A Novel Method to Constrain Tidal Quality Factor from A Non-synchronized Exoplanetary System

We propose a novel method to constrain the tidal quality factor, $Q'$, from a non-synchronized star-planet system consisting of a slowly rotating low-mass star and a close-in Jovian planet, taking into account the tidal interaction and the magnetic braking. On the basis of dynamical system theory, the track of the co-evolution of angular momentum for such a system exhibits the existence of a forbidden region in the Ωₒrb -- Ωₛpin plane , where Ωₛpin and Ωₒrb denote the angular velocity of the stellar spin and planetary orbit, respectively. The forbidden region is determined primarily by the strength of the tidal interaction. By comparing (Ωₒrb,Ωₛpin) of a single star-planet system to the forbidden region, we can constrain the tidal quality factor regardless of the evolutionary history of the system. The application of this method to the star-planet system, NGTS-10 -- NGTS-10 b, gives Q' 10⁸, leading to an tight upper bound on the tidal torque. Since this cannot be explained by previous theoretical predictions for non-synchronized star-planet systems, our result requires mechanisms that suppress the tidal interaction in such systems.