The dynamics of ringed small bodies

The dynamics of ringed small bodies

In 2013, the startling discovery of a pair of rings around the Centaur 10199 Chariklo opened up a new subfield of astronomy - the study of ringed small bodies. Since that discovery, a ring has been discovered around the dwarf planet 136108 Haumea, and a re-examination of star occultation data for the Centaur 2060 Chiron showed it could have a ring structure of its own.

The reason why the discovery of rings around Chariklo or Chiron is rather shocking is because Centaurs frequently suffer close encounters with the giant planets in the Centaur region, and these close encounters can not only fatally destroy any rings around a Centaur but can also destroy the small body itself.

In this research, we determine the likelihood that any rings around Chariklo or Chiron could have formed before the body entered the Centaur region and survived up to the present day by avoiding ring-destroying close encounters with the giant planets. And in accordance with that, develop and then improve a scale to measure the severity of a close encounter between a ringed small body and a planet.

We determine the severity of a close encounter by finding the minimum distance obtained between the small body and the planet during the encounter, dmin, and comparing it to the critical distances of the Roche limit, tidal disruption distance, the Hill radius and 'ring limit'. The values of these critical distances comprise our close encounter severity scale.

The ring limit is defined as the close encounter distance between a planet and a ringed small body in a hyperbolic or parabolic orbit about the planet for which the effect on the ring is just noticeable in the three-body planar problem. The effect is considered just noticeable if the close encounter changes the orbital eccentricity of the orbit of any ring particle by 0.01. In the first version of our scale, the ring limit is set equal to a constant value of 10 tidal disruption distances for each planet, and the effect of the velocity at infinity, v1, of the orbit of the small body about the planet is ignored.

The method of backwards numerical integration of clones is used to determine the time intervals from now backwards in time within which Chariklo and Chiron have been injected into the Centaur region. The results show that Chariklo likely entered the Centaur region during the last 20 Myr and Chiron within the last 8.5 Myr from somewhere in the Trans-Neptunian region. We record dmin for all close encounters between each clone and each giant planet during these time intervals and use the severity scale to determine the likelihood that the close encounters could have destroyed any rings around each body during its time interval.

From this, it is seen that ring-destroying close encounters are so extremely rare that it is statistically likely that each body's rings could have originated outside the Centaur region assuming that the effects of viscous dispersion are negated by other stabilizing factors such as shepherd satellites and self-gravitating rings.

Furthermore, the results demonstrate that both Chariklo and Chiron have chaotic orbits but Chariklo's orbit exhibits a degree of stable chaos that Chiron's does not. Their half-lifes are 3 Myr and 0.7 Myr respectively.

The accuracy of our close encounter severity scale is improved by finding the ring limits for simulated close encounters between hypothetical one-ringed small bodies and planets in the 3-body planar problem. The effects of planet mass, small body mass, v1, and ring orbital radius are fully accounted for. When velocity effects are taken into account, we discover that the ring limit forms a curve in dmin - v1 space, the ring limit has a lower bound of approximately 1.8 tidal disruption distances regardless of the small body mass or ring orbital radius, and that the ring limit equals this lower bound for parabolic orbits only.

Our data is then used to find an analytical solution for a ring limit upper bound curve for Chariklo-planet encounters. We present three different methods for using this curve. To test our results, The ring limits found from all three methods are compared to 27 previously published dmin values for Charikloplanet encounters in the seven-body non-planar problem.

Only one dmin value is found to be greater than the ring limit and that all ring limits are within 4.4 tidal disruption distances for each planet. We conclude
that these values are more accurate than the crude value of 10 tidal disruption distances used in the first version of our close encounter severity scale.

Future work is discussed and may include simulations of Chariklo, Chiron or Haumea in which the ring particles and possibly satellites are included.

This work is partitioned as follows: Chapter One introduces the topic and states the research questions; Chapters Two, Three and Four are the three papers either published or submitted for publication; and Chapter Five summarizes
the overall conclusions.