The Retrograde Ring Of Dwarf Planet Quaoar

The stability scenario about rings around celestial minor bodies and exoplanets has changed significantly in the past decade. There is still no consensus on how these ring systems form, evolve, and remain stable.

So far, four ring systems have been discovered around small Solar System bodies by observing stellar occultations. These include the centaurs Chariklo (Braga-Ribas et al., 2014) and possibly Chiron (Ortiz et al., 2015), and the trans-Neptunian dwarf planets Haumea (Ortiz et al., 2017) and Quaoar (Morgado et al., 2023; Pereira et al., 2023).

The dwarf planet Quaoar was the first small celestial body to have an observed ring outside its Roche limit. The first ring, Q1R, is 4,057±6 km away from Quaoar and exists outside its Roche limit (~1,780 km). Later, a second ring, called Q2R, was discovered much closer to Quaoar at a distance of 2,520±20 km, also outside its Roche limit.

Recently, studies about the evolution and stability of the Q1R ring of Quaoar have been done in order to explain the ring stability outside the Roche limit (Morgado et al., 2023; Rodriguez et al., 2023; Sickafoose & Lewis, 2024). However, a detailed investigation of the stability of Quaoar's Q2R ring is still needed.

In this work, we study the evolution and stability of the Q2R ring of Quaoar through numerical integrations. We use an adapted version of the Mercury package (Chambers, 1999), including the gravitational effects of J2 and C22 coefficients of Quaoar shape and the Weywot satellite perturbation. We explore the combined effects of oblateness (J2) and ellipticity (C22) of Quaoar ellipsoidal shape in a test particle around it in the location of the Q2R ring. We also investigate prograde and retrograde orbits.

Our results show that the Q2R ring is unstable for a prograde orbit around Quaoar up to ~200 years (Fig. 1), regarding its ellipsoidal shape parameters of 545 km x 458 km x 395 km and a rotational period of 17.7 h (Kiss et al., 2024). The instability is due to the ellipticity of the Quaoar shape, which acts to clean the region where the Q2R ring is located.

However, when a retrograde orbit for the Q2R ring is assumed around Quaoar, the Q2R ring becomes stable for at least 25,000 years (Figs. 1 and 2), keeping a radial variation of only ~40 km that corroborates with observational data thresholds. In addition, the stability is due to the oblateness of the Quaoar shape, which keeps the ring stable for a long time.

This result is consistent with that obtained recently in the case of the exoplanet J1407b, for which it was hypothesized that the giant ring surrounding it may exhibit retrograde motion, which would explain its long-term stability (Mamajek et al., 2012; Van Werkhoven et al., 2014; Kenworthy et al., 2015; Kenworthy & Mamajek, 2015). In general, it is well known that retrograde orbits are more stable than prograde ones (see, for instance, Hamilton and Burns (1991); Scheeres (1994); Vieira Neto, E. et al. (2006); Amarante et al. (2021); Amarante et al. (2022)).

In this context, the surprising discovery of two rings around Quaoar located beyond its Roche limit and the hypothesis of a retrograde ring around the exoplanet J1407b represent significant challenges to current models of planetary ring formation, evolution, and stability (Hedman, 2023).

Considering this scenario, our results indicate that the Q2R ring may be in a retrograde orbit around Quaoar, explaining its stability in long-term simulations.

Fig. 1: Radial distance evolution from Quaoar of a test particle initially located at Q2R ring over 200 years. The red line denotes a prograde orbit, while the blue line represents a retrograde orbit around Quaoar.

Fig. 2: Radial distance evolution from Quaoar of a test particle initially located at Q2R ring over 25,000 years. The red line denotes a prograde orbit around Quaoar, while the blue line represents the retrograde orbit.