The tidal quality of the hot Jupiter WASP-12b

Abstract: WASP-12b stands out among the planets of its class of hot Jupiters because of the observed fast orbital decay attributed to tidal dissipation. The measured rate of the orbital period is $\stackrel{\bf\centerdot}{\textstyle{P}}{\rm orb}\,=\,-\,29\pm3\;\mbox{ms/yr}\;$=$\;(9.2\pm1.0)\times10^{-10}\;\mbox{s/s}$. In the literature heretofore, all attempts to explain this high rate were based on the assumption that the orbital evolution is dominated by the tides in the star. Since the modified tidal quality factor in yellow dwarfs is insufficient to warrant such a decay rate, a hypothesis was put forward that the star may actually be a subgiant. Using the latest data from the Gaia mission, we deduce that WASP-12a at $1.36\,{M{Sun}}$ is an evolving dwarf at an early stage of post-turn-off evolution that has not yet depleted hydrogen in its core. Its unremarkable position in the color-magnitude diagram and the existence of close planets orbiting red giants of similar mass contradict the hypothesis of an abrupt boost of tidal quality due to structural internal changes. On the other hand, the previous research neglected the tidal dissipation in the planet assuming it to be negligible due to the likely synchronisation of its rotation and a presumed high quality factor. We critically reassess this assumption in the light of recent astrometric results for Jupiter and Saturn. Assuming that the structure of WASP-12b is similar to that of our Jupiter and Saturn, we find that the observed orbital decay is well explained by the tides in the planet. The estimated value of the planet's modified quality factor coincides almost precisely with that of our Jupiter.