Research Article

A Giant Impact Origin of Pluto-Charon

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Science  28 Jan 2005:
Vol. 307, Issue 5709, pp. 546-550
DOI: 10.1126/science.1106818

Abstract

Pluto and its moon, Charon, are the most prominent members of the Kuiper belt, and their existence holds clues to outer solar system formation processes. Here, hydrodynamic simulations are used to demonstrate that the formation of Pluto-Charon by means of a large collision is quite plausible. I show that such an impact probably produced an intact Charon, although it is possible that a disk of material orbited Pluto from which Charon later accumulated. These findings suggest that collisions between 1000-kilometer-class objects occurred in the early inner Kuiper belt.

The Pluto-Charon pair shares key traits with the Earth-Moon system. Each satellite mass is substantial compared to its planet: Charon's mass is 10 to 15% of Pluto's mass, and the Moon's mass is ∼1% of Earth's mass. All other satellite-to-planet mass ratios in our solar system are less than ∼2 × 10–4. The orbits of Charon and the Moon are consistent with a scenario in which each satellite formed much closer to its planet, and torques due to tides raised on the planet by the satellite subsequently caused the satellite's orbit to expand to its current separation. The angular momentum of both pairs is large, within a factor of several of the critical angular momentum for rotational stability of a single object containing the total system mass.

In both cases, an origin by “giant impact,” in which a large oblique collision with the growing planet produced its satellite and provided the system with its angular momentum, is favored (14). However, to date, the viability of this mode of origin has only been demonstrated for the Earth-Moon case. Models of lunar-forming impacts (47) produce disks orbiting the planet containing about 1 to 3% of the planet's mass, and as such the feasibility of forming the proportionally more massive Charon has been unknown. Although giant impacts are believed common in the final stage of terrestrial planet formation in the inner solar system (8), their role in the outer solar system and the Kuiper belt [a disk of objects orbiting exterior to Neptune between about 30 and 50 astronomical units (AU)] is more uncertain (9). The origin of Pluto-Charon provides a key constraint to this issue and to the population of objects in the primordial Kuiper belt.

Properties of the distant Pluto-Charon pair [supporting online material (SOM) text] remain somewhat uncertain. Pluto and Charon have physical radii of RP ≈ 1150 to 1200 km and RC ≈ 590 to 620 km, and their densities are ρP ≈ 1.8 to 2.1 g/cm3 and ρC ≈ 1.6 to 1.8 g/cm3, indicating rock-ice compositions with about 50 to 80% rock by mass (10). Scaling the angular momentum of the Pluto-Charon binary, LPC, by the quantity $Math$ (where RPC is the radius of an equivalent spherical object containing the total Pluto-Charon system mass, MPC, and G is the gravitational constant) gives the normalized system angular momentum, JPCLPC/L′, which is in the range 0.33 < JPC < 0.46 for a Charon-to-Pluto mass ratio, q, in the range 0.1 < q < 0.15.

Here, I present smooth particle hydrodynamic (SPH) simulations to show that giant impacts can produce Pluto-Charon–type systems with q > 0.1 and J ∼ 0.4. In SPH, an object is described by a multitude of overlapping particles, each of which represent a three-dimensional (3D) distribution of matter of a specified composition, whose properties are tracked in time in a Lagrangian manner. In these simulations, particles are evolved due to gravity, compressional heating and expansional cooling, and shock dissipation (11), and the Analytic Equation of State, M-ANEOS (12, 13), is used with material constants by Pierazzo and Melosh (14). For a full description of the SPH technique, see (15), from whose work the code used here is directly descended.

The SPH simulations involved between N = 2 × 104 and 1.2 × 105 particles and a simulated time of 1 to 4 days. Given that the appropriate differentiation state and composition of the colliding objects is uncertain, I considered three initial compositions: (i) SER: 100% undifferentiated serpentine [Mg3Si2O5(OH)4, a hydrated silicate containing ≈ 14% H2O by weight]; (ii) IDI: 40% water ice, 42% dunite, and 18% iron by mass and differentiated into an ice mantle, rock core, and iron inner core; and (iii) SIM: 50% serpentine and 50% water ice in an undifferentiated mixture. These objects range from uniform to highly differentiated, with rock mass fractions between 43 and 86% and bulk densities between ∼1.5 to 2.5 g/cm3.

I modeled a variety of impacts that were all capable of providing an angular momentum within the range for Pluto-Charon. The collision of two nonspinning equal density objects delivers a normalized angular momentum (16) $Math$(1) where b′ ≡ sin ξ is the scaled impact parameter, ξ is the angle between the surface normal and the impact trajectory (a grazing impact has b′ = 1), γ is the impactor-to-total mass ratio, $Math$, and (vimp/vesc) is the ratio of the impact velocity to the mutual escape velocity, with $Math$, where v is the relative velocity at large separation. Here, $Math$, where MT is the total colliding mass, and Rimp and Rtar are the impactor and target radii, respectively. A preimpact spin [due to earlier impacts (8, 17)] that had a component in the same rotational sense as the impact (“prograde”) would increase Jimp. For the case of prograde spin vectors normal to the plane of the impact, the additional contribution is $Math$(2) where Jimp = Jcol + Jspin, Kimp and Ktar are the moment of inertia constants of the colliding objects, Timp and Ttar are the preimpact spin periods of the impactor and target, and the minimum period for rotational stability is $Math$ hours (ρ/2g/cm3)–1/2, where ρ is the density of the objects. Here, collisions with 0.5 < b′ < 1, 1 < (vimp/vesc) < 2.5 (or 0 < v < 2.5 km/s), 0.13 < γ < 0.5, and with (18) and without preimpact spin are simulated.

Results. An impact between predifferentiated (IDI composition) identical objects, each of which contained 0.53 MPC (so that γ = 0.5) and had an initial prograde 7-hour day, produces a planet-disk system (Fig. 1). This b′ = 0.83 collision had vimp = vesc and Jimp = 0.43, of which 14% was contained in preimpact spin. The resulting disk mass (Fig. 1) is 12% of the planet's mass, and 70% of the disk has equivalent circular orbits exterior to the Roche limit, aR (19). Of the initial impact angular momentum, 7% escapes (contained in 1% of the mass), 44% is in orbiting material, and ∼50% is in the final planet that forms with a spin period of 2.6 hours. The final planet-disk system has Jf = 0.40, where $Math$ is the normalized system angular momentum, with Mf the total bound mass and Rf = (3Mf/4πρ)1/3. I estimated the mass of the satellite (MsqMp) that would accumulate from the disk based on models of lunar accretion (20). Assuming that disk material with mass MD and angular momentum LD will either be accreted onto the planet of mass Mp or into a single satellite with semimajor axis as ≈ 1.2aR (20, 21) $Math$(3) For this case (Fig. 1), q ≈ 0.12.

A collision involving undifferentiated SER objects, a smaller impactor (γ = 0.3), and no initial spin produces a planet-moon system (Fig. 2). A very grazing collision (b′ = 0.96) is needed to supply sufficient angular momentum for this smaller γ and vimp = vesc. The result is a binary with q = 0.125, eccentricity e = 0.50, a 3500-km (or 3.25 Rp) periapse separation, and a normalized final angular momentum Jf = 0.36. The planet's rotation period is 5.2 hours, with 55% of the initial angular momentum contained in the satellite.

Table 1 and table S1 detail simulations that produced a planet-moon or planet-disk system within the plausible mass-ratio range for Pluto-Charon together with Jimp ≥ 0.33. Results from 120 simulations that had 0.3 < Jimp < 0.6 and MTMPC are shown in Fig. 3 and fig. S1. Resulting planet-moon systems had satellite semimajor axes ranging from 3.7 to 21 Rp, periapses from 2.5 to 5 Rp, and 0.1 < e < 0.8. Intermediate outcomes to those in Fig. 3 would be expected for values between those sampled here (0.3 < γ < 0.5).

Table 1.

Parameters and results of impacts that yield moons with 0.1 < q < 0.15. Simulations here involved undifferentiated objects. The preimpact spin state of the objects is shown by the fraction ; superscripts i and it correspond, respectively, to Ls contained in the impactor or the impactor and target. Lorb is the angular momentum of the satellite, and Jf is the normalized final bound system angular momentum.

Run MT/MPC γ bvimp/vescJimpLs/LimpLesc/LimpMesc/MTLorb/LimpJfq
5 1.00 0.3 0.852 1.00 0.508 0.38it 0.06 0.010 0.378 0.486 0.102
6 1.00 0.3 0.785 1.00 0.483 0.40it 0.01 0.002 0.365 0.480 0.108
33 1.00 0.3 0.853 1.20 0.397 0.04i 0.00 0.000 0.514 0.397 0.115
1 1.00 0.3 0.918 1.00 0.379 0.10i 0.00 0.000 0.584 0.379 0.120
19 1.00 0.3 0.853 1.00 0.333 0.05i 0.00 0.000 0.529 0.333 0.125
20 1.00 0.3 0.957 1.00 0.356 0.00 0.00 0.000 0.545 0.356 0.125
7 1.00 0.3 0.958 1.00 0.379 0.06i 0.00 0.000 0.447 0.379 0.131
16 0.95 0.5 0.899 1.00 0.452 0.12i 0.00 0.000 0.508 0.452 0.144
21 0.95 0.5 0.862 1.05 0.454 0.11i 0.00 0.000 0.505 0.454 0.148
22 1.00 0.3 0.924 1.05 0.372 0.03i 0.00 0.000 0.588 0.372 0.149

The formation of intact moons is correlated with the impactor's differentiation state, with b′ > 0.8 collisions by undifferentiated impactors typically yielding moons on stable orbits, whereas IDI impactors with b′ > 0.8 did not. From basic thermal arguments (22), an early impactor containing ∼30 to 50% of Pluto's mass would likely have been undifferentiated. Compared to the disk-producing impacts, the intact moon cases surround the (q, J) region of the Pluto-Charon system much more completely (Fig. 3 and fig. S1) and produce 0.1 < q < 0.15 satellites for b′ > 0.8, Jimp > 0.3, and vimp ≤ 1.2vesc. This greater range in Jimp and vimp than the successful disk-producing cases (SOM text and table S1) corresponds to a greater range in the other impact variables (Eqs. 1 and 2), with successful intact moon cases occurring for 0.3 ≤ γ ≤ 0.5 and with or without initial spins. Given these data, the formation of an intact Charon appears the more probable mode of origin.

Whereas both massive disks and intact moons are produced by very oblique impacts (b′ > 0.8), the moon cases typically involve a higher fractional partitioning of mass and angular momentum into orbiting material than the disk cases. This is primarily due to a difference in the nature of the gravitational torques that allow for orbital emplacement. For disk cases, impactor material is sheared into trailing spiral-arm structures (Fig. 1, D and E) (7), a configuration that is effective in transporting angular momentum from radially inner to outer portions. This torque causes inner arm material to accrete onto the planet, whereas the outermost material either goes into bound orbit or escapes. In the intact moon cases, the angular momentum exchange occurs primarily between the distorted figure of the target planet and a condensed region of impactor material (Fig. 2, B to E), and so in these cases the angular momentum sacrificed to lift material into stable orbit is to a much greater degree derived from the planet, resulting in characteristically slower rotating planets and higher angular momentum and mass satellites. Intact moon formation is aided by a prograde spin of the impactor after the initial impact, which helps to counteract the shearing of impactor material due to differential Kepler motion; this can result from an initial prograde impactor or retrograde target spin, or from a highly grazing impact.

One overall implication of my simulations is that collisionally producing systems with JJPC is correlated with the production of satellites that have (Ms/Mp) = qO(10–1). A second result is that oblique collisions with vimp ≥ 1.3vesc (or v ≥ 0.9 km/s for MTMPC) do not produce massive disks or satellites orbiting the primary, and this was true for all of the simulations.

The differentiation state and composition of Pluto and Charon could have been affected by a Charon-forming impact. For disk-producing cases, ice initially at temperatures T ∼ 150 K in the region of the initial impact achieved a maximum T ∼ 300 K (ΔT ∼ 150 K), with most of the ice heated to T ∼ 200 K (ΔT ∼ 50 K), consistent with previous estimates (2). In moon-producing impacts, the satellite material experienced little heating (ΔT ∼ 30 K), because it had for the most part avoided direct impact with the planet, whereas the target was heated more substantially (Fig. 2).

For Pluto, the short-term heating processes associated with a large impact in combination with general accretional heating (Eacc/MP ∼ 3/5[GMP/RP] could provide up to ΔT ∼ 300 K) and long-lived radiogenic heating (ΔT ≤ 285 K after 400 million years) seems most consistent with substantial melting and a differentiated state (22), although uncertainty associated with the rheology of rock-ice mixtures can affect this conclusion. The case for differentiation is much weaker for smaller Charon (22), and the results here reinforce this (23), particularly in the intact formation mode.

For vimp/vesc ∼ unity and MTMPC, there is not appreciable vaporization of water ice, and successful impacts (Table 1 and table S1) lose only between 0 and 8% of their mass to escaping material. Thus, the increase in the overall rock-to-ice ratio of the pair as a result of a Charon-forming impact is expected to be modest to none. The intact moons contain material originating from the impactor with a similar bulk composition. In the collisions involving mixed compositions that produced disks, the denser components of the colliding objects migrated inward into the central planet (Fig. 1, D and E), leaving a disk of the preferentially lower density material (SOM text). Thus, if the impactor and proto-Pluto had similar overall ice-rock fractions, forming Charon from a disk implies ρC < ρP, whereas forming the satellite intact implies ρC ∼ ρP. Both cases imply that the current total rock-ice fraction of the pair is similar to that of its progenitors.

Discussion. This work identifies a range of impacts capable of producing Pluto-Charon–type systems. The impacts are low-velocity (v < 0.9 km/s) oblique collisions by an impactor containing 30 to 50% of the Pluto-Charon system's mass, which often involve some preimpact spin of a magnitude similar to that estimated for other outer solar system bodies (24). The broadest range of successful impacts involves the intact formation of Charon rather than its accretion from an impact-generated disk. An intact formation implies similar planet and satellite densities, an initially eccentric satellite orbit, and characteristically larger possible satellite-to-planet mass ratios.

What is the probability of such an event? For random impact orientation (8), ∼30% of collisions have b′ > 0.8. The frequency of large impacts in the early Kuiper belt is uncertain, as the current belt is believed to contain only a small portion of its original mass (25) and to be more dynamically excited now ($Math$ km/s) than when large objects formed there [$Math$ km/s (26)]. Recent accretion simulations that produce ∼ 103-km Kuiper belt objects (KBOs) (26) predict a large-body cumulative size distribution No(>R) ∞ Rq with q′ ∼ 3. This implies several tens of objects as large as those considered here (800 < R-km < 1100) to be consistent with the formation of ∼ 105 KBOs with R > 50 km as estimated from current surveys (26). A “particle-in-a-box” estimate gives the characteristic time between large impacts in the Kuiper belt region $Math$(4) $Math$ $Math$ where Δa and Hvrel/Ω are the width and height of the disk annulus, respectively, Torb ≡ 2π/Ω is the orbital period, f ≡ [1 + (vesc/vrel)2] is the gravitational focusing factor, and vrel is the relative velocity between large embryos of radius Re and number Ne. In the current belt, f ∼ unity and large collisions occur too infrequently to be relevant.

If the early Kuiper belt contained a substantially greater number (27) of 103-km-class KBOs than the current belt [with such objects later lost, e.g., through dynamical scattering (28)] and/or had much lower characteristic relative velocities and strong gravitational focusing, large impacts would have been more common. In the primordial accretionary epoch, estimated velocities for R ∼ 103 km objects are vrelO(10–2 to 10–1) km/s (26) or f > 102 for vesc ∼ 1 km/s with τcol < 109 years. Large objects formed through so-called oligarchic growth with low vrel could have become orbitally isolated from one another and thus have grown primarily through the accretion of small material (9, 26). However, it seems probable that such isolation would have been periodically overcome, as growing large bodies would have become increasingly dynamically crowded, leading to episodes of mutual collisions among “battling oligarchs” (9). Furthermore, the sweeping of Neptune's mean-motion resonances through the Kuiper belt as that planet began migrating outward (29) may have itself instigated large collisions in previously dynamically stable zones and/or acted to increase the surface density of large objects captured within resonances (3).

The low-velocity impacts that produce q > 0.1 have v < 0.9 km/s, which is consistent with a collision in the early Kuiper belt. However, the timing of a Charon-forming impact relative to the capture of Pluto-Charon into the 3:2 resonance with Neptune is uncertain. The binary could have formed first, at an orbital distance ∼ 5 AU closer to the Sun than Pluto's current semimajor axis, and the pair later captured as Neptune's 3:2 migrated past them, with Pluto's e ≈ 0.25 orbital eccentricity obtained subsequently (29, 30). If Pluto had been captured in the 3:2 before the Charon-forming impact, an appropriate v with a large nonresonant impactor might still have resulted (for example, in its current orbit, Pluto's e provides a velocity relative to circular orbits of 0.5 to 0.8 km/s at its periapse and apoapse), but such an impact would have likely dislodged Pluto from resonance (31, 32). Although recapture could occur (33), the probability of this is low if the pair had a substantial orbital eccentricity (i.e., <10% for e > 0.15) (34). A more promising scenario involves the collision of Pluto and an impactor both already trapped in the 3:2, as in this case, a lower relative velocity due to the difference in their forced and/or free eccentricities (32) could result, and the postimpact pair might then remain in resonance.

The tendency for oblique low-velocity collisions between similarly sized objects to produce substantial amounts of material in bound orbit suggests that the impact generation of satellites is a common outcome of late-stage accretion, with the Earth-Moon (q = 0.01 and J = 0.115) and Pluto-Charon offering examples of the potential range of q and J in systems produced by such events. Requiring (vimp/vesc) < 1.3 for forming large satellites based on the simulations here implies that binary systems produced through such singular impacts would have (from Eqs. 1 and 2) J ≲ 0.8.

Supporting Online Material

SOM Text

Fig. S1

Table S1

References

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