Limits of Standard Tidal Models at Quaoar: Matching Weywot's Orbit, Missing the Spin

TL;DR

The paper tests whether standard tidal theories can explain the Quaoar–Weywot system, focusing on Weywot’s nearly circular orbit and Quaoar’s slow rotation. It uses two tidal frameworks, the constant phase lag (CPL) model and the Andrade creep-tide (ACT) approach, to perform 4.5 Gyr orbit-averaged integrations. With nominal Weywot mass, both models reproduce Weywot's orbital distance, damp eccentricity, and yield negligible current tidal torques, but Quaoar's spin remains effectively primordial. Explaining Quaoar's 17.7 h rotation would require Weywot to be 5–10× more massive and a finely tuned initial eccentricity, conflicting with occultation masses and implying unrealistically dense satellites, external torques, or a largely primordial spin as likely influences on Quaoar's rotational evolution. The best-fitting viscoelastic parameters suggest Quaoar is a partially differentiated body with roughly equal rock and warm-ice masses (150–180 K).

Abstract

Weywot, Quaoar's small satellite, follows a nearly circular orbit at a distance of 12.9 times Quaoar's diameter and coexists with a compact ring system. Nevertheless, Quaoar's flattening of 0.16, slow 17.7hr rotation and Weywot's low mass are difficult to reconcile with conventional tidal-evolution theory. We assess whether standard tides can reproduce the present-day architecture of the Quaoar-Weywot system and identify the initial conditions required. Orbit-averaged integrations spanning 4.5Gyr were carried out with two formalisms: (i) a constant phase-lag (CPL) and (ii) an Andrade creep-tide (ACT) framework. With the nominal Weywot mass, both tidal prescriptions converge on Weywot's observed orbital distance for a wide range of initial orbital distances and eccentricities; eccentricity is damped and present-day tidal torques are negligible, rendering the orbit quasi-stationary. Quaoar's spin, however, remains essentially unchanged from its inferred primordial period based on its present-day flattening, and does not reproduce the observed value. A match is possible only if Weywot is 5-10x more massive than current estimates and if its initial eccentricity is finely tuned; such scenarios are inconsistent with occultation-derived masses and imply an implausibly dense satellite. Based on the best fitting viscoelastic parameters, the most plausible composition for Quaoar is found to be a partially differentiated dwarf planet containing roughly equal masses of silicate rock and H2O-dominated warm (150-180K) ices. Standard tidal models reproduce Weywot's semimajor axis but cannot account for Quaoar's slow 17.7hr rotation without invoking an unrealistically massive satellite or external torques, suggesting that non-tidal processes - such as a largely primordial spin, early satellite loss, or a retrograde secondary giant impact - must have influenced Quaoar's rotational evolution.