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 $0.5 (1 + b^4/a^4)(b/a)^{-4/3} (c/a)^{-α_c}$ where $b/a$ and $c/a$ are the body axis ratios and index $α_c \approx 1.05$ is consistent with the random lattice mass spring model simulations but $α_c = 4/3$ 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.