Mon. Not. R. Astron. Soc. 000, 1–8 (2017) Printed 15 March 2021 (MN LATEX style file v2.2) Rings under close encounters with the giant planets: Chariklo vs Chiron R. A. N. Araujo1, O. C. Winter1, R. Sfair1 1UNESP - Sao˜ Paulo State University, Grupo de Dinamicaˆ Orbital e Planetologia, CEP 12516-410, Guaratingueta,´ SP, Brazil ABSTRACT In 2014, the discovery of two well-defined rings around the Centaur (10199) Chariklo were announced. This was the first time that such structures were found around a small body. In 2015, it was proposed that the Centaur (2060) Chiron may also have a ring. In a previous study, we analyzed how close encounters with giant planets would affect the rings of Chariklo. The most likely result is the survival of the rings. In the present work, we broaden our analysis to (2060) Chiron. In addition to Chariklo, Chiron is currently the only known Centaur with a presumed ring. By applying the same method as Araujo, Sfair & Winter (2016), we performed numerical integrations of a system composed of 729 clones of Chiron, the Sun, and the giant planets. The number of close encounters that disrupted the ring of Chiron during one half-life of the study period was computed. This number was then compared to the number of close encounters for Chariklo. We found that the probability of Chiron losing its ring due to close encounters with the giant planets is about six times higher than that for Chariklo. Our analysis showed that, unlike Chariklo, Chiron is more likely to remain in an orbit with a relatively low inclination and high eccentricity. Thus, we found that the bodies in Chiron-like orbits are less likely to retain rings than those in Chariklo-like orbits. Overall, for observational purposes, we conclude that the bigger bodies in orbits with high inclinations and low eccentricities should be prioritized. Key words: minor planets: individual (2060) Chiron, planets and satellites: dynamical evo- lution and stability, planets and satellites: rings 1 INTRODUCTION ing Chariklo. As a result, these studies identified the cases where the encounters were disruptive, removing the ring, and those where A stellar occultation of (10199) Chariklo revealed the exis- the ring was not removed but suffered a significant change in its tence of an associated pair of narrow well-defined rings (Braga- orbit around Chariklo. The conclusion of Araujo, Sfair & Winter Ribas et al. 2014). This was the first detection of a ring system (2016) was that the ring would survive without any significant or- orbiting a minor body. The detection was confirmed in later occul- bital change for more than 90% of the clones. A similar result was arXiv:1807.02096v1 [astro-ph.EP] 5 Jul 2018 tations (Berard´ et al. 2017). later obtained by Wood et al. (2017). Chariklo is the largest body defined as a Centaur. Centaurs The possible existence of a ring around (2060) Chiron, an- exist in chaotic orbits among the giant planets and frequently have other Centaur, was suggested by Ortiz et al. (2015). This indication, close encounters with them. The lifetime of a Centaur is on the which has not yet been confirmed, raises the question of whether order of ten million years (Tiscareno & Malhotra (2003), Horner, the results found for Chariklo‘s rings (Araujo, Sfair & Winter 2016) Evans & Bailey (2004a), Horner, Evans & Bailey (2004b), Araujo, are also valid for Chiron‘s ring system since their present orbital Sfair & Winter (2016)). elements and the system configuration (i.e., the size of the Centaur The existence of a ring system around a minor body in such a and location of the rings) are different. wild orbital environment leads to the next question: Are the rings of Chariklo stable during close encounters with the giant planets? Therefore, in the present work, we reproduce the study of the In a previous work, Araujo, Sfair & Winter (2016) addressed this close encounters for a set of clones of Chiron, similar to what was question by performing numerical simulations with a set of 729 done for Chariklo. Then, we identify the differences in the results clones of Chariklo with similar initial orbits around the Sun given for Chiron and those for Chariklo caused by the differences in Ch- the gravitational perturbations of Jupiter, Saturn, Uranus and Nep- iron’s ring system and and by their distincts orbital evolutions. tune. Throughout these simulations, all the close encounters be- The structure of this paper is as follows. In Section 2, we dis- tween Chariklo and each giant planet were recorded. Using a se- cuss the physical and orbital differences between Chariklo, Chiron lection of the strongest close encounters, a new set of numerical and their rings. In Section 3, we explain our experimental method; simulations was made considering rings of massless particles orbit- in Section 4, we explain our results; and in Section 5, we summa- c 2017 RAS 2 R. A. N. Araujo, O. C. Winter, R. Sfair Table 1. Physical parameters and heliocentric orbital elements of (10199) Chariklo and (2060) Chiron Mass (kg) Radius (km) a (au) e i (deg) Ring Orbital radii (km) 1 18 Chariklo 7:986 × 10 124 15:74 0:171 23:4 R1 = 390:6 , R2 = 404:8 Chiron2 2 × 1018 74 13:64 0:3827 6:9 324 1 Braga-Ribas et al. (2014) and Araujo, Sfair & Winter (2016) 2 Mass and Radius from NASA-PFS (2014). Orbital elements obtained from JPL’s Horizons system for the Epoch MJD 57664 (a - semimajor axis, e - eccentricity, i - orbital inclination). Ring Orbital Radii from Ortiz et al. (2015) . Table 2. Orbital distributions of the clones of Chariklo and Chiron equivalent radius of Chiron of 109 km (Fornasier, et al. 2013), but this value may be overestimated since the emissions of the body Chariklo1 Chiron Delta2 and rings may overlap and cannot be separated. Although there is 15:720 6 a 6 15:760 13:620 6 a 6 13:660 ∆a = 0:005 an uncertainty of the size of Chiron and, consequently, an uncer- 0:1510 6 e 6 0:1910 0:363 6 e 6 0:403 ∆e = 0:005 tainty of its mass value, we will later discuss that this is not a factor ◦ ◦ ◦ ◦ ◦ 23:36 6 i 6 23:44 6:91 6 i 6 6:99 ∆i = 0:01 in the problem addressed here. Orbital semimajor axis and ∆a in astronomical units. Chariklo opened the door to a new and interesting subfield of 1 From Araujo, Sfair & Winter (2016) astronomy - that of ringed small bodies. The two well-defined nar- 2 Defined following Horner, Evans & Bailey (2004a) row rings of Chariklo were revealed by stellar occultations (Braga- Ribas et al. 2014; Berard´ et al. 2017). The possibility that Chiron may also have rings was proposed by Ortiz et al. (2015). More de- rize our main results giving a prospect for detecting rings aroud tails about the rings are given in Section 4. Centaurs. The stability of the rings of Chariklo was analysed by Araujo, Sfair & Winter (2016). In that work we showed that the rings are more likely to survive during the lifetime of Chariklo as a Centaur 2 CHIRON VS CHARIKLO and, thus, that the Centaurs in general may experience a propitious environment for the existence of rings. Here, we follow a similar Chiron and Chariklo are dynamically classified as Centaurs. approach with the difference that in the present work we consider Although there is no consensus on the definition of Centaurs, it Chiron instead of Chariklo. Our goal is to study the stability of a hy- is generally well accepted that the Centaur population is made up potetical ring system around Chiron. The results are then contrasted of small bodies whose orbits mainly evolve in the region between to previous results obtained for Chariklo. This approach will then Jupiter and Neptune (see the discussion in Araujo, Sfair & Winter allow us obtain statistical statements (subject to assumptions) for (2016)). the possible existence of rings around Centaurs as a general popu- The crossing of orbits of Centaurs with the giant planets and, lation. consequently, the close encounters experienced by them, are quite frequent. This leads to a characteristic chaotic orbital evolution of the Centaurs (see, e.g., Tiscareno & Malhotra (2003); Bailey & Malhotra (2009); Levison & Duncan (1997); Horner, Evans & Bai- 3 METHOD ley (2004a,b)). Chiron was the first known object of the population of Cen- Araujo, Sfair & Winter (2016) considered 729 clones of taurs (Kowal, Liller & Marsden 1979). Chariklo was discovered Chariklo. The clones were defined from the osculating orbit of the later in 1997 by the Spacewatch program1. The two exhibit dis- Centaur (Table 1), where the semimajor axis, the eccentricity and tinct orbital and physical characteristics. From Table 1, we see that the orbital inclination varied within the ranges presented in Table Chariklo is almost twice as large as Chiron and that the orbit of 2. In an analogous fashion, 729 clones of Chiron were also made Chariklo is less eccentric and more inclined than the orbit of Chi- from its osculating orbit (Table 1) using the ranges presented in ron. Table 2. They were considered nine values for the semimajor axis For the size and mass of Chiron, we used the lower values going from 13.620 au until 13.660 au (taken every ∆a = 0:005 presented in NASA-PFS (2014). The lower values of the mass and au), nine values for the eccentricity, going from 0.363 until 0.403 size of Chiron were chosen to make them as different as possible (taken every ∆e = 0:005 au) and nine values for the orbital in- ◦ ◦ ◦ from those of Chariklo.