Synchronisation of a tidal binary by inward orbital migration. The case of Pluto and Charon

TL;DR

The paper challenges the standard outward tidal-recession view for Pluto–Charon by proposing that mutual synchronization can arise from inward orbital migration via capture, with Charon descending from a larger initial separation. It develops a simplified analytical framework to identify catching-up conditions and validates these ideas through detailed Darwin–Kaula tidal simulations that include viscoelastic Andrade rheology for both bodies. The results show that inward migration can produce the present doubly synchronous state with modest tidal heating (approximately $2$–$9$ TW for Pluto and up to $8$ TW for Charon) and only brief episodes of higher spin–orbit resonances, consistent with Pluto’s retrograde rotation and the absence of widespread tidal fractures. The study highlights the importance of formation and migration history for tidal evolution and opens avenues for integrating thermal evolution and applying the approach to other planetary-moon systems.

Abstract

It is usually assumed that mutual synchronisation of a tidal two-body system happens through tidal recession, assuming the reduced Hill sphere is not reached. However, synchronisation can be achieved also via tidal approach, provided the Roche limit is not crossed. For each of the two scenarios, hereafter referred to as Scenario 1 and Scenario 2, respectively, we derive the condition under which the evolving synchronicity radius catches up with the tidally evolving orbit. We consider these two scenarios for the Pluto-Charon system, examine the impact origin hypothesis of Charon's formation, and propose that capture is a likelier option. We investigate Scenario 2, both analytically and numerically, where the orbital evolution of Charon starts at a higher altitude than present and undergoes tidal descent. In Scenario 2, the greater initial orbital separation between the partners reduces tidally induced thermal processes and fracturing, as compared to Scenario 1. In several study cases, we also observe temporary locking of Charon into higher spin-orbit resonances (3:2 to 7:2) in the first 0.5Myr of the system's evolution.

Figures (4)

• Figure 1: . The cubical hyperbola represents all synchronous states given by equation (\ref{['6']}), with the green-coloured branch indicating long-term stable equilibria, and the red-coloured part showing the loci of intrinsically unstable equilibria. The blue dashed and dotted lines represent two evolution tracks described by equation (\ref{['5']}). The track on the right results in a stable capture of Pluto. The one on the left traverses the critical point. The vertical dashed line corresponds to an approximately estimated Roche radius. The light blue-shaded area of the plot marks all initial conditions that may in principle result in long-term synchronisation of Pluto. The states marked with white disks and labelled "1" and "2" are possible initial conditions that could lead to the current state of the system, which is shown with the green disk and labelled "3". The $1\rightarrow 3$ dynamical history corresponds to Scenario 1, with a tidally receding moon. The $2\rightarrow 3$ track illustrates Scenario 2, with a moon tidally approaching the planet.
• Figure 2: Tidal evolution of the Pluto-Charon system. An initially prograde Pluto and initially retrograde Charon are considered, with various initial rotation rates and a fixed initial eccentricity $e_0=0.4$. Top left (a): semimajor axis ratio $a/a_{\rm{p}}$ (where $a_{\rm{p}}$ is the present semimajor axis value). Top right (b): eccentricity. Bottom left (c): spin rates ${\Omega}/n$ (shades of blue) and ${\Omega}_{\rm{m}}/n$ (shades of red). Bottom right (d): tidally dissipated power, $\dot{E}$ and $\dot{E}_{\rm{m}}$. Comment: In accordance with the adopted sign convention, the bottom left panel shows the spin rate $\Omega$ of an actually prograde Pluto as negative, while the depicted spin $\Omega_{\rm{m}}$ of a retrograde Charon is positive.
• Figure 3: Tidal evolution of the Pluto-Charon system. An initially prograde Pluto and initially retrograde Charon are considered, with various initial eccentricities and fixed initial spin-orbit ratios of $\Omega_0/n_0=-50$ and $\Omega_{\rm{m}0}/n_0=50$. Top left (a): semimajor axis ratio $a/a_{\rm{p}}$ (where $a_{\rm{p}}$ is the present semimajor axis value). Top right (b): eccentricity. Bottom left (c): spin rates ${\Omega}/n$ (shades of blue) and ${\Omega}_{\rm{m}}/n$ (shades of red). Bottom right (d): tidally dissipated power $\dot{E}$ and $\dot{E}_{\rm{m}}$.
• Figure 4: Tidal evolution of the Pluto-Charon system. Initially prograde Pluto and Charon with various initial ratios of rotation rates $\Omega_{\rm{m}0}/\Omega_0$ and the initial eccentricity $e_0=0.4$. Top left (a): semimajor axis ratio $a/a_{\rm{p}}$ (where $a_{\rm{p}}$ is the present semimajor axis value). Top right (b): eccentricity $e$. Bottom left (c): spin rates ${\Omega}/n$ (shades of blue) and ${\Omega}_{\rm{m}}/n$ (shades of red). Bottom right (d): tidally dissipated power, $\dot{E}$ and $\dot{E}_{\rm{m}}$.