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

Abstract

We propose a novel method to constrain the tidal quality factor, $Q'$, from an observed non-synchronized star-planet system consisting of a slowly rotating low-mass star and a close-in Jovian planet, taking into account the co-evolution of stellar spin and planetary orbit due to the tidal interaction and the magnetic braking. On the basis of dynamical system theory, the track of the co-evolution of angular momentum from the fast rotator regime for such a system exhibits the existence of a forbidden region in the $\Omega_\mathrm{orb}$ -- $\Omega_\mathrm{spin}$ plane , where $\Omega_\mathrm{spin}$ and $\Omega_\mathrm{orb}$ 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 ($\Omega_\mathrm{orb},\Omega_\mathrm{spin}$) 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 $Q' \gtrsim 10^8$, 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.