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