(Canup, 2004). Both the impactor and the target are assumed to be differentiated bodies with a 30 wt% iron core and a 70 wt% silicate mantle. In these low-velocity collisions, the impactor loses kinetic energy during its grazing collision with the target, before it is dispersed into a disk around the target. The resulting proto-lunar disk is therefore mainly composed of impactor material. We will call this the ‘‘canonical scenario’’. When the assumption that no mass is lost is dropped however, the collisional angular momentum is no longer tightly constrained, as lost mass also carries away angular momentum. The total collisional angular momentum can therefore be con- siderably higher than the final angular momentum in the Earth–Moon system. With this additional degree of freedom, new regions in the collision parameter space be- come feasible. Apart from the disk mass, another interesting quantity is the origin of the mate- rial which ends up in the proto-lunar disk, especially for the silicate part. We call the fraction of target silicate to total silicate material in the disk fT ¼ ðMsilc targ =Msilc tot Þdisk ð1Þ where Msilc targ and Msilc tot denote the mass of the silicate fraction of the disk derived from the target, and the total disk mass, respectively. If we define a similar target-derived silicate fraction for the post-impact Earth, we can deduce a deviation factor dfT ¼ Msilc targ . Msilc tot disk . Msilc targ . Msilc tot post-impact Earth À 1 ð2Þ which directly reflects the compositional similarity between the silicate part of the proto-lunar disk and the silicate part of the post-impact Earth. Isotopic measurements show (Wiechert et al., 2001; Zhang et al., 2012) a strong isotopic similarity between the silicate fractions of today’s Moon and Earth. Assum- ing isotopic heterogeneity of the pre-impact bodies, this suggests that either the material of the bodies mixed during the collision or re-equilibrated their isotopic signatures after the collision. Either scenario is represented by a dfT $ 0 between to- day’s Earth and the Moon. The value of dfT right after the impact thus serves as a starting point, from which a re-equilibration mechanism leads to todays value of dfT $ 0. In a typical simulation of the canonical scenario, only about 30% of the disk material and 90% of the material of the post-impact Earth is derived from the target (the proto-Earth) respectively (Canup, 2004), yielding a dfT of À67%. 4. Results The new class of collisions presented here falls into the broad regime of slow hit-and-run collisions (Asphaug et al., 2006) with impact velocities between 1.20 and 1.40 vesc . Hit-and-run occurs up to half the time for collisions with impact colors. In the canonical scenario, the impactor grazes around the target’s mantle and is deformed. Due to the low impact velocity, material supposed to end up in or bit around the Earth must not be decelerated too strongly in order to retain enough velocity to stay in orbit. This is only achieved for the parts of the impactor mantle most distant to the point of impact, and some minor part of the target’s mantle. Bu if impact velocity is increased from 1.00 (cA08) to 1.30 vesc (cC01), parts from dee- per within the target mantle receive the right amount of energy for orbit insertion while the outer regions of the target mantle, retain too much velocity and leave the system, thereby removing mass and angular momentum. Both processes work to wards increasing the target material fraction in the proto-lunar disk. While in run Fig. 1a. Five snapshots from the 30° impact angle and 1.30 vesc impact velocity case (cC06) showing cuts through the impact plane. Color coded is the type and origin o the material. Dark and light blue indicate target and impactor iron; Red and orange show corresponding silicate material. The far right shows the situation at the time of impact. At 0.52 h, it can be seen how the impactor ploughs deep through the targets mantle and pushes considerable amount of target material into orbit. A spiral arm of material forms and gravitationally collapses into fragments. The oute portions of the arm mainly consist of impactor silicates and escapes due to having retained a velocity well above escape velocity. The silicate fragments further inward are stronger decelerated and enter eccentric orbits around the target. The impactor’s iron core also looses much of its angular momentum to the outer parts of the spiral arm and re-impacts the proto-Earth. (For interpretation of the references to color in this figure legend, the reader is referred to the web version o this article.) A. Reufer et al. / Icarus 221 (2012) 296–299 297 ༷ʑͳ݄ܗγφϦΦ [Reufer et al., Icarus, 2012] with less angular momentum. angular momentum by add- pactors generated successful wer-spinning planets. Because m is carried away with debris giant impacts, the spin period ases. Thus, the spin state of d to be near fission before or ming impact in our scenario entry in Table 1). However, is near the stability limit. Our candidate Moon-forming events have more than double the kinetic energy of previous scenarios, and the impact velocities were suf- ficient to substantially vaporize silicates (33). As a result, the silicate atmosphere and vapor-rich disk are more massive and hotter than found in previous work (34). At the resolution of the simulations, the projectile-to-target mass ratio is uniform from the atmosphere to the Roche radius. f the rth’s mpact or at −0.3 spin- f 2.3 Gray oche w of ower down spin enote and Earth e disk terial arth’s mpact e S1). view de- lue), and ensity ne of which 38 SCIENCE www.sciencemag.org on November 25, 2012 www.sciencemag.org Downloaded from [Ćuk & Stewart, Science, 2012] into a single moon at an orbital distance of about 3.8 R⊕ , where R⊕ is Earth’s radius (19, 20), MM MD ≈1:9 LD MD ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2:9GM⊕R⊕ p − 1:1 − 1:9 Mesc MD ð1Þ where Mesc is the mass that escapes from the disk as the Moon accretes. To estimate MM , we used Eq. 1 and made the favorable assumption that Mesc = 0. We tracked the origin (impactor versus tar- get) of the particles in the final planet and the disk. To quantify the compositional difference be- tween the silicate portions of the disk and planet, we define a deviation percentage dfT ≡ [FD,tar /FP,tar − 1] × 100 (2) where FD,tar and FP,tar are the mass fractions of the silicate portions of the disk and of the planet derived from the target’s mantle, respectively (21). Identical disk-planet compositions have dfT = 0, whereas a disk that contains fractionally more impactor-derived silicate than the final planet has dfT < 0, and a disk that contains fractionally less impactor-derived silicate than the final planet has dfT > 0. Prior impact simulations (1–3, 14, 15) that consider g ≡ Mimp /MT ≈0.1 to 0.2 produce disks with −90% ≤ dfT ≤ −35% for cases with MM > ML , where ML is the Moon’s mass. Results with larger impactors having g = 0.3, 0.4, and 0.45 are shown in Figs. 1 and 2 and Table 1. As the relative size of the impactor (g) is increased, there is generally a closer compositional match be- tween the final disk and the planet. For g ≥ 0.4, some disks have both sufficient mass and an- gular momentum to yield the Moon and nearly identical silicate compositions to that of the final Fig. 1. An SPH simulation of a moderately oblique, low-velocity (v∞ = 4 km s–1) collision between an impactor and target with similar masses (Table 1, run 31). Color scales with particle temperature in kelvin, per color bar, with red indicating tempera- tures >6440 K. All particles in the three-dimensional simulation are overplotted. Time is shown in hours, and distances are shown in units of 103 km. After the initial impact, the plan- ets recollided, merged, and spun rapidly. Their iron cores migrated to the center, while the merged structure developed a bar- type mode and spiral arms (24). The arms wrapped up and finally dispersed to form a disk containing ~3 lunar masses, whose silicate composition dif- fered from that of the final planet by less than 1%. Because of the near symmetry of the colli- sion, impactor and target material are distributed approximately proportion- ately throughout the final disk, so that the disk’s dfT value does not vary ap- preciably with distance from the planet. Fig. 2. Compositional differ- ence between the disk and final planet (dfT ) (Eq. 2) produced by simulations with (A) g = 0.3 and (B) g = 0.4 (triangles) and 0.45 (squares) versus the pre- dicted mass of the moon that would accrete from each disk (MM ) (Eq. 1) scaled to the final planet’s mass (MP ). There is a change in y axis scales between the two plots. Gray, purple, dark REPORTS on November 25, 2012 www.sciencemag.org Downloaded from [Canup, Science, 2012] ༷ʑͳ G.I. γφϦΦ ͕ఏҊ͞Ε͍ͯΔ͕ ͲΕશͯͷ੍ ݅Λຬ͓ͨͯ͠Βͣ ܾఆଧ͕ແ͍
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