THE RINGS OF CHARIKLO UNDER CLOSE ENCOUNTERS WITH THE GIANT PLANETS
R. A. N. Araujo, R. Sfair, and O. C. Winter
UNESP - Univ. Estadual Paulista, Grupo de Dinâmica Orbital e Planetologia, CEP 12516-410, Guaratingueta, SP, Brazil;
ran.araujo@gmail.com, rsfair@feg.unesp.br, ocwinter@gmail.com
Received 2015 December 11; accepted 2016 April 5; published 2016 June 15
ABSTRACT
The Centaur population is composed of minor bodies wandering between the giant planets that frequently perform
close gravitational encounters with these planets, leading to a chaotic orbital evolution. Recently, the discovery of
two well-defined narrow rings was announced around the Centaur 10199 Chariklo. The rings are assumed to be in
the equatorial plane of Chariklo and to have circular orbits. The existence of a well-defined system of rings around
a body in such a perturbed orbital region poses an interesting new problem. Are the rings of Chariklo stable when
perturbed by close gravitational encounters with the giant planets? Our approach to address this question consisted
of forward and backward numerical simulations of 729 clones of Chariklo, with similar initial orbits, for a period of
100 Myr. We found, on average, that each clone experiences during its lifetime more than 150 close encounters
with the giant planets within one Hill radius of the planet in question. We identified some extreme close encounters
that were able to significantly disrupt or disturb the rings of Chariklo. About 3% of the clones lose their rings and
about 4% of the clones have their rings significantly disturbed. Therefore, our results show that in most cases (more
than 90%), the close encounters with the giant planets do not affect the stability of the rings in Chariklo-like
systems. Thus, if there is an efficient mechanism that creates the rings, then these structures may be common
among these kinds of Centaurs.
Key words: minor planets, asteroids: individual (10199 Chariklo) – planets and satellites: dynamical evolution and
stability – planets and satellites: rings
1. INTRODUCTION
Among the orbits of the giant planets there is a population of
small objects called Centaurs. There is no consensus on the
definition of the Centaur population. According to the Minor
Planet Center (MPC) of the IAU, Centaurs are celestial bodies
with a perihelion beyond the orbit of Jupiter and with
semimajor axes smaller than the semimajor axis of Neptune.
1
Similarly, the Jet Propulsion Laboratory (JPL)/NASA defines
the Centaur population as objects with semimajor axes between
5.5 and 30.1 AU.
2
Duffard et al. (2014) classify Centaurs as
celestial bodies with orbits mostly in the region between Jupiter
and Neptune that typically cross the orbits of the giant planets.
A similar definition is also found in Horner et al. (2004b).
2060 Chiron was the first observed body of this population
(Kowal et al. 1979). Since then, the number of known Centaurs
has grown. Currently, more than 400 objects are cataloged
3
,
and from the flux of short period comets Horner et al. (2004a)
estimated the total number of objects with a diameter >1kmto
be approximately 44,000.
The Centaur 10199 Chariklo was discovered in 1997 by the
Spacewatch program.
4
In 2013, a stellar occultation revealed
the existence of symmetric features encircling Chariklo, the
second largest known Centaur. Braga-Ribas et al. (2014)
showed that these structures are a system of two narrow and
well-defined rings. This discovery was the first example of
minor bodies within the select group of ringed objects.
In Braga-Ribas et al. (2014), the authors estimated that the
rings have orbital radii of approximately 391 km and 405 km,
and widths of 7 km and 3 km, respectively. They are assumed
to be in the equatorial plane of Chariklo, with circular orbits.
From the orbital positions of the rings, they also estimated the
density of the central body to be 1 g cm
−3
. Apart from the
equivalent radius of 124 km, derived from the same stellar
occultation, little information about the physical properties of
Chariklo is available. Table 1 summarizes some of the physical
and orbital parameters of Chariklo and its rings.
A detailed study of the orbital evolution of the Centaurs was
presented by Horner et al. (2004a), where they analyzed the
orbital evolution of 32 cataloged objects through numerical
simulations of an ensemble of particles under the influence of
the Jovian planets. They followed the particles both forward
and backward in time and registered the dynamical evolution
and fate of the particles. The orbital radius shows that Chariklo
orbits between Saturn and Uranus, corresponding to a typical U
class object, i.e., those whose evolution is controlled by Uranus
(Horner et al. 2003). For Chariklo, they found the half-life to be
10.3 (9.68) Myr.
The Centaur objects are transient. Therefore, a source is
required to maintain a steady-state population. The idea of
bodies coming from regions of the solar system beyond
Neptune and populating the region between the planets is well-
accepted.
Levison & Duncan (1997) estimated, through numerical
integrations, the number of comets transiting between the inner
and outer solar system originating from the Kuiper Belt as
≈1.2 × 10
7
. Horner et al. (2004a) estimated a flux of one body
coming from the Kuiper Belt and joining the Centaur
population every 125 years. Sisto & Brunini (2007), present
the scattered disk objects (SDO; bodies with a distance to the
perihelion of q < 30 AU and semimajor axes of a > 50 AU) as
the most probable source of the Centaurs. Emel’Yanenko et al.
(2007), analyzed the role of the Oort cloud in determining the
flux of cometary bodies through the planetary system. They
The Astrophysical Journal, 824:80 (7pp), 2016 June 20 doi:10.3847/0004-637X/824/2/80
© 2016. The American Astronomical Society. All rights reserved.
1
MPC, www.minorplanetcenter.org/iau/lists/Unusual.html.
2
JPL, http://ssd.jpl.nasa.gov/sbdb_help.cgi?class=CEN.
3
MPC, www.minorplanetcenter.net/iau/lists/Centaurs.html.
4
Spacewatch Program, http://spacewatch.lpl.arizona.edu/discovery.html.
1
concluded that a substantial fraction of all known cometary
bodies may have a source in the Oort cloud, including the
Centaur population, which they defined as the population of
small bodies with a perihelion 5 < q < 28 AU and
a < 1000 AU. Following the same definition for Centaurs,
Emel’Yanenko et al. (2013) suggest that more than 90% of all
Centaurs with a > 60 AU and ≈50% with a < 60 AU come
from the Oort cloud. In Brasser et al. (2012), the Oort cloud is
also indicated out as the source of Centaurs, in particular those
with high inclination. In that work the Centaur population is
defined as small bodies with a perihelion between 15 and
30 AU and a semimajor axis shorter than 100 AU. They
showed that these objects probably originated from the Oort
cloud rather than the Kuiper Belt or the scattered disc.
Throughout its orbital evolution a Centaur is strongly
perturbed by the giant planets. Horner et al. (2004b), illustrate
in detail the effects of these perturbations on the orbit of five
selected Centaurs. The close encounters with the giant planets
are quite frequent. As consequence, the Centaurs present a
characteristic chaotic orbital evolution.
The existence of a small body with a well-defined system of
circular rings within such a perturbed population poses an
interesting new problem. This scenario has motivated the
development of the present work. We investigated the stability
of the rings of Chariklo when perturbed by close encounters
with the giant planets. We analyzed how effective the close
encounters are at disturbing or disrupting the rings of Chariklo.
Furthermore, the development of this study may allow us to
quantitatively evaluate how propitious the region of the
Centaurs is for such small bodies with their own systems of
rings. A brief qualitative discussion on this subject is presented
by Ortiz et al. (2015), where it is proposed that the Centaur
Chiron may also have rings. The possible existence of two
small bodies with systems of rings belonging to the same
population is quite interesting, and indicates that such systems
may be more frequent than expected.
Since our goal is to analyze the stability of the rings of
Chariklo when they are perturbed by close encounters with the
giant planets, here we classify an object as a Centaur when its
orbit is mainly in the region between Jupiter and Neptune (as in
Duffard et al. 2014), with a maximum semimajor axis value of
a 50 AU.
The structure of this paper is as follows. In Section 2,we
present the initial conditions and the numerical method adopted
in order to identify the close encounters of Chariklo with the
giant planets. In Section 3, we present the selection of the
extreme close encounters, i.e., those encounters that could be
capable of disrupting the rings of Chariklo. In Section 4,we
describe how the rings were simulated during a close
encounter. In Sections 5–7
we present the results, and Section 8
provides our final comments and the major conclusions of
the work.
2. CLOSE ENCOUNTERS WITH THE GIANT PLANETS
The first step consisted on selecting a representative sample
of close encounters of Chariklo with the giant planets. We
considered a system composed of the Sun, the giant planets of
the solar system (Jupiter, Saturn, Uranus, and Neptune), and a
sample of clones, i.e., objects with the same mass and radius as
Chariklo, but with small deviations in their orbits.
The clones were created following the procedure presented
in Horner et al. (2004a), where 729 clones were created from
the original orbit assuming a variation of semimajor axis of
0.005 AU, a variation of eccentricity of 0.005, and a variation
of inclination of 0°.01.
The orbital elements of Chariklo and of the planets were
obtained through JPL’s Horizons system for the epoch MJD
56541. For the orbit of Chariklo at this epoch we have a =
15.74 AU, e = 0.171, and i = 23°.4.
Considering these orbital elements, and taking the amplitude
of variation as in Horner et al. (2004a) in such way that we
have 729 clones, we created the clones of Chariklo orbiting the
Sun as follows: 15.720 a 15.760 AU, taken every
0.005 AU; 0.151 e 0.191, taken every 0.005; and 23°.36
i 23, 44°, taken every 0°.01. The choice of these values
resulted in nine values of semimajor axes, nine values of
eccentricities, and nine values of inclination. The combination
of these values resulted in 729 clones, each one with
different values of a, e, and i. Considering that Chariklo
has an equivalent radius of 124 km and a density of 1 g cm
−3
(Braga-Ribas et al. 2014), we estimated its mass as
M
C
= 7.986 × 10
18
kg. We performed backward and forward
numerical integrations of the system composed of the Sun, the
giant planets, and the clones, for a time span of 100 Myr, using
the adaptive time-step hybrid sympletic/Bulirsch– Stoer algo-
rithm from M
ERCURY (Chambers 1999).
Throughout the numerical integrations the clones did not
interact with each other, but they could collide with the planets
or escape from the system. The collisions were defined by the
relative distance between the clones and the planets. If the
clone–planet distance was smaller than the radius of the planet
Table 1
Orbital and Physical Parameters of Chariklo and its Rings
Chariklo Rings
a
a
15.74 AU
R1 R2
e
a
0.171 Orbital radius (km)
b
390.6 ± 3.3 404.8 ± 3.3
i
a
23°.4 Width (km)
b
7.17 ± 0.14
-
+
3
.4
1.4
1.1
Equivalent radius (km)
b
124 Radial separation (km)
b
14.2 ± 0.2
Mass (kg)
c
7.986 × 10
18
Gap between rings (km)
b
8.7 ± 0.4
Notes.
a
Orbital elements obtained from JPL’s Horizons system for the epoch MJD 56541. According to JPL the uncertainties in a, e, and i are
of the order 10
−5
,10
−6
, and 10
−5
, respectively.
b
Braga-Ribas et al. (2014).
c
Calculated considering a density of 1 g cm
−3
, the equivalent radius of Chariklo and a spherical body.
2
The Astrophysical Journal, 824:80 (7pp), 2016 June 20 Araujo, Sfair, & Winter
in question, then we had a collision. The physical radius of the
planet was determined by M
ERCURY, assuming a spherical
planet with uniform density. We consider ejections as being the
ejections from the Centaur population defined by the relative
distance to the Sun of 100 AU. This value was adopted taking
into account that if a clone reached the distance of 100 AU and
was still in a elliptical orbit, then necessarily the semimajor axis
of the clone had to be greater than 50 AU, i.e., the clone was no
longer classified as a Centaur, according to our definition.
As a result of the integrations, we see in the histograms in
Figure 1 that more than 50% of our sample was lost (ejections
or collisions) in 10 Myr, for both backward and forward
integrations. These results show that the evolution of our
sample is in agreement with the predicted evolution of the
Centaurs, which have an estimated mean lifetime of about
10 Myr (Tiscareno & Malhotra 2003). We also note that there
is a kind of symmetry in the results, which indicates that
Chariklo is currently in the middle of its median dynamical
lifetime as a Centaur.
At the end of the forward integrations, we found that ≈94%
of the 729 clones were lost in the time span of 100 Myr, 683
clones being lost through ejections and four clones through
collisions (three with Saturn and one with Jupiter). For the
backward integration, we found that ≈99% of the clones were
lost in 100 Myr, with 719 ejections and four collisions (three
with Jupiter and one with Saturn).
Once we characterized the evolution of the sample of clones
as a whole, we then selected all close encounters of the clones
within 1 Hill radius with each giant planet occurring within
10 Myr (the mean lifetime of the Centaurs). For this time span,
60159 close encounters were registered for the forward
integration and 65293 encounters for the backward integration.
From Table 2 we see that in this case Uranus dominates,
followed by Saturn, Jupiter, and Neptune, for both the backward
and forward integrations. This result is in agreement with works
on the dynamics of Centaurs, which state that the dynamics of
bodies with similar orbits to the orbit of Chariklo should be
guided by Uranus, as discussed in Horner et al. (2004a).
However, we are interested in analyzing how the close
encounters of Chariklo with the giant planets might affect its
rings. Therefore, we selected from among all the registered
close encounters those that are expected to perturb or disrupt
the rings. The details of this analysis and the results obtained
are described in the following.
3. EXTREME CLOSE ENCOUNTERS
In order to select the extreme close encounters, i.e.,
encounters with the giant planets that are expected to
Figure 1. Histograms of the fraction of Chariklo clones lost within 100 Myr as a function of time. (a) Backward integration. (b) Forward integration. Throughout the
numerical integration the clones could be lost by ejection or collisions with one of the giant planets or with the Sun. The ejection distance was considered to be
100 AU and the collisions were defined by the physical radius of the planets and of the Sun.
Table 2
Registered Close Encounters of the Clones with Each of the Giant Planets within 1 Hill Radius and within 1 and 10 Rupture Radii (r
td
)
in the Time Span of 10 Myr, for both Forward and Backward Integrations
Planet Hill Radius
a
r
td
a
Forward Encounters Backward Encounters
(Planetary (Planetary 1 Hill r
td
11< r
td
10 1 Hill r
td
11< r
td
10
Radius) Radius) Radius
b
Radius
c
Jupiter ≈740 ≈5 16.6% 5 36 18.3% 5 47
Saturn ≈1100 ≈4 26.0% 1 34 24.2% 0 25
Uranus ≈2700 ≈5 48.0% 0 18 46.9% 2 13
Neptune ≈4600 ≈5 9.4% 0 2 10.6% 1 5
Notes.
a
The Hill radius and the rupture radius in terms of the radius of the planet in question.
b
Percentage relative to 60159 encounters.
c
Percentage relative to 65293 encounters.
3
The Astrophysical Journal, 824:80 (7pp), 2016 June 20 Araujo, Sfair, & Winter
significantly affect the rings of Chariklo, we calculated the tidal
disruption radius (r
td
). According to Philpott et al. (2010), the
distance of a close encounter at which the tidal disruption of a
binary may occur is given by:
⎛
⎝
⎜
⎞
⎠
⎟
»
+
ra
M
MM
3
1
Btd
Pl
12
13
()
where a
B
is the semimajor axis of the binary, M
Pl
is the mass of
the planet, and M
1
and M
2
are the masses of the components of
the binary.
For a particle orbiting Chariklo with a
B
= 410 km (the
approximate outer limit of the ring), we calculated the r
td
for
encounters with each one of the giant planets. These values are
presented in Table 2. It is important to point out that this is an
approximate value since it does not take into account the
relative velocity of the bodies at the moment of the encounter.
Araujo et al. (2008) showed that not just the distance of the
encounter, but also the relative encounter velocity determine
how significantly a body will be disturbed by a close encounter.
Such effects were also discussed by Araujo & Winter (2014)
when they compared their numerical analysis of the disruption
of Near-Earth Asteroid (NEA) binaries due to close encounters
with the Earth with the analytical prediction given by
Equation (1), showing the dependence of the results on the
relative velocity of the encounters.
Nevertheless, for our purposes the approach given by
Equation ( 1 ) is adequate. Knowing that this value is an
approximation, we then selected from all the registered close
encounters those that had a minimum distance within 10r
td
. For
the forward integration, we see that most of these (about 3/4)
occurred with Jupiter and Saturn (Table 2). Very few
encounters occurred within 1r
td
(none with Uranus or
Neptune). For the backward integration, we see that the
extreme encounters with Jupiter and Saturn still prevail, but
here we note the occurrence of a few encounters within 1r
td
with Uranus and Neptune. We explored the effects of each of
these extreme encounters (10r
td
) on the particles of
Chariklo’s rings, as described in the following.
4. SIMULATING THE RINGS
As the second step of our study, we numerically simulated
the extreme close encounters, including massless particles
around Chariklo. According to Section 2, a close encounter is
registered when a clone of Chariklo crosses the limit of 1 Hill
radius of any of the giant planets. At this crossing moment, we
recorded the position and the velocity of these bodies relative to
the Sun. These values are the initial conditions for the
simulations of the extreme close encounters, i.e., encounters
with minimum distance within 10r
td
. Thus, at this step, the
numerical simulations always involve the Sun, the bodies
performing the close encounter (the planet and Chariklo), and a
sample of particles orbiting Chariklo.
We considered particles with circular equatorial orbits,
radially distributed from 200 km to 1000 km, taken every
20 km. For each radial distance 100 particles were considered
in a random angular distribution. Such a combination of values
resulted in a total of 4100 particles orbiting Chariklo.
The pole orientation of Chariklo was considered to be
perpendicular to the orbital plane. This is a reasonable
approach since the rings are assumed to be in the equatorial
plane of Chariklo, and we are interested in the maximized
radial perturbations of the rings.
The encounters were simulated for a time span of 1 year
using the adaptive time-step Gauss– Radau numerical integra-
tor, keeping the accuracy at 10
−12
(Everhart 1985, pp.
185–202). Throughout the integration, the particles could
collide with Chariklo or be ejected. The collisions were defined
by the equivalent radius of Chariklo (124 km). The ejections
were defined by the energy of the two-body problem Chariklo
particle.
According to Table 2, 96 close encounters were simulated
for the forward case and 98 for the backward case. The results
of these simulations and their implications are presented in
Table 3 and they are discussed in the following sections.
5. CATASTROPHIC ENCOUNTERS
We classify as catastrophic those close encounters that led to
the complete removal of the particles in the region of the rings
of Chariklo. Knowing that the particles of the rings are
distributed in the range of ≈390 km to ≈405 km, we defined
that there was a catastrophic encounter if at the end of our
simulation particles distributed beyond 380 km were lost by
ejection or collision as defined in Section 4. The results
presented in Table 3 show that in about 10% of the simulations
the rings were removed from Chariklo due to close gravita-
tional encounters with the giant planets, for both the backward
and forward integrations.
For the forward integration, we found that only extreme
encounters with Jupiter and Saturn were able to fully remove
the rings. For the backward integration there were a few cases
where Uranus and Neptune were able to do so. Our data
suggest that Uranus and Neptune might have influenced the
existence of the rings in the past, but from now on Jupiter and
Saturn would play this role. However, more simulations are
required to investigate whether this is a real difference in the
forward/backward evolution or the result of a statistical artifact
due to the small number of extreme close encounters.
In the cases of forward integration in time, after the removal
of the rings, Chariklo remained as a Centaur for much less than
a million years, i.e., the rings were destroyed in the very last
stage of Chariklo’s orbital evolution among the giant planets.
In the cases of backward integration in time, the removal of the
rings occurred long before Chariklo completed its first million
years as a Centaur, i.e., in its first stage of orbital evolution
among the giant planets.
6. DISTURBING ENCOUNTERS
There were cases in which the particles of the rings were not
removed, but their orbits were significantly changed due to a
significant perturbation caused by an encounter with a giant
planet. In Figure 2, we present an example of the effects of
such an encounter with Jupiter. The plots show the maximum
final variation in semimajor axis and eccentricity among the
hundred particles that share the same initial radial position. As
expected, the values increase with the radial distance. In the
region of the rings (indicated by the vertical lines) the
semimajor axis changes by more than 30 km and the
eccentricity grows up to more than 0.5.
The results of the encounters that produced at least some
noticeable variations (Δ e 0.01)
on the orbits of the rings are
4
The Astrophysical Journal, 824:80 (7pp), 2016 June 20 Araujo, Sfair, & Winter
Table 3
Registered Catastrophic and Disturbing Encounters of the Rings of Chariklo due to Extreme Close Encounters
with Each of the Giant Planets over a Time Span of 10 Myr
Forward Encounters Backward Encounters
Catastrophic
a
Disturbing
b
Survival Time
c
Catastrophic
a
Disturbing
b
Survival Time
c
[Max:Min](years) [Max:Min](years)
Jupiter 6 9 [16,125:221,739] 616[−49,245:−546,550]
Saturn 4 7 [56,650:623,559] 07 L
Uranus 0 0 L 31[−1,371,579:−4,401,849]
Neptune 0 0 L 12 −1,499,269
Notes.
a
Rings are completely removed.
b
External particles removed but the rings survive.
c
Minimum and maximum survival time registered among the clones after they suffered a catastrophic encounter, excluding the immediate ejection cases.
Figure 2. An example of a disturbing close encounter caused on the ring by a
close encounter with Jupiter. (a) Maximum final change in eccentricity. (b)
Maximum final change in semimajor axis (km). The plots show the maximum
final changes among the hundred particles that share the same initial radial
position. The vertical lines indicate the boundary of the ring region. The
encounter was performed with a minimum distance of 6.6 planet radii, with a
relative velocity of
=
¥
V 8.00
km s
−1
. The encounter resulted in a critical
radius of R
C
= 460 km, meaning that no particles in the region of the rings
were removed.
Table 4
List of Significant Disturbing Encounters (Δe 0.01) with the Giant Planets
for both Forward and Backward Integration within the Time Span of 10 Myr
Minimum Encounter
¥
V
Maximum Maximum Survival
Distance (km s
−1
) Ring Ring Time
b
(Planet Radius)
a
Δa (km) Δe (years)
Jupiter—Forward
6.6 4.00 35.28 0.54 451,203
6.9 4.67 7.61 0.28 509,333
8.5 5.81 34.40 0.45 43,868
8.8 3.76 28.20 0.32 6891
9.2 5.03 44.33 0.57 1,140,000
15.4 7.00 0.04 0.02 55,034
16.0 7.78 0.02 0.01 59,483
Saturn—Forward
6.8 4.87 24.77 0.34 22,115
7.4 3.12 30.13 0.53 337,731
8.2 4.42 1.23 0.07 87,594
9.3 5.29 0.68 0.06 253,520
10.4 3.63 0.14 0.031 573,463
Jupiter—Backward
4.2 9.87 25.59 0.20 −217,796
8.3 4.17 17.34 0.40 −18,259
8.4 4.96 13.63 0.33 −23,770
8.4 10.32 65.85 0.51 −8,204
8.5 7.23 2.42 0.20 −280,371
11.1 4.93 0.065 0.03 −84,066
11.1 5.20 5.74 0.19 −153,800
11.9 6.62 2.33 0.10 −537,024
13.4 3.17 0.28 0.04 −309,943
13.5 7.40 0.06 0.02 −36,896
14.4 1.25 0.03 0.01 −98,210
15.4 5.72 0.02 0.01 −45,522
16.7 9.65 0.03 0.01 −1,634,011
Saturn—Backward
7.9 2.68 13.79 0.300 −405,570
Uranus—Backward
10.8 3.00 3.73 0.11 −2,504,843
Notes. The immediate ejection cases were excluded.
a
The minimum encounter distance given in terms of the radius of the planet in
question.
b
Survival time after a disturbing encounter.
5
The Astrophysical Journal, 824:80 (7pp), 2016 June 20 Araujo, Sfair, & Winter
