A novel method to constrain tidal quality factor of low-mass stars without age using close-in gaseous planet systems

For a close-in planet orbiting a solar-type star, the tidal star-planet interaction causes AM transport from the planet to the star. However, due to the difficulty of understanding the physical mechanisms of tides and estimating the age and initial condition of the system, the quantitative constraint on the tidal interaction is still insufficient. We focus on the co-evolution of AM of star-planet systems consisting of a non-tidally-locked low-mass star and a close-in gaseous planet, taking into account the magnetic braking and tidal interactions. Considering the track of AM co-evolution as the dynamical system enables us to confirm the existence of a forbidden region in the Ω_rot - Ω_orb phase diagram, where Ω_rot and Ω_orb denote the angular velocity of the stellar rotation and planetary orbit, respectively. The boundary of this region is characterized by the strength of the magnetic braking and the tidal interaction and does not depend on the age or initial condition of the star-planet system unless the initial stellar rotation is too slow compared to the planetary orbit. Then, using this forbidden region, we can constrain tidal interaction quantitatively. We have adopted it into observed star-planet systems and found that tidal interaction is weaker than the theoretical prediction for a non-tidally-locked star-planet system. Our result indicates that a theoretical re-examination of the tidal interaction is needed.