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 Ω_orb – Ω_spin plane , where Ω_spin and Ω_orb 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 (Ω_orb,Ω_spin) 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' ≳ 10^8, 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.