Simulating Quaoar’s Ring with Confinement by Weywot

The large Trans-Neptunian object (50000) Quaoar has one known moon, Weywot [1].  Based on stellar occultation data from 2018-2021, a ring named Q1R was reported around Quaoar at an orbital radius of 4148.4±7.4 km and with variable width and optical depth [2]. Occultation data from 2022 were analyzed to reveal two rings [3]. Deriving a similar pole orientation to [2], the dense part of Q1R was interpreted to be ring arcs located at a radius of 4057.2±5.8 km, having Lorentzian shape extending over 60 km and full-width-at-half-maximum of 5 km, with peak normal optical depth τ=0.4 and a minimum arc length of multiple hundreds of km [3]. The more tenuous, continuous portion of Q1R had a typical width of 80-100 km and normal optical depth of τ=0.003 [3]. Secondary events from one location were consistent with a second ring, Q2R, at a radius of 2520±20 km, typical width of 10 km, and a normal optical depth of τ=0.004 [3].

The location of Q1R is well outside the Roche limit, implying that the material should coalesce over reasonable timescales. [2] and [3] pointed out that the ring is close to a 3:1 spin-orbit resonance with Quaoar as well as the inner 6:1 mean-motion resonance with Weywot, both of which could act to perturb and/or confine material. Following on numerical models showing that a single satellite can confine ring material outside the Roche limit at Chariklo [4], we present global collisional simulations of ring material near the 6:1 mean-motion resonance in a system with parameters that mirror those of the Quaoar/Weywot system. 

We begin with simulations of low optical depth material, τ=0.01, spread uniformly over a 200 km radial range on roughly circular orbits to explore where the resonant forcing would cause material to be confined into a narrow ring. We then simulate a higher optical depth distribution, τ=0.1, that covers only the range of radii that were confined in the initial simulation. To model the 6:1 resonance with an eccentric moon, the simulations are global and include collisions only, not self-gravity, with oversized particles 20 m in radius, and a velocity-dependent coefficient of restitution from [5]. Notably, these simulations do not yet explore the impact of being outside the classical Roche limit. 

We find that a narrow ring of material is confined near resonance after a few hundred orbits. The width of the material that is pulled into the ring scales with the orbital eccentricity and mass of the simulated Weywot.

In addition, we present a handful of new stellar occultation datasets by Quaoar between 2019 and 2024, some light curves of which contain detections of Q1R. Synthetic occultations from the numerical simulations can be compared with the occultation data to better constrain the physical properties of ring material. This work is supported by NSF AST Award Number 2206306.

[1] Brown, M. E. and T.-A. Suer (2007). Satellites of 2003 AZ_84, (50000), (55637), and (90482). International Astronomical Union Circular 8812. 

[2] Morgado, B. E., et al. (2023). A dense ring of the trans-Neptunian object Quaoar outside its Roche limit. Nature 614, 239.

[3] Pereira, C. L., et al. (2023). The two rings of (50000) Quaoar. A&A 673, id.L4.

[4] Sickafoose, A. A. and M. C. Lewis, Numerical Simulations of (10199) Chariklo’s Rings with a Resonant Perturber, PSJ, 5(2), id. 32, 2024.

[5] Bridges, F., Hatzes, A. & Lin, D. (1984). Structure, stability and evolution of Saturn's rings. Nature 309, 333–335.