Exoplanets synchronization: Learning from Venus' retrograde rotation

TL;DR

The paper investigates how habitable-zone, Earth-like exoplanets acquire rotation states under the joint action of gravitational tides and atmospheric torques, using Venus as a prototype. It applies the creep tide theory to compute tidal torques and couples them with an atmospheric torque term, analyzing both zero-obliquity and full 3D models to study obliquity, precession, and phase diagrams; stationary solutions depend on the torque balance parameter $b$ and the ratio $\Gamma$ of tidal to atmospheric relaxation rates. The authors show that atmospheric torque can destabilize synchronous rotation and create stable asynchronous states, including prograde and retrograde, and that retrograde rotation can emerge smoothly as the atmosphere forms, without requiring collisions. These results imply that thick atmospheres can imprint long-lived spin states on rocky exoplanets in the HZ, influencing climate, observables, and habitability assessments.

Abstract

Context: Planets in the HZ can have dense atmospheres affecting their rotations. Over time, the rotation tends to stationary solutions that can be synchronous or asynchronous. Aims: Our understanding of Venus's rotational dynamics is revisited to look at what might happen to exoplanets in the habitable zone of a solar-type star. Methods. The creep tide theory is used to calculate the gravitational tidal torque. Mathematical analysis is used to study the differential equation resulting from the joint contributions of tidal and atmospheric torques. Results. The formation of a dense atmosphere can alter the primordial rotation of the planet. One possibility is that it gradually becomes retrograde. The rotation of Venus is an example.

Figures (12)

• Figure 1: Variation of the rotational elements of the planet before and after the rotation reversal: Top and Middle: Obliquity and Equinox before and after the rotation reversal. Bottom: Rotation period (red) and Orbital period (blue). Longitude of the First Equinoctial Point (intersection of the planet's equator and orbit).
• Figure 2: Motion of the pole in the interval $660 < t < 720$ (kyr). Polar coordinates: Obliquity and Longitude of the First Equinoctial Point ($\Omega_{\rm I pl}$). The line $\beta = 90^\circ$ (dashed) is crossed from the outside in.
• Figure 3: Left: Tidal evolution of the obliquity and rotation period of a prograde naked Venus whose rotation period at t=0 is 10 days. Magenta: Case of a planet with the same tidal relaxation as the solid Earth ($\gamma=2\times 10^{-7} {\rm s}^{-1}$). Blue: A softer case ($\gamma =2\times 10^{-6} {\rm s}^{-1}$). Right: Zoom of the evolution in the neighborhood of the synchronization.
• Figure 4: Same as fig. \ref{['fig:prograde']} for a cluster of close initial conditions.
• Figure 5: Top: Phase diagram for $e=0.006773$ and relaxation factors $2\times 10^{-7} {\rm s}^{-1}$ (solid line), $7\times 10^{-7}{\rm s}^{-1}$ and $2\times 10^{-6}{\rm s}^{-1}$ (dashed lines). Bottom: Same as top for $e=0.3$.