Tidal spin down rates of homogeneous triaxial viscoelastic bodies

TL;DR

This study uses numerical simulations to quantify how the shape and internal composition of triaxial bodies affect their tidal spin down rates, revealing that non-spherical shapes and ice content significantly influence orbital evolution.

Contribution

It introduces a mass-spring model to estimate tidal drift rates of triaxial viscoelastic bodies, providing a new analytical approximation that accounts for shape and composition effects.

Findings

Non-spherical bodies have faster tidal drift rates than spherical ones.

Shape ratios significantly influence the orbital semi-major axis drift rate.

Ice-rich bodies exhibit even faster tidal evolution, but not enough to explain Haumea's satellite orbit.

Abstract

We use numerical simulations to measure the sensitivity of the tidal spin down rate of a homogeneous triaxial ellipsoid to its axis ratios by comparing the drift rate in orbital semi-major axis to that of a spherical body with the same mass, volume and simulated rheology. We use a mass-spring model approximating a viscoelastic body spinning around its shortest body axis, with spin aligned with orbital spin axis, and in circular orbit about a point mass. The torque or drift rate can be estimated from that predicted for a sphere with equivalent volume if multiplied by $0.5 (1 + b^4/a^4)(b/a)^{-4/3} (c/a)^{-\alpha_c}$ where $b/a$ and $c/a$ are the body axis ratios and index $\alpha_c \approx 1.05$ is consistent with the random lattice mass spring model simulations but $\alpha_c = 4/3$ suggested by scaling estimates. A homogeneous body with axis ratios 0.5 and and 0.8, like Haumea, has orbital semi-major axis drift rate about twice as fast as a spherical body with the same mass, volume and material properties. A simulation approximating a mostly rocky body but with 20\% of its mass as ice concentrated at its ends has a drift rate 10 times faster than the equivalent homogeneous rocky sphere. However, this increase in drift rate is not enough to allow Haumea's satellite, Hi'iaka, to have tidally drifted away from Haumea to its current orbital semi-major axis.