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 semimajor 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 + b4/a4)(b/a)-4/3(c/a)-αc where b/a and c/a are the body axis ratios and index αc ≈ 1.05 is consistent with the random lattice mass-spring model simulations but αc = 4/3 suggested by scaling estimates. A homogeneous body with axis ratios 0.5 and 0.8, like Haumea, has orbital semimajor 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 per cent 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 semimajor axis.