Ellipsoidal Modeling Framework for TNOs: the triaxial shape of (50000) Quaoar and its implications for Weywot and the dynamical environment

The three-dimensional shapes of Trans-Neptunian Objects (TNOs) are notoriously difficult to determine due to their slow orbital motion and minimal variations in aspect angle over human timescales. To overcome this geometric degeneracy, we developed a versatile modeling framework capable of deriving ellipsoidal shapes by simultaneously combining stellar occultations and rotational light curves, including parameterizations of localized surface albedo. We applied this methodology to the large TNO (50000) Quaoar, jointly modeling 37 stellar occultation events and two photometric datasets. Our MCMC analysis demonstrates that Quaoar is best represented by a triaxial shape with equatorial semi-axes $a = 620.7^{+3.3}_{-2.8}$ km and $b = 546.5^{+6.0}_{-5.6}$ km, and a polar semi-axis $c = 511.5^{+5.3}_{-5.5}$ km, yielding a bulk density of $1.663 \pm 0.127$ g cm$^{-3}$. By isolating Quaoar's barycentric motion from the astrometric offsets, we determined the mass of its satellite, Weywot, to be $(1.485 \pm 0.360) \times 10^{18}$ kg, corresponding to a system mass ratio of $q = 0.0012 \pm 0.0003$ and a satellite bulk density of $0.95 \pm 0.60$ g cm$^{-3}$. Furthermore, dynamical simulations using the derived triaxial gravitational field reveal that potential additional satellites can only maintain stable orbits beyond 2.4 Quaoar radii, as inner bodies would be strongly perturbed. Regarding the ring system, particles at the location of the secondary ring (Q2R) location exhibit libration associated with the 5:7 spin-orbit resonance (SOR). Similarly, particles at the location of the main ring (Q1R) location show libration of the 2:6 SOR angle for orbital eccentricities larger than 0.2, providing a plausible mechanism for the azimuthal width variations observed in Q1R.