The evolution of a Pluto-like system during the migration of the ice giants

Icarus xxx (2014) xxx–xxx

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The evolution of a Pluto-like system during the migration of the ice giants Pryscilla Pires a,⇑, Silvia M. Giuliatti Winter a, Rodney S. Gomes b a b

Univ. Estadual Paulista – UNESP, Grupo de Dinâmica Orbital e Planetologia, Av. Ariberto Pereira da Cunha, 333, Guaratinguetá-SP 12516-410, Brazil Observatório Nacional, R. Gen. José Cristino, 77, Rio de Janeiro-RJ 20921-400, Brazil

a r t i c l e

i n f o

Article history: Received 20 December 2013 Revised 17 April 2014 Accepted 17 April 2014 Available online xxxx Keywords: Planetary dynamics Trans-Neptunian objects Pluto, satellites

a b s t r a c t The planetary migration of the Solar System giant planets in the framework of the Nice model (Tsiganis, K., Gomes, R., Morbidelli, A., Levison, H.F. [2005]. Nature 435,459–461; Morbidelli, A., Levison, H.F., Tsiganis, K., Gomes, R. [2005]. Nature 435, 462–465; Gomes, R., Levison, H.F., Tsiganis, K., Morbidelli, A. [2005]. Nature 435, 466–469) creates a dynamical mechanism which can be used to explain the distribution of objects currently observed in the Kuiper belt (e.g., Levison, H.F., Morbidelli, A., Vanlaerhoven, C., Gomes, R., Tsiganis, K. [2008]. Icarus 196, 258–273). Through this mechanism the planetesimals within the disk, heliocentric distance ranging from beyond Neptune’s orbit to approximately 34 AU, are delivered to the belt after a temporary eccentric phase of Uranus and Neptune’s orbits. We reproduced the mechanism proposed by Levison et al. to implant bodies into the Kuiper belt. The capture of Pluto into the external 3:2 mean motion resonance with Neptune is associated with this gravitational scattering model. We verified the existence of several close encounters between the ice giants and the planetesimals during their outward radial migration, then we believe that the analysis of the dynamical history of the plutonian satellites during this kind of migration is important, and would provide some constrains about their place of formation – within the primordial planetesimal disk or in situ. We performed N-body simulations and recorded the trajectories of the planetesimals during close approaches with Uranus and Neptune. Close encounters with Neptune are the most common, reaching approximately 1200 in total. A Pluto similarly sized body assumed the hyperbolic trajectories of the former primordial planetesimal with respect to those giant planets. We assumed the current mutual orbital configuration and sizes for Pluto’s satellites, then we found that the rate of destruction of systems similar to that of Pluto with closest approaches to Uranus or Neptune <0.10 AU is 40%, i.e. these close approaches can lead to ejections of satellites or to changes in the satellites eccentricities at least 1 order of magnitude larger than the currently observed. However, we also found that the number of closest approaches which the minimum separation to Uranus or Neptune <0.10 AU is negligible, reaching 6%. In the other 60% of close encounter histories with closest approaches >0.10 AU, none of the systems have been destroyed. The latter sample concentrates 94% of closest approaches with the ice giants. Recall that throughout the early history of the Solar System giant impacts were common (McKinnon, W.B. [1989]. Astrophys. J. 344, L41–L44; Stern, A. [1991]. Icarus 90; Canup, R.M. [2005]. Science 307, 546–550). Also, impacts capable of forming a binary like Pluto-Charon can occur possibly prior to 0.5–1 Gyr (Kenyon, S.J., Bromley, B.C. [2014]. Astron. J. 147, 8), and small satellites such as Nix and Hydra can grow in debris from the giant impact (e.g., Canup, R.M. [2011]. Astron. J. 141, 35). Thus, we conclude that if Pluto and its satellites were emplaced into the KB from lower heliocentric orbits, then the Pluto system could survive the encounters that may have happened for emplacement of the Plutinos through the mechanism proposed by Levison et al. Ó 2014 Elsevier Inc. All rights reserved.

1. Introduction The dwarf planet Pluto is a member of the trans-Neptunian belt, also known as Edgeworth-Kuiper belt (KB or Kuiper belt, ⇑ Corresponding author. Fax: +55 12 3123 2868. E-mail address: [email protected] (P. Pires).

hereafter), a complex structure of numerous bodies orbiting the Sun beyond Neptune’s orbit up to about 60 astronomical units (AU). Estimates give that the current mass is within the range 0.01–0.1 Earth masses (Gladman et al., 2001; Bernstein et al., 2004; Chiang et al., 2007), which means that the belt has lost a large fraction of its original mass, about 10–30 Earth masses (Stern, 1996; Stern and Colwell, 1997; Kenyon and Luu, 1998;

http://dx.doi.org/10.1016/j.icarus.2014.04.029 0019-1035/Ó 2014 Elsevier Inc. All rights reserved.

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Kenyon and Luu, 1999; Kenyon and Bromley, 2004), over the years. Numerical simulations such as those in Tsiganis et al. (2005), Morbidelli et al. (2005), and Gomes et al. (2005) – Nice model – require the original planetesimal disk mass to be 35 Earth masses. The simulations of Gomes et al. (2005) aimed to explain the origin of the late heavy bombardment (LHB) of the inner Solar System. The model of Gomes et al. yield the quantity of approximately 0.14 Earth masses for the current trans-Neptunian disk. Today there are 1260 objects classified as trans-Neptunian objects1 (TNOs) with absolute visual magnitude up to 12.4. Many TNOs are locked in external p : q mean-motion resonances (MMRs) with Neptune, where p and q are integers. This means that the orbital period of a TNO captured into resonance is a nearly integer multiple with that of Neptune. Some resonances have a large number of bodies, such as 3:2 (whose members are known as Plutinos), 5:3, 7:4, 2:1 and 5:2. The fraction of TNOs locked in MMRs with Neptune ranges from 10% to 20% (Trujillo and Brown, 2001; Kavelaars et al., 2009). Regarding the plutino population, estimates give the existence of approximately 25,000 with diameters larger than 50 km (Kavelaars et al., 2009; Murray-Clay and Schlichting, 2011). Pluto is the largest body in 3:2 resonance with Neptune and one of the numerous multiple system in the outer Solar System. So far, five satellites were observed around Pluto: Charon (Christy and Harrington, 1978), Nix and Hydra (Weaver et al., 2006), Kerberos and Styx (Showalter et al., 2012; Showalter et al., 2013). Charon is the largest satellite, with a diameter of about 1200 km and an enough mass to be in a nearly round shape. The Charon/Pluto mass ratio is 0.1163 (Tholen et al., 2008), which implies that the PlutoCharon center of mass is outside Pluto. Each member of the binary rotates every 6.4 days, and the Pluto-Charon system has a 6.4 days orbit. Thus, the pair is in a double synchronous state. The small satellites are most likely to have irregular shapes; Nix’s radius is estimated to be 44 km, while those of Styx, Kerberos and Hydra are 5 km, 7 km and 36 km, respectively. To obtain the radii for Nix and Hydra, Tholen et al. (2008) assumed a Charon-like density of 1.63 g/cm3, while to obtain the sizes of Styx and Kerberos, Showalter et al. (2012, 2013) assumed geometric albedos of 0.35, comparable to that of Charon. All four small moons lie outside Charon’s orbit with semimajor axes approximately 42,000– 66,000 km from the center of mass of the system (e.g., Buie et al., 2006; Tholen et al., 2008; Showalter et al., 2013), forming a very compact multiple system. The stability of Nix and Hydra were discussed in Nagy et al. (2006) and Pires dos Santos et al. (2011), while Youdin et al. (2012) showed that the stability of Kerberos, over the age of the Solar System, requires lower masses for Nix and Hydra of the order of 1016 kg. None of the three cited references has shown that Styx is in a stable orbit. Although, it might be as close as possible to the innermost stable orbit around Pluto-Charon (Pires dos Santos et al., 2011; Kenyon and Bromley, 2014). Nowadays, it is largely accepted that a giant impact between two similarly sized bodies originated the Pluto-Charon binary (McKinnon, 1989; Canup, 2005). The origin of Charon through a giant impact is favoured due to the high angular momentum of the Pluto system, as well as a giant collision is also favoured to model the formation of the Earth–Moon pair (Canup and Asphaug, 2001; Canup, 2004). Through smooth particle hydrodynamic simulations Canup (2005) showed that the formation of Charon is viable in a large oblique collision. The results show the formation of the binary as a result of such collision, with Charon in a very eccentric orbit relative to Pluto (e < 0.8) and very close to it (a approximately 3–15 Pluto’s radii, Rp , where 1 Rp

1 Minor Planet Public Data Center: http://www.minorplanetcenter.net/iau/lists/ t_tnos.html.

corresponds to 1150 km). At the time of the satellite’s formation, Pluto was spinning fast. Torques due to tides raised by Charon on Pluto transferred angular momentum from the spin of the primary to the orbit of Charon, thus the satellite evolved to its present orbit and had its eccentricity damped, while Pluto’s spin period slowed down (e.g.,Fernandez and Ip, 1984). For comparison, the current semimajor axis and eccentricity of Charon are 17Rp and 0.0035 (Tholen et al., 2008), respectively. The model of Canup (2011) suggests that debris from the Charon-forming impact (Canup, 2005) lead to the formation of the small plutonian satellites. However, the main issue with Canup’s model is that most of the material from the impact resides in a ring just outside the binary system (a up to 30 Rp ), while the current orbital radii of the satellites are larger than that. It remains to be show how these tiny bodies achieved their current distances. The origin of the smaller satellites is heavily debated (e.g., Lithwick and Wu, 2008a; Cheng, 2011; Peale et al., 2011), and many scenarios have been proposed (Stern et al., 2006; Ward and Canup, 2006; Lithwick and Wu, 2008b; Pires dos Santos et al., 2012). The most promising scenario is that of Kenyon and Bromley (2014), who show that throughout the early history of the Solar System, giant impact that produces the Pluto-Charon binary could happen in a non-negligible rate. After the impact, both Pluto and Charon accrete and eject the debris around the binary to a  20 Pluto’s radii. The massive circumbinary disk surrounding Pluto-Charon was composed of 0.1–1 km particles, and the binary transferred angular momentum to the disk or ring. As a consequence, the disk has spread close to the current positions of Styx-Hydra. After the collisional damping has overcome the secular perturbations from the binary, small satellites growth began. As the satellites grow, they scatter away smaller objects and migrate through the disk. At the end, Kenyon and Bromley were able to show that the mechanism of collisional evolution within a ring or a disk of debris can yield satellites, especially with radius between 10 and 80 km, at similar positions as Pluto’s known small satellites. At this time, we will briefly present scenarios from the literature that have been proposed to explain the origin of the resonance-locked orbit of Pluto and the Kuiper belt formation. After, we will explain why we choose to use one of them as a framework. The theory presented by Malhotra (1993, 1995) have been proposed to explain how Pluto ended up occupying the 3:2 MMR with Neptune. This theory is based on the late stages of the planetary formation, when the giant planets were already formed and they were scattering away the remnant planetesimal debris in the interplanetary region. Briefly, as Jupiter effectively ejects those planetesimals scattered inwards by Uranus and Neptune onto hyperbolics orbits, Uranus and Neptune moved considerably outwards due to the angular momentum conservation. This way, the exterior mean motion resonances with Neptune moved outwards as well, capturing not only Pluto in resonance, but also other KBOs – Kuiper belt objects. In these models the test particles were spread to at least 50 AU in near-circular and low-inclination orbits, and the high eccentricity of Pluto would be a consequence of the capture into resonance caused by the outward migration of Neptune. In the light of Pluto’s current orbital eccentricity, Malhotra (1993) estimates that an initially circular Pluto migrated at least 5 AU after its capture into 3:2 MMR with Neptune. An issue with this model is that the 3:2 population presents a distinct inclination distribution – objects with low and high inclinations. The ‘‘resonance capture mechanism’’ does not explain the different inclination distribution observed in this population (Gomes, 2003). To overcome this problem, the primordial disk should match the current inclination distribution of this population (Hahn and Malhotra, 2005; Levison et al., 2008; Murray-Clay and Schlichting, 2011).

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Levison et al. (2008), L08 hereafter, used the evolution of the giant planets as predicted by Tsiganis et al. (2005) to propose an explanation of the main features of the Kuiper belt, including the implantation of the cold population into the KB. According to this scenario, after the last encounter between Uranus and Neptune, the latter is scattered to a semimajor axis 28 AU with high eccentricity of approximately 0.3. However, the inclination was kept low by conservation of angular momentum. Following, Neptune’s large eccentricity increases the widths of its MMRs, which overlap and create a chaotic region interior to 2:1 resonance. At this time planetesimals within the disk, which initially extended to 34 AU, could visit the unstable region. As Neptune migrates outwards and its eccentricity is damped out by interactions with the disk, the width of the MMRs decreases and the chaos disappears, allowing particles that happen to be at this ‘‘new’’ stable region remain trapped. Despite some issues, such as the mean eccentricity of their final classical population of KBOs is too large, this model has the virtue to match well the inclination distribution of the Plutinos, besides other important features of the KB. We preferred to use the evolution of L08 instead of using that of Tsiganis et al. due to the fact that in all simulations we performed, following the evolution of the Nice model, a very few number of objects was left in the Kuiper belt at the end of 4.5 Gyr, which is not a good outcome for our work (more details, see Section 2). Besides, the dynamical evolution of the giants planets as in Tsiganis et al. (2005) is chaotic, where a small change in the initial conditions of the planets leads to a completely different result in the end: escape of a giant planet from the Solar System, for example, is a possible outcome. A major advantage of using the evolution as proposed by L08 is the possibility of controlling the planetary evolution by implementing fictitious forces into the numerical integrator. In this way, we can spread an initial set of thousands of particles over multiple runs without changes in the final results provoked by chaos, since all runs present the same orbital evolution for each planet. This approach allows us to perform the numerical simulations in a shorter period of time. All difficulties of using numerical simulations, such as those in Tsiganis et al. (2005), were also discussed in L08. Differently from the Nice model papers, the simulations in L08 and here do not go through 4.5 Gyr, however the majority of the close encounters between particles and planets occurs just few million years after the beginning of our integrations. Thus, we believe that shorter numerical simulations (see Section 2) are enough for our purposes. Here, we use the outward migration of Neptune, as envisioned by L08, to verify the dynamical effects of the giant planets on Pluto-like systems during the dynamical instability of Uranus and Neptune’s orbits. Kenyon and Bromley (2014) claim that giant impacts as the one believed to have formed Pluto-Charon were common during the early history of the Solar System, with a frequency of 1 per 100–300 Myr. This result suggest that the binary could have been formed closer to the Sun and not in situ. If the giant impact leads to a few small satellites orbiting Pluto-Charon (e.g., Canup, 2011), then they should remain bound to the binary despite the disruptional perturbation of close approaches with the giant planets. This paper is divided as follows: in Section 2 we present the methodology and the results, and in Section 3 our conclusions.

2. Close encounters between a Pluto-like system and the Solar System ice giants 2.1. The migration of the Solar System giants We explore the evolution of multiple systems similar to that of Pluto following the planetary migration proposed by L08, where

Uranus and Neptune had, after their last mutual encounter, highly eccentric orbits. This assumption is consistent with results obtained in many simulations of the Nice model for the evolution of Jupiter, Saturn, Uranus and Neptune (Tsiganis et al., 2005). The Nice model reproduces numerically the evolution that the outer Solar System may have gone after the gas-disk phase is terminated. In this model, the initially low-inclination and nearly circular orbits of the giant planets (Morbidelli et al., 2009) evolve in semimajor axes as a consequence of the interaction with the planetesimal disk to conserve the angular momentum of the system (e.g., Fernandez and Ip, 1984). The disk was assumed to have 35 Earth masses with an outer edge at 34 AU, and the Solar System giants to be in a compact configuration with a ranging from 5.5 to 14 AU. The collisional grinding of the planetesimal disk is neglected in the ‘‘Nice’’ simulations and also in this work. For large particles (>100 km in radius) the collisional grinding can be neglected before the LHB – period of slow migration (e.g., O’Brien et al., 2005; Kenyon et al., 2008). The massive planetesimal disk just outside the orbits of the ice giants is the main ingredient to trigger the orbital migration of the giant planets and the implantation of planetesimals into the KB (Tsiganis et al., 2005; Levison et al., 2008). Thus, the primordial trans-Neptunian disk should remain massive for 600 Myr – LHB period. In favor of the Nice model, the size-distribution assumed to the planetesimal disk resembles to that currently observed in the Kuiper belt, so as O’Brien et al. (2005) showed, collisions of the disk particles before the LHB do not alter significantly its total mass. To evaluate if close approaches with the giant planets would disrupt a Pluto-like system (further details in Section 2.2), we performed a numerical integration following the Run-B of L08 by using the hybrid package of Mercury 6.2 (Chambers, 1999). We begin with an initial swarm of 60,000 test particles; of these, half is in the inner disk and the other half in the outer disk. Particles were placed in orbits with initial semimajor axes ranging uniformly from 20 to 34 AU with eccentricities and inclinations randomly selected between 0 and emax and 0° and imax , respectively. The initial conditions of the disk are present in Table 1. These initial orbital conditions follow the results presented by the Nice model, where the outer part of the disk is colder (planetesimal orbits with smaller eccentricities and inclinations). We included the four giants of the Solar System with the following initial conditions: Jupiter with a ¼ 5:2 AU and Saturn with a ¼ 9:6 AU, on near-circular and low-inclination orbits; Uranus with a ¼ 17:5 AU and e ¼ 0:2, and Neptune with a ¼ 29:0 AU and e ¼ 0:3. Uranus and Neptune’s inclinations are on the order of 1°. We used a modified version of Mercury 6.2 built into mfo-user routine to apply user defined forces only to Uranus and Neptune. The orbital migration of the ice giants and the damping of their orbital eccentricities are employed by adding exponential forms as in Malhotra (1995):

a ¼ af  Da expðt=sa Þ

ð1Þ

e ¼ e0 expðt=se Þ

ð2Þ

where the indexes 0 e f mean initial and final, respectively, a and e are the semimajor axis and eccentricity of Uranus or Neptune at time t, Da ¼ af  a0 , and s is an exponential timescale that can be Table 1 Initial orbital elements of the planetesimal disk related to the Sun. Parameter

Inner disk

Outer disk

a (AU) e i (°)

20–29 0.0–0.3 0–10

29–34 0.0–0.15 0–5

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adjusted to have the desired final configuration of the planets. The migration and damping are parameterized by the respective timescales sa ¼ 3 Myr and se ¼ 1 Myr. However, to avoid the evolution of both to be chaotic, we included the soft gravitational force as in L08, with the constant  ¼ 0:8 AU:

f UN ¼

GMN M U ðx2UN

þ 2 Þ

3=2

xUN

ð3Þ

where MU and MN refer to the mass of Uranus and Neptune, respectively, and xUN is the relative position vector of both of them. We did not apply any fictitious force for controlling their inclinations. The numerical integration is performed by adopting an accuracy parameter of 1012 and a step size of 200 days for the time-span of 108 years in three steps: migration and damping, only migration, and without any migration or damping. The first step lasts approximately 1 My. After the eccentricities of Uranus and Neptune are damped, they continue migrating outwards until 10My – second step. At the end of the migration phase the system was integrated for a further 9  107 yr to eliminate bodies that happen to be unstable in the Kuiper belt. After this timescale, the ice giants may still be migrating (e.g., Nesvorny´ and Morbidelli, 2012). Similar procedure was adopted by L08, however the last step in their numerical simulations took 1 billion years. At the end of our 108 years of integration, the planets have final orbits very similar to their current ones. The final semimajor axes for Uranus and Neptune differ by DaU ¼ 0:1 AU and DaN ¼ 0:2 AU, respectively, from their present values, whereas the planets’ final eccentricities are on the order of 0.01 and 0.001, respectively. The inclinations are kept low during the entire integration. Particles are eliminated when passing more than 60 AU from the Sun or when they physically collide with one of the massive bodies. The orbital evolution of the four giant planets are shown in Figs. 1–3. Figs. 4 and 5 are snapshots of the orbital eccentricity and inclination distributions of the particles captured as Kuiper belt objects, respectively. They show a large number of particles located near first and second order mean motion resonances with Neptune. For the 3:2 resonance, the eccentricity ranges from 0.1 to 0.3, while the inclination ranges from 0 to 20°. Therefore, in terms of a–e and a–i distributions, these results are in a good agreement with the current observations (e.g., Gladman et al., 2008; Kavelaars et al., 2009). However, our final configuration of the Kuiper belt has some issues. Our a–e distribution (Fig. 4) does not reproduce the

Fig. 2. Eccentricity vs time of the Solar System giants.

Fig. 3. Inclination vs time of the Solar System giants.

Fig. 4. Semimajor axes vs eccentricity of the particles captured as Kuiper belt objects. Vertical lines indicate the nominal location of external mean motion resonances with Neptune. Fig. 1. The evolution of each planet are indicated by three curves: the aphelion (Q) and the perihelion distances (q) are represented by the upper and lower curves, respectively. The middle one corresponds to the semimajor axes (a). The letters J, S, U and N indicate each giant planet of the Solar System.

outer edge of the classical belt at the 2:1 MMR with Neptune (at 48 AU), particularly at low eccentricity. Instead, the disk extends up to 46 AU. Also, the 5:4 and 4:3 MMRs are notably populated,

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Fig. 5. Semimajor axes vs inclination of the particles captured as Kuiper belt objects. Vertical lines indicate the nominal location of external mean motion resonances with Neptune.

5

Fig. 6. Libration of the resonant angle of a particle captured into the 3:2 MMR with Neptune.

which is also a discrepancy with observational data (e.g., Gladman et al., 2008). Finally, the extended scattered disk of TNOs was not reproduced by our simulations, even though these objects are associated with the gravitational scattering by Neptune, and the region ranging from 40 to 42 AU was not depleted at low inclination (Fig. 5), as expected (Duncan et al., 1995; Morbidelli et al., 1995). Although many important aspects of the KB were not reproduced well in our simulations, our main goal is to reproduce the orbital distribution of the Plutinos, so we can use the sample of close encounters of these bodies with Uranus and Neptune as initial condition for a subsequent analysis. To accurately determine which particles are locked into the 3:2 resonance, we firstly selected those within 0.5 AU from the resonance location, with final e > 0:1 and i > 5 . Following, we analyzed the libration of the resonant angle:

/ ¼ 3k  2kp  -

ð4Þ

where kp and k are the mean longitudes of Neptune and the test particle, respectively, and - is the longitude of pericenter of the particle. At the end, a particle is considered trapped into the 3:2 MMR if its resonant angle (/) librates over the last 50 My of the numerical integration. 106 objects satisfy the above criteria, which represents 5% of the total population of our final Kuiper belt. Although the retention efficiency is small, our integrations are intended to verify the effects of the implantation of a Pluto-like system into the KB rather than to reproduce the final configuration of the trans-Neptunian disk. Thus, we do not consider the lower retention fraction an issue at this point. Trujillo et al. (2001) claim that the entire resonant population is roughly 10% of the total population of the KB, while Kavelaars et al. (2008) predict that 20% of KBOs are trapped only in the 3:2 MMR with Neptune. Our results is more consistent with Trujillo et al. In the sequence, we can refer to those particles captured into the 3:2 resonance as pre-selected. Fig. 6 shows an example of a particle classified as resonant following our criteria. The libration is about 180°. In Fig. 7 we present the time variation of the heliocentric distance of a pre-selected particle. Its final semimajor axis is about 40 AU, and the large separation between the maximum and the minimum distances from the Sun is an indicative of its large orbital eccentricity, since we selected particles with final e > 0:1. This plot shows the outward migration of the planetesimal before its capture into the 3:2 MMR with Neptune at approximately 10 Myr.

Fig. 7. Orbital evolution of a particle locked in 3:2 MMR with Neptune. Three curves are plotted: the maximum heliocentric distance (Q), the semimajor axis (a), and the minimum heliocentric distance (q). The horizontal solid line indicates the nominal resonance location according to the final position of Neptune obtained in our simulations.

During the migration of the Solar System giants, we recorded the positions and velocities of the planetesimals passing less than 1.3 AU from the planets (for conversion, 1.3 AU corresponds to approximately 1.5 Neptune’s Hill radii). A single planetesimal can have several close approaches with a planet, thus we have a complete history for each of the pre-selected particles approaching any of the planets at the end of 108 years. In the Fig. 8 we present a typical situation: the same particle having many close approaches with Neptune. The black points mark the beginning of each close approach for particles passing less than 0.5 AU from a planet. In the sequence, we will only use approaching trajectories just like those tagged with black points. In this way, we can use this data to recreate the close encounters between Pluto-like systems and the ice giants. Neptune is the planet with the largest number of close encounters with the pre-selected planetesimals. In total, we have 106 close encounter histories with Neptune, and 23 with Uranus. There are no encounters between Jupiter or Saturn and the pre-selected particles. Fig. 9 presents the histograms of the number of encounters occurred within 0.5 AU from Uranus and Neptune for each planetesimal flagged as Plutino. The medians indicate that half of the particles have less than ten encounters <0.5 AU with Uranus or Neptune.

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Fig. 8. Example of a close encounter history of a particle trapped into the 3:2 MMR with Neptune. The black points mark the beginning of each close approach for particles passing less than 0.5 AU from the planet, and the lines show the Neptuneocentric distances vs time.

Firstly, we checked if all close encounters produce temporary captures by the planets. A particle is considered captured if at any point, during its orbital evolution, its 2-body energy becomes negative with respect to a planet. In these numerical simulations we consider the following planets with their present values for masses and radii: Sun (central body) at 0, 0, 0 in cartesian coordinates, Uranus or Neptune; and the close encounter trajectories of the pre-selected particles. We monitored the orbital energy of each particle with respect to the planet involved during the entire encounter, i.e. each particle is integrated since the moment it enters and until it is outside a radius of 1.3 AU from each of the two planets. Since, all close encounters do not lead to temporary captures by the ice giants the entire database of encounters can be used in the next section. 2.2. The gravitational effects of Uranus and Neptune on Pluto-like systems

planetesimal in a reference frame centered at the Sun, and the satellites in a frame centered at the planetesimal. The code has already been used for numerical approaches (e.g., Gaspar et al., 2013; Araujo and Winter, 2013). We have the heliocentric positions and velocities of the planet and planetesimal at the beginning of each close encounter

0

50 40 30 0

10

20

Number of particles

15 10 5

Number of particles

60

20

70

We performed numerical simulations by using the Gauss-Radau algorithm (Everhart, 1985) to determine the gravitational effects of the ice giants planets on Pluto-like systems. This numerical integrator allows us to place the orbits of a planet and a massive

Fig. 10. Left panel: Example of a close encounter between Neptune and B1 which the minimum Neptuneocentric distance is <300 Neptune radii (<0.05 AU); right panel: time variation of the energy constant of S2 with respect to Pluto. This close encounter resulted in the escape of S2.

0

20

40

60

80

100

Number of encounters < 0.5 AU

120

0

10

20

30

40

50

60

70

Number of encounters < 0.5 AU

Fig. 9. Left panel: histogram of the number of encounters for each particle that occurred within 0.5 AU from Uranus; right panel: histogram of the number of encounters for each particle that occurred within 0.5 AU from Neptune. The vertical dashed lines are the medians of the distributions.

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<0.5 AU in a close encounter history. From now on, we will work with systems composed by four bodies: B1, B2, S1 and S2, where B1 assumes the encounter trajectory of the former planetesimal. The initial conditions of B1, B2, S1 and S2, aim to replicate the masses, radii and mutual orbital elements of Pluto, Charon, Nix and Hydra, respectively, derived from Tholen et al. (2008). Nix and Hydra’s masses in Tholen et al. are on the order of 1017 kg. In all simulations B1, B2, S1 and S2 are treated as massive bodies. Nevertheless, we ran a sample of close encounter integrations by considering B2, S1 and S2 as massless test particles which presented no changes in the survivability of the systems. We consider a Pluto-like system destroyed by a close encounter if (1) B2, S1 or S2 become unbound to B1 (the constant energy changes from negative to positive), (2) if a collision happens, or (3) if the mutual orbital configuration of the satellites changes considerably from the initial parameters: e change at least one order of magnitude and i varies more than 10°. It is worth to remember that all Pluto’s small satellites are nearly coplanar and have nearly circular orbits: eC ¼ 0:0035, eN ¼ 0:0119, eH ¼ 0:0078; iC ¼ 96:168 , iN ¼ 96:190 , iH ¼ 96:362 , where the eccentricities of Nix and Hydra are related to the barycenter of the system (e.g., Tholen et al., 2008; Showalter et al., 2012, 2013). In other words, if the moons end up, after the close encounter integrations, into highly inclined or eccentric orbits, then a suitably strong damping

200 150 100 0

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Fig. 11. The Plutocentric orbital elements vs time for a satellite similar to Charon during a closest approach in a given history.

mechanism would be necessary. Unfortunately, we miss this mechanism. The numerical integrations are performed, in a heliocentric reference frame, as follows: at the beginning B1 assumes the hyperbolic trajectory with respect to Uranus or Neptune in a history of close encounters; the whole system (Sun, planet, B1, B2, S1 and S2) is integrated until the distance planet-B1 is larger than 1.3 AU (about 10 yr). If none of the above criteria of destruction are met, the final mutual configuration of B1–B2, S1 and S2 is recorded. B1 assumes the next hyperbolic close encounter trajectory in the same close encounter history, until we have numerically integrated all upcoming trajectories in all histories of close encounters. In other words, we evolved B1 through a sequence of encounters that a test particle had in the migrating simulations. If a collision or ejection occurs in one of the close encounter integrations in a given history, this integration is automatically interrupted and resumed. Focusing in close encounters with Neptune, our simulations have shown that the main mechanism for destruction of B1–B2– S1–S2 system is the increase of the satellite orbital eccentricity, i.e. one of the satellites is driven onto a escape orbit (1st criteria). This event depends strongly on the closest approach distance. In 60% of close encounter histories with closest approach <0.05 AU, B1 had lost at least one of its satellites. 30% of all of these systems passing less than 0.10 AU, had lost at least one of the satellites S1 or S2. A typical change in the B1-satellite 2-body energy, leading to an ejection of the satellite, can be seen in Fig. 10. The minimum Neptuneocentric distance is smaller than 300 RN , or 0.05 AU. In each close encounter history with closest approaches >0.10 AU, 100% of all systems survived the outward migration driven by Neptune. Despite the gravitational effects of Neptune on the Pluto-like systems, they remained intact. In Fig. 11 we present the time variation of the orbital elements of a B1’s satellite during a closest approach >0.10 AU in a given history. As we can see, B2 ends in a nearly circular orbit with respect to B1. For close encounters with Uranus, we have only one close encounter history with closest approaches <0.05 AU, 5 histories with closest approaches <0.10 AU. The most common mechanism for destruction of the B1 systems with minimum encounter distance <0.10 AU is the increase in S2’s eccentricity (the outermost satellite) by 1 order of magnitude (3rd criteria). The Pluto-like systems are considered to have been destroyed in 60% of these cases (4 out of 6 histories). In all other cases, histories with closest approaches >0.10 AU, the Pluto-like systems are considered to have survived emplacement into the KB.

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Fig. 12. Left panel: The cumulative number of encounters with Neptune passing less than a given value. Right panel: the planet is Uranus. Aiming clarity, we had 17 and 2 closest approaches <0.05 AU to Neptune and Uranus, respectively; and 79 and 12 closest approaches <0.10 AU to Neptune and Uranus, respectively.

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All B1 systems which survived the scattering by Neptune presents a variation in orbital inclination of about 1°. Close encounters with Uranus or Neptune in which the minimum planetocentric distance is smaller than 0.10 AU can lead to disruptions of the Pluto-like systems. The closest few approaches determine if a system similar to that of Pluto survive or not. These kind of approaches represent approximately 6% (81 out of 1400) in all histories of close encounters. In Fig. 12 we present the cumulative number of encounters passing less than a given value from Neptune and Uranus. The number of closest approaches <0.10 AU are negligible compared to the whole sample. Close encounters between the already formed and evolved Pluto-like system and the ice giants that may have occurred during the formation of the Kuiper belt destroy 16% of the close encounter histories (21 out of 129), or those B1 systems. Therefore, if the Pluto system had been formed within the primordial disk rather than in situ, and later migrated outwards driven by Neptune, our results suggest that Pluto and its satellites may have remained intact during the period of dynamical instability in the outer Solar System. Although we have focused on the interactions of a Pluto-like system and the ice giants and verified that this system can survive the emplacement into the Kuiper belt, it remains to be show how the Pluto’s small outer moons were driven from smaller Plutocentric orbital radii (e.g., Canup, 2005, 2011) to their current positions, located from approximately 38 to 58 Pluto radii. Helpful information regarding the composition of Nix and Hydra’s surfaces and subsequently their origin can be obtained after the New Horizons fly-by through the Pluto system in 2015. Ice-rich surfaces could indicate that they are remnants from Pluto-Charon (Canup, 2011).

3. Conclusion We have run N-body numerical simulations to determine the gravitational effects of the Solar System giant planets on Pluto-like systems. Initially, we had the giant planets migrating as proposed to form the current architecture of the outer Solar System (Tsiganis et al., 2005; Levison et al., 2008), and a disk of massless planetesimals interacting with the planets. At the end, we had the number of planetesimals captured in MMRs with Neptune. We selected only those locked into the exterior 3:2 MMR, bodies currently known as Plutinos. By making B1, a Pluto-sized object, assume the hyperbolic trajectories of the former primordial planetesimal with respect to Uranus and Neptune, we verify if a given encounter leads to disruption of hypothetical plutonian systems. We have not considered the small satellites Styx or Kerberos, since there is not enough information about their orbits and sizes. As we have shown, close encounters with Neptune are the most common during the scattering of planetesimals, reaching up 1165 closest approaches distributed into 106 close encounters histories; meanwhile Uranus had 235 closest approaches spread out over 23 histories. Close encounter histories with at least 1 closest approach <0.10 AU represent 40% of the total (53 out of 129); of these, the majority (60%) of the B1 systems are not destroyed. In 60% of close encounter histories with closest approaches >0.10 AU, none of the systems have been destroyed. This latter sample concentrate 94% of the closest approaches with the ice giants. Thus, as the results indicate, approximations with the ice giants that lead to destruction of a Pluto-like system are rare. Recall that throughout the early history of the Solar System giant impacts were common (McKinnon, 1989; Stern, 1991; Canup, 2005). Also, impacts capable of forming a binary like Pluto-Charon can occur possibly prior to 0.5–1 Gyr (Kenyon and

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Please cite this article in press as: Pires, P., et al. The evolution of a Pluto-like system during the migration of the ice giants. Icarus (2014), http://dx.doi.org/ 10.1016/j.icarus.2014.04.029