Application of Manifold Corrections in Tidal Evolution of Exoplanetary Systems

Abstract

The discovery of numerous close-in planets has updated our knowledge of planet formation. The tidal interaction between planets and host stars has a significant impact on the orbital and rotational evolution of the close planets. Tidal evolution usually takes a long time and requires reliable numerical methods. The manifold correction method, which strictly satisfies the integrals dissipative quasiintegrals of the system, exhibits good numerical accuracy and stability in the quasi-Kepler problem. Different manifold correction methods adopt different integrals or integral invariant relations to correct the numerical solutions. We apply the uncorrected five- and six-order Runge–Kutta–Fehlberg algorithm [RKF5(6)], as well as corrected by the velocity scaling method and Fukushima’s linear transformation method to solve the tidal evolution of exoplanet systems. The results show that Fukushima’s linear transformation method exhibits the best performance in the accuracy of the semimajor axis and eccentricity. In addition, we predict the tidal timescale of several current close exoplanetary systems by using this method.