2023ApJ...956...45H

Planetary obliquity plays a significant role in determining the physical properties of planetary surfaces and climate. As direct detection is constrained due to the present observation accuracy, kinetic theories are helpful for predicting the evolution of planetary obliquity. Here the coupling effect between the eccentric Kozai-Lidov effect and the equilibrium tide is extensively investigated; the planetary obliquity is observed to follow two kinds of secular evolution paths, based on the conservation of total angular momentum. The equilibrium timescale of the planetary obliquity t_eq varies along with r_t, which is defined as the initial timescale ratio of the tidal dissipation and secular perturbation. We numerically derive the linear relationship between t_eq and r_t with the maximum likelihood method. The spin-axis orientation of S-type terrestrials orbiting M-dwarfs reverses over 90° when r_t > 100, then enters the quasi-equilibrium state between 40° and 60°, while the maximum obliquity can reach 130° when r_t > 10⁴. Numerical simulations show that the maximum obliquity increases with the semimajor axis ratio a₁/a₂, but is not so sensitive to the eccentricity e₂. The likelihood of an obliquity flip for S-type terrestrials in general systems with a₂ < 45 au is closely related to m₁. The observed potentially oblique S-type planets HD 42936 b, GJ 86 Ab, and τ Boo Ab are explored and found to have a great possibility of rotating head-down over the secular evolution of spin.