Planetary inward migration as the potential cause of GJ 504’s fast rotation and bright X-ray luminosity

Context. The discovery of an increasing variety of exoplanets in very close orbits around their host stars raised many questions about how stars and planets interact and to what extent host stars’ properties may be influenced by the presence of close-by companions. Understanding how the evolution of stars is impacted by the interactions with their planets is indeed fundamental to disentangling their intrinsic evolution from star-planet-interaction (SPI) induced phenomena. In this context, GJ 504 is a promising candidate for a star that underwent strong SPI. Its unusually short rotational period (P rot ∼ 3.4 days), while being in contrast with what is expected of single-star models, could result from the inward migration of a close-by, massive companion (M pl ≥ 2 M J ), pushed towards its host by the action of tides. Moreover, its brighter emission in the X-ray luminosity may hint at a rejuvenation of the dynamo process sustaining the stellar magnetic field, which is a consequence of the SPI-induced spin-up. Aims. We aim to study the evolution of GJ 504 and establish whether by invoking the engulfment of a planetary companion we can better reproduce its rotational period and X-ray luminosity. Methods. We simulated the past evolution of the star by assuming two different scenarios: ‘star without close-by planet’ and ‘star with close-by planet’. In the second scenario, we use our SPI code to investigate how the inward migration and eventual engulfment of a giant planet driven by stellar tides may spin-up the stellar surface and rejuvenate its dynamo. We compare our theoretical tracks with archival-rotational-period and X-ray data of GJ 504 collected from the all-sky surveys of the ROentgen Survey with an Imaging Telescope Array (eROSITA) on board the Russian Spektrum-Roentgen-Gamma mission (SRG). Results. Despite the large uncertainty on the stellar age, we find that the second evolutionary scenario characterised by the inward migration of a massive planetary companion is in better agreement with the short rotational period and the bright X-ray luminosity of GJ 504; thus, it strongly favours the inward migration scenario over the one in which close-by planets have no tidal impact on the star.