Evolution of the Planetary Obliquity: The Eccentric Kozai-Lidov Mechanism Coupled with Tide

Abstract

The planetary obliquity plays a significant role in determining physical properties of planetary surfaces and climate. As direct detection is constrained due to the present observation accuracy, kinetic theories are helpful to predict the evolution of the planetary obliquity. Here the coupling effect between the eccentric Kozai-Lidov (EKL) effect and the equilibrium tide is extensively investigated, the planetary obliquity performs to follow two kinds of secular evolution paths, based on the conservation of total angular momentum. The equilibrium timescale of the planetary obliquity $t_{\mathrm{eq}}$ 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 $t_{\mathrm{eq}}$ and $r_t$ with the maximum likelihood method. The spin-axis orientation of S-type terrestrials orbiting M-dwarfs reverses over $90^{\circ }$ when $r_t>100$, then enter the quasi-equilibrium state between $40^{\circ }$ and $60^{\circ }$, while the maximum obliquity can reach $130^{\circ }$ when $r_t>10^4$. Numerical simulations show that the maximum obliquity increases with the semi-major axis ratio $a_1$/$a_2$, but is not so sensitive to the eccentricity $e_2$. The likelihood of obliquity flip for S-type terrestrials in general systems with $a_2<45$ AU is closely related to $m_1$. The observed potential oblique S-type planets HD 42936 b, GJ 86 Ab and $\tau$ Boot Ab are explored to have a great possibility to be head-down over the secular evolution of spin.

18 pages, 12 figures, accepted for publication in ApJ

References in corpus (26)

• The Gaia mission
• The Transiting Exoplanet Survey Satellite
• The James Webb Space Telescope
• The fast spin-rotation of a young extrasolar planet
• Hot Jupiters from Coplanar High-eccentricity Migration
• Steady-state planet migration by the Kozai-Lidov mechanism in stellar binaries
• Chaos in the Test Particle Eccentric Kozai-Lidov Mechanism
• Gl86B: a white dwarf orbits an exoplanet host star
• On the tidal origin of hot Jupiter stellar obliquity trends
• Chaotic Tides in Migrating Gas Giants: Forming Hot and Transient Warm Jupiters via High-Eccentricity Migration
• Formation of Ultra-Short-Period Planets by Obliquity-Driven Tidal Runaway
• Chaotic Dynamics of Stellar Spin Driven by Planets Undergoing Lidov-Kozai Oscillations: Resonances and Origin of Chaos
• CHES: a space-borne astrometric mission for the detection of habitable planets of the nearby solar-type stars
• Dynamics of Colombo's Top: Generating Exoplanet Obliquities from Planet-Disk Interactions
• Dynamics of Colombo's Top: Tidal Dissipation and Resonance Capture, With Applications to Oblique Super-Earths, Ultra-Short-Period Planets and Inspiraling Hot Jupiters
• The Origin of Systems of Tightly Packed Inner Planets with Misaligned, Ultra-Short-Period Companions
• The Stationary Points of the Hierarchical Three Body Problem
• How do External Companions Affect Spin-Orbit Misalignment of Hot Jupiters?
• An ablating super-Earth in an eccentric binary from the Dispersed Matter Planet Project
• Kepler-1656b's Extreme Eccentricity: Signature of a Gentle Giant
• System Architecture and Planetary Obliquity: Implications for Long-Term Habitability
• Non-Trivial Oblique Spin Equilibria of Super-Earths in Multi-planetary Systems
• Tidal excitation of the obliquity of Earth-like planets in the habitable zone of M-dwarf stars
• Extremely Inclined Orbit of S-type Planet $\gamma$ Cep Ab Induced by Eccentric Kozai-Lidov Mechanism
• Mutual Inclination of Ultra-Short-Period Planets with Time Varying Stellar J2-moment
• The Gliese 86 Binary System: A Warm Jupiter Formed in a Disk Truncated at $\approx$2 AU

Cited by in corpus (3)

• Closeby Habitable Exoplanet Survey (CHES). I. Astrometric Noise and Planetary Detection Efficiency due to Stellar Spots and Faculae
• Re-recognized universality of Kozai oscillation on three-body dynamics
• Planetary Obliquity Excitation Through Pre-Main Sequence Stellar Evolution