $\iota$ Hor andthe subgiant HIP 84827. The former is crucial in this context because itsstellar parameters (hence the evolutionary stage) is well constrained fromasteroseismic observations. Regardless of the zero point offsets, ourdifferential approach allows us to put tight constraints on the age of GJ 504with respect to $\iota$ Hor, thereby minimising the internal uncertainties. Wefound that the surface gravity of GJ 504 is 0.2 $\pm$ 0.07 dex lower than thatof the main-sequence star $\iota$ Hor, suggesting a past turn-offevolution[...]

A critical reassessment of the fundamental properties of GJ 504: Chemical composition and age