Tidal spin down rates of homogeneous triaxial viscoelastic bodies

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.

accepted for publication in MNRAS

References in corpus (5)

• Tidal dissipation in stars and giant planets
• Tidal friction in close-in satellites and exoplanets. The Darwin theory re-visited
• High Precision Photometry of Extreme KBO 2003 EL61
• The Creation of Haumea's Collisional Family
• Stress field and spin axis relaxation for inelastic triaxial ellipsoids

Cited by in corpus (7)

• The Short Rotation Period of Hi'iaka, Haumea's Largest Satellite
• Modeling the Formation of the Family of the Dwarf Planet Haumea
• Beyond Point Masses. III. Detecting Haumea's Nonspherical Gravitational Field
• Non-principal axis rotation in binary asteroid systems and how it weakens the BYORP effect
• A direct N-body integrator for modelling the chaotic, tidal dynamics of multi-body extrasolar systems: TIDYMESS
• Simulations of wobble damping in viscoelastic rotators
• Low rock mass fraction within trans-Neptunian objects inferred from the spin-orbit evolution of Orcus-Vanth and Salacia-Actaea