The Astronomical Journal, 154:208 (8pp), 2017 November https://doi.org/10.3847/1538-3881/aa9184 © 2017. The American Astronomical Society. All rights reserved. Tritonʼs Evolution with a Primordial Neptunian Satellite System Raluca Rufu1 and Robin M. Canup2,3 1 Department of Earth and Planetary Sciences, Weizmann Institute of Science, Rehovot 76100, Israel; [email protected] 2 Southwest Research Institute, Boulder, CO 80302, USA Received 2017 August 1; revised 2017 October 3; accepted 2017 October 3; published 2017 November 6 Abstract The Neptunian satellite system is unusual. The major satellites of Jupiter, Saturn, and Uranus are all in prograde, low-inclination orbits. Neptune on the other hand, has the fewest satellites, and most of the system’s mass is within one irregular satellite, Triton. Triton was most likely captured by Neptune and destroyed the primordial regular satellite system. We investigate the interactions between a newly captured Triton and a prior Neptunian satellite system. We find that a prior satellite system with a mass ratio similar to the Uranian system or smaller has a substantial likelihood of reproducing the current Neptunian system, while a more massive system has a low probability of leading to the current configuration. Moreover, Triton’s interaction with a prior satellite system may offer a mechanism to decrease its high initial semimajor axis fast enough to preserve small irregular satellites (Nereid-like) that might otherwise be lost during a prolonged Triton circularization via tides alone. Key words: planets and satellites: dynamical evolution and stability – methods: numerical 1. Introduction 105 years. Yet, it is unclear whether Triton can induce mutual collisions among such satellites before it experiences a disruptive Models of giant planet gas accretion and satellite formation collision. Due to its retrograde orbit, collisions between Triton suggest that gas giants may typically have prograde regular and a prograde moon would generally have higher relative satellite systems formed within circumplanetary gas disks velocities than those between two prograde moons. A disruptive produced during their gas accretion, consistent with the general ( collision onto Triton is inconsistent with its current inclined orbit properties of the satellite systems of Jupiter and Saturn e.g., (Jacobson 2009), as Triton would tend to re-accrete in the local Stevenson et al. 1986;Lubowetal.1999;Canup&Ward2002; Laplace plane. Mosqueira & Estrada 2003;Sasakietal.2010;Ogihara& The objective of this study is to explore how interactions ) ’ Ida 2012 . The origin of Uranus satellites remains unclear, as they (scattering or collisions) between Triton and putative prior ’ may have similarly formed as a result of Uranus limited gas satellites would have modified Tritonʼsorbitandmass.We accretion (e.g., Pollack et al. 1991; Mosqueira & Estrada 2003; evaluate whether the collisions among the primordial satellites Canup & Ward 2006), or as a result of a giant impact (e.g., are disruptive enough to create a debris disk that would Slattery et al. 1992), or a combination of both (Morbidelli accelerate Triton’s circularization, or whether Triton would et al. 2012). experience a disrupting impact first. We seek to find the mass Neptune has substantially fewer and mostly smaller satellites of the primordial satellite system that would yield the current than the other gas planets. The one massive satellite, Triton, is architecture of the Neptunian system. If the prior satellite highly inclined, therefore it was likely captured from a system is required to have a substantially different mass ratio separated KBO binary (Agnor & Hamilton 2006). If Neptune compared to Jupiter, Saturn, and Uranus, this would weaken had a primordial (pre-Triton) satellite system with a mass ratio the hypothesis that all the satellites in these systems accreted -4 of mMsat Nep ~ 10 as suggested by Canup & Ward (2006), in a similar way. Alternatively, more stochastic events (e.g., then Tritonʼs mass approaches the minimum value required for giant impacts) may have a greater influence on satellite a retrograde object to have destroyed the satellite system. Thus, formation for icy giants. the existence of Triton places an upper limit on the total mass of such a primordial system. The high initial eccentricity of Tritonʼs orbit may decay 2. Methods 9 ( by tidal dissipation in less than 10 years Goldreich et al. We perform N-body integrations using SyMBA code ) 1989; Nogueira et al. 2011 . However, the perturbations from (Duncan et al. 1998, based on previous work of Wisdom & an eccentric Triton destabilize small irregular satellites Holman 1991) of a newly captured Triton together with a 5 (Nereid-like) on a timescale of 10 years (Nogueira et al. hypothetical prograde satellite system for 107 years including 2011). Moreover, Ćuk & Gladman (2005) argue that Kozai effects of Neptuneʼs oblateness. The SyMBA code can cycles increase Triton’s mean pericenter, increasing the effectively resolve close encounters among orbiting bodies, circularization timescale beyond the age of the solar system. and perfect merger is assumed when an impact is detected. That study proposes that perturbations on pre-existing prograde We consider a primordial prograde satellite system com- satellites induced by Triton lead to mutual disruptive collisions posed of four satellites with similar mass ratios compared to between the pre-existing satellites. The resulting debris disk Neptune as Ariel, Umbriel, Titania, and Oberon to Uranus interacts with Triton and drains angular momentum from its (Laskar & Jacobson 1987). The total mass ratio of the satellite -4 orbit, reducing the circularization timescale to less than system is 1.04´ 10 (hereafter MUSats), in agreement with the common mass ratio for gaseous planets predicted by Canup & 3 Planetary Science Directorate. Ward (2006). Tritonʼs initial orbits are chosen from previous 1 The Astronomical Journal, 154:208 (8pp), 2017 November Rufu & Canup Table 1 Dynamical Survival Results: aT, Triton’s Initial Semimajor axis in Neptune Radii, qT, Triton’s Initial Pericenter in Neptune Radii, incT, Triton’s Initial Inclination # # Triton’s Survival # Triton’s Fall onto Planet # Triton’s Escape Set aRT []Nep qRT [ Nep] incT [] deg 0.3MUSats MUSats 3MUSats 0.3MUSats MUSats 3MUSats 0.3MUSats MUSats 3MUSats 1a 300 8.1 105 9 8 2 0 1 6 1 1 2 2a 300 8.1 157 10 7 3 0 3 7 0 0 0 3 300 8.1 157 10 0 1 0 10 6 0 0 3 4 1004 8.0 157 9 0 0 0 8 7 1 2 3 5 1004 8.0 105 6 4 0 1 2 4 3 4 6 6 128 8.0 157 10 2 0 0 8 10 0 0 0 7 128 8.0 105 10 5 2 0 5 7 0 0 1 8 512 8.0 157 9 1 1 0 7 5 1 2 4 9 512 8.0 105 8 4 1 0 2 5 2 4 4 10 2000 8.0 157 1 1 0 0 2 1 9 7 9 11 2000 8.0 105 2 2 1 0 2 1 8 6 8 12 300 6.8 105 10 3 2 0 2 5 0 5 3 13 512 8.0 175 10 0 0 0 9 9 0 1 1 14 300 6.8 175 10 0 0 0 10 8 0 0 2 15a 512 8.0 157 10 7 0 0 2 9 0 1 1 16a 512 8.0 105 10 7 1 0 0 3 0 3 6 17 512 12.5 157 10 4 2 0 5 5 0 1 3 18 512 17.5 157 10 6 1 0 2 4 0 2 5 19 1004 29 157 10 9 1 0 0 5 0 1 4 20 1004 37.9 157 10 9 5 0 0 0 0 1 5 Note. a Semimajor axis are similar to Ariel, Umbriel, Titania, and Oberon. studies of typical captured orbits (Nogueira et al. 2011; see Higher impact angles require higher energies to disrupt a Table 1 for full list of initial conditions). We choose to test body, as the velocity is not tangential to the normal plane. A three retrograde initial inclinations (105°, 157°, 175°). Tidal modified impact kinetic energy is required to incorporate the evolution over the simulated time is small and thus neglected geometric effects, (Nogueira et al. 2011). For each set of initial conditions, 10 ⎛ ⎞ simulations were performed with randomly varying longitude aMM12+ K* = ⎜ ⎟K* ()2 a ⎝ ⎠ of ascending nodes, argument of periapsis, and mean anomaly MM12+ of all the simulated bodies. In 16 sets of initial conditions, the assumed primordial satellites have the same ratio between the where α is the volume fraction of the smaller body (M ) semimajor axis and planet’s Hill sphere as Uranus’s satellites. 2 that intersects the second body (M1; Movshovitz et al. In four sets of initial conditions, the exact semimajor axes ) of Uranus’s satellites are assumed. Using the same initial 2016; Leinhardt & Stewart 2012 . The disrupting relation orbital parameters, we perform additional simulations with two transforms to different satellite system total mass ratios, 0.35´ 10-4 and -4 3.13´ 10 , corresponding to 0.3 MUSats and 3 MUSats, respec- KcUa* = ()3 tively. Overall, our statistics include 200 simulations for each satellite mass ratio. where c is the geometrical factor derived from the collision outcomes with three tested angles. The collisions were tested 2.1. Disruption Analysis on a limited number of impacting angles (direction of velocity We use disruption scaling laws, derived by Movshovitz et al. relative to the line connecting the centers at contact, 0°,30°, (2016) for non-hit-and-run impacts between two gravity- and 45°); therefore, we assume that the relation of c on the dominated bodies, to estimate whether the impacts recorded impact angle (θ) is given by the following step function: by the N-body code are disruptive.