A Novel Method to Constrain Tidal Quality Factor from A Nonsynchronized Exoplanetary System

Abstract We propose a novel method to constrain the tidal quality factor, <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi>Q</mml:mi> <mml:mo accent="false">′</mml:mo> </mml:math> , from an observed nonsynchronized star–planet system consisting of a slowly rotating low-mass star and a close-in Jovian planet, taking into account the coevolution 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 coevolution of angular momentum from the fast-rotator regime 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 the (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 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi>Q</mml:mi> <mml:mo accent="false">′</mml:mo> <mml:mo>≳</mml:mo> <mml:msup> <mml:mrow> <mml:mn>10</mml:mn> </mml:mrow> <mml:mrow> <mml:mn>8</mml:mn> </mml:mrow> </mml:msup> </mml:math> , leading to a tight upper bound on the tidal torque. Since this cannot be explained by previous theoretical predictions for nonsynchronized star–planet systems, our result requires mechanisms that suppress the tidal interaction in such systems.