[Paper Review] The Effect of Charon's Tidal Damping on the Orbits of Pluto's Three Moons

Yoram Lithwick, Yanqin Wu|ArXiv.org|Feb 20, 2008

Astro and Planetary Science2 references3 citations

TL;DR

This paper investigates whether tidal damping by Charon could circularize the orbits of Pluto's moons Nix and Hydra via secular interactions, where they transfer eccentricity to Charon, which then damps it via tides with Pluto. However, resonant forcing from 2:1 and 3:1 mean motions disrupt this mechanism, making it unlikely to explain their current low eccentricities; instead, the authors suggest in-situ formation with primordial low eccentricities, while Hydra’s observed eccentricity may stem from 3:2 resonance with Nix.

ABSTRACT

Pluto's recently discovered minor moons, Nix and Hydra, have almost circular orbits, and are nearly coplanar with Charon, Pluto's major moon. This is surprising because tidal interactions with Pluto are too weak to damp their eccentricities. We consider an alternative possibility: that Nix and Hydra circularize their orbits by exciting Charon's eccentricity via secular interactions, and Charon in turn damps its own eccentricity by tidal interaction with Pluto. The timescale for this process can be less than the age of the Solar System, for plausible tidal parameters and moon masses. However, as we show numerically and analytically, the effects of the 2:1 and 3:1 resonant forcing terms between Nix and Charon complicate this picture. In the presence of Charon's tidal damping, the 2:1 term forces Nix to migrate outward and the 3:1 term changes the eccentricity damping rate, sometimes leading to eccentricity growth. We conclude that this mechanism probably does not explain Nix and Hydra's current orbits. Instead, we suggest that they were formed in-situ with low eccentricities. We also show that an upper limit on Nix's migration speed sets a lower limit on Pluto-Charon's tidal circularization timescale of >10^5 yrs. Moreover, Hydra's observed proper eccentricity may be explained by the 3:2 forcing by Nix.

Motivation & Objective

• To investigate whether tidal damping by Charon could explain the low eccentricities and coplanarity of Pluto’s small moons Nix and Hydra.
• To assess whether secular interactions transfer eccentricity from Nix and Hydra to Charon, followed by tidal damping in Charon-Pluto system.
• To evaluate the impact of 2:1 and 3:1 resonant forcing terms between Nix and Charon on orbital evolution and eccentricity damping.
• To determine whether the observed orbital properties of Hydra, including its non-zero eccentricity, can be explained by mutual resonant forcing with Nix.
• To derive constraints on Pluto-Charon’s tidal circularization timescale from observed migration limits on Nix.

Proposed method

• Uses N-body simulations to model the dynamical evolution of Pluto, Charon, and Nix, incorporating tidal damping and resonant forcing.
• Applies secular perturbation theory to derive analytical expressions for eccentricity damping rates, including contributions from 2:1 and 3:1 resonant terms.
• Derives the effective damping rate γ3:1 for Nix by solving coupled differential equations for complex eccentricity vectors, accounting for time-varying forcing.
• Evaluates the migration rate of Nix due to 2:1 resonance with Charon using resonant angle evolution and forcing amplitude calculations.
• Models the 3:2 resonant interaction between Nix and Hydra to estimate forced eccentricities and compare with observed values.
• Uses numerical and analytical methods to compute the impact of resonant forcing on eccentricity damping and orbital migration, comparing with tidal damping timescales.

Experimental results

Research questions

• RQ1 Can tidal damping by Charon explain the low eccentricities of Nix and Hydra, given that direct tidal interaction with Pluto is too weak?
• RQ2 How do 2:1 and 3:1 resonant forcing terms between Nix and Charon affect the efficiency of eccentricity damping via secular transfer?
• RQ3 Does the 3:2 resonance between Nix and Hydra explain Hydra’s observed non-zero eccentricity of 0.0052?
• RQ4 What constraints does the observed migration speed of Nix place on the tidal circularization timescale of the Pluto-Charon system?
• RQ5 Is the forced resonant migration scenario proposed by Ward & Canup (2006) viable given the conflicting tidal and resonance requirements?

Key findings

• The 2:1 resonant forcing term between Nix and Charon drives outward migration of Nix, which disrupts the proposed eccentricity damping mechanism.
• The 3:1 resonant forcing term alters the eccentricity damping rate and can even induce eccentricity growth, undermining the damping process.
• The mechanism of eccentricity transfer to Charon followed by tidal damping is therefore unlikely to explain the current low eccentricities of Nix and Hydra.
• The observed proper eccentricity of Hydra (0.0052) is quantitatively consistent with forcing from the 3:2 resonance with Nix, suggesting this is the origin of its non-zero eccentricity.
• An upper limit on Nix’s migration speed implies a lower bound on Pluto-Charon’s tidal circularization timescale of >10^5 years.
• The in-situ formation of Nix and Hydra with low initial eccentricities remains the most plausible explanation for their current orbital properties.