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Current lunar origin scenarios suggest that Earth's Moon may have resulted from the merger of two (or more) smaller moonlets. Dynamical studies of multiple moons find that these satellite systems are not stable, resulting in moonlet collision or loss of one or more of the moonlets. We perform Smoothed Particle Hydrodynamic (SPH) impact simulations of two orbiting moonlets inside the planetary gravitational potential and find that the classical outcome of two bodies impacting in free space is altered as erosive mass loss is more significant with decreasing distance to the planet. Depending on the conditions of accretion, each moonlet could have a distinct isotopic signature, therefore, we assess the initial mixing during their merger, in order to estimate whether future measurements of surface variations could distinguish between lunar origin scenarios (single vs. multiple moonlets). We find that for comparable-size impacting bodies in the accretionary regime, surface mixing is efficient, but in the hit-and-run regime, only a small amount of material is transferred between the bodies. However, sequences of hit-and-run impacts are expected, which will enhance the surface mixing. Overall, our results show that large scale heterogeneities can arise only from the merger of drastically different component masses. Surfaces of moons resulting from the merger of comparable-sized components have little material heterogeneities, and such impacts are preferred, as the relatively massive impactor generates more melt, extending the lunar magma ocean phase., accepted for publication. 17 pages, 9 Figures

Introduction: A common outcome of a giant impact event is the formation of a circumplanetary debris disk, and in some cases, the capture of the surviving impactor, which results in a system composed of a primary, secondary, and a debris disk. The material in the debris disk may be accreted by the primary body (and secondary, if it exists), escape the system, or coalesce into larger clumps. A classic example of a system thought to originate by such an impact event is the Pluto-Charon binary system (Canup, 2005, 2011), in which all six bodies (including the other smaller satellites) lie approximately on the same plane and have nearly circular orbits. Such impacts are simulated using smoothed particle hydrodynamics (SPH) codes including self gravity. The equation of state (EOS) governs the relationship among the thermodynamic variables of the simulated material. The specific EOS used in the simulation may influence the final post-impact structure. In order to quantify the typical differences, we compare two approaches, one simple analytic and one tabulated EOS. Tillotson (Tillotson, 1962) is a widely used analytic EOS and is computationally fast, but it lacks important details such as the treatment of phase changes. Sesame (Bennett et al., 1978) is a commonly used tabulated EOS and is more accurate, but is computationally slower and may be poorly sampled in the required thermodynamic phase-space. Here we show a set of SPH impact simulations that assume similar geometric and dynamic initial conditions but different EOS. Methods: We performed ~100 SPH simulations using SWIFT code (Schaller et al., 2018), simulating Pluto-like impacts with 105-106 particles. The initial bodies are assumed to be differentiated, with target to impactor mass ratio of 1 or 7/3, impact angle, ξ, of 0, 30, 45, 60°. Impact velocity was chosen to be relatively small, 1-1.1 times the escape velocity. The impactor was either spin-less or rotating with a period of 5 or 10 hours. This parameter space was motivated by previous simulations (Canup, 2011) for the formation of the Pluto-Charon system. We compare results using the Tillotson and Sesame EOS. The simulations were stopped after 4 days, the typical time for the central body to relax to a stable spherical shape. We developed an algorithm to detect post-impact clumps. Two particles were considered in contact if their mutual distance was smaller than their combined smoothing lengths. The orbital elements of each clump (“satellitesimal”, defined as 100 particles in pairwise contact, equivalent to ~10-3Mpluto) were computed and studied. Results: Disk systems were formed for impact angles >30°, in using both EOSs. Satellitesimals, when formed, showed different properties. Figure 1 panels (a,b) show the final snapshots of an impact that produced a debris disk and several satellitesimals highlighted in color corresponding to their masses. In this example, a more massive debris disk with a larger number of satellitesimals is obtained when using Tillotson EOS than using Sesame. Moreover, in addition to the target body, at least one large satellitesimal was formed in each of the simulations, but their composition, mass, and orbital elements differ between the EOSs. In comparing the Sesame run to Tillotson, the largest satellitesimal has a mass of 0.015Mpluto (with water fraction of 0.16) and 0.008Mpluto (with water fraction of 0.30) respectively. Its orbital elements are e=0.67, a=10.07Rpluto for Sesame runs, and e=0.15, a=3.2Rpluto for Tillotson. At smaller masses, using Tillotson EOS produces a greater number of clumps, as seen in Figure 1c. Three more satellitesimals were formed (some beyond the plot limits of 1b), with e=0.86, 1.35, 0.10. Note that the satellitesimal mass is an order of magnitude smaller than Charon, so alone they do not predict Charon’s formation (Canup, 2011). In the final snapshot, a greater fraction of debris disk particles lie within the Roche limit (computed using present-day Charon’s density (McKinnon et al., 2017)) in the Sesame simulation, whereas the Tillotson disk extends to a greater distance. In terms of mass, angular momentum, and composition, the debris disks are similar (0.025 versus 0.033 of the total mass; 0.19 versus 0.25 of the total angular momentum; water fraction of 0.44 versus 0.37 for Sesame and Tillotson respectively). We note the execution time was 2-3 times longer for the simulations using Sesame than Tillotson, a factor which may be considered in choosing EOS. Exploring the parameter space, we note that head-on impacts (ξ~0°) produce a merged single body, with the vast majority of ejected particles accreted by the planet, and the rest ejected to space. Oblique, faster than escape velocity impacts (vimp/vesc=1.1 and ξ=60°) resulted in two unbound bodies, with little mass transfer between the two, consistent with previous studies of planetary impacts (Leinhardt & Stewart, 2012). References: Bennett, B. I., Johnson, J. D., Kerley, G. I., & Rood, G. T. (1978). Recent developments in the Sesame equation-of-state library. https://doi.org/10.2172/5150206 Canup, R. M. (2005). A Giant Impact Origin of Pluto-Charon. Science, 307(5709), 546–550. Canup, R. M. (2011). On a Giant Impact Origin of Charon, Nix, and Hydra. The Astronomical Journal, 141(2), 35. Leinhardt, Z. M., & Stewart, S. T. (2012). Collisions Between Gravity-Dominated Bodies. I. Outcome Regimes and Scaling Laws. The Astrophysical Journal, 745(1), 79. McKinnon, W. B., Stern, S. A., Weaver, H. A., Nimmo, F., Bierson, C. J., Grundy, W. M., et al. (2017). Origin of the Pluto–Charon system: Constraints from the New Horizons flyby. Icarus. https://doi.org/10.1016/j.icarus.2016.11.019 Schaller, M., Gonnet, P., Chalk, A. B. G., & Draper, P. W. (2018, May 1). SWIFT: SPH With Inter-dependent Fine-grained Tasking. Astrophysics Source Code Library. Retrieved from https://ui.adsabs.harvard.edu/abs/2018ascl.soft05020S Tillotson, J. H. (1962). Metallic equations of state for hypervelocity impact (No. Rep. GA-3216 ). General Dynamics San Diego CA.

Forming the Moon by a high-angular momentum impact may explain the Earth-Moon isotopic similarities, however, the post-impact angular momentum needs to be reduced by a factor of 2 or more to the current value (1 L_EM) after the Moon forms. Capture into the evection resonance, occurring when the lunar perigee precession period equals one year, could remove the angular momentum excess. However the appropriate angular momentum removal appears sensitive to the tidal model and chosen tidal parameters. In this work, we use a constant-time delay tidal model to explore the Moon's orbital evolution through evection. We find that exit from formal evection occurs early and that subsequently, the Moon enters a quasi-resonance regime, in which evection still regulates the lunar eccentricity even though the resonance angle is no longer librating. Although not in resonance proper, during quasi-resonance angular momentum is continuously removed from the Earth-Moon system and transferred to Earth's heliocentric orbit. The final angular momentum, set by the timing of quasi-resonance escape, is a function of the ratio of tidal strength in the Moon and Earth and the absolute rate of tidal dissipation in the Earth. We consider a physically-motivated model for tidal dissipation in the Earth as the mantle cools from a molten to a partially molten state. We find that as the mantle solidifies, increased terrestrial dissipation drives the Moon out of quasi-resonance. For post-impact systems that contain >2 L_EM, final angular momentum values after quasi-resonance escape remain significantly higher than the current Earth-Moon value., accepted to JGR-Planets

Impacts between planetary-sized bodies can explain the origin of satellites orbiting large ( R > 500 km) trans-Neptunian objects. Their water rich composition, along with the complex phase diagram of water, make it important to accurately model the wide range of thermodynamic conditions material experiences during an impact event and in the debris disk. Since differences in the thermodynamics may influence the system dynamics, we seek to evaluate how the choice of an equation of state (EOS) alters the system’s evolution. Specifically, we compare two EOSs that are constructed by different approaches: either by a simplified analytic description (Tillotson), or by interpolation of tabulated data (Sesame). Approximately 50 pairs of Smoothed Particle Hydrodynamics impact simulations were performed, with similar initial conditions but different EOSs, in the parameter space in which the Pluto–Charon binary is thought to form (slow impacts between Pluto-size, water rich bodies). Generally, we show that impact outcomes (e.g., circumplanetary debris disk) are consistent between EOSs. Some differences arise, importantly in the production of satellitesimals (large intact clumps) that form in the post-impact debris disk. When utilizing an analytic EOS, the emergence of satellitesimals is highly certain, while when using the tabulated EOS it is less common. This is because for the typical densities and energies experienced in these impacts, the analytic EOS predicts very low pressure values, leading to particles artificially aggregating by a tensile instability.

The hypothesis of lunar origin by a single giant impact can explain some aspects of the Earth-Moon system. However, it is difficult to reconcile giant impact models with the compositional similarity of the Earth and Moon without violating angular momentum constraints. Furthermore, successful giant impact scenarios require very specific conditions such that they have a low probability of occurring. Here we present numerical simulations suggesting that the Moon could instead be the product of a succession of a variety of smaller collisions. In this scenario, each collision forms a debris disk around the proto-Earth that then accretes to form a moonlet. The moonlets tidally advance outward, and may coalesce to form the Moon. We find that sub-lunar moonlets are a common result of impacts expected onto the proto-Earth in the early solar system and find that the planetary rotation is limited by impact angular momentum drain. We conclude that, assuming efficient merger of moonlets, a multiple impact scenario can account for the formation of the Earth-Moon system with its present properties.