SUPPLEMENTARY INFORMATION

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1 SUPPLEMENTARY INFORMATION DOI: /NGEO1828 Projectile Remnants in Central Peaks of Lunar Impact Craters Authors: Z. Yue 1, 2, B. C. Johnson 3, D. A. Minton 2, H. J. Melosh 2,3 *, K. Di 1, W. Hu 1, Y. Liu 1 Affiliations: 1 State Key Laboratory of Remote Sensing Science, Institute of Remote Sensing Applications, Chinese Academy Sciences, Beijing, Beijing, China Department of Earth, Atmospheric and Planetary Sciences, Purdue University, West Lafayette, Indiana, USA Department of Physics, Purdue University, West Lafayette, Indiana, USA Methods The first numerical simulation of impact cratering was performed for Meteor Crater, Arizona 1 and has continued to develop to the present. In this research we used the code isale (impact- SALE), which was developed from the SALE (Simplified Arbitrary Lagrangian Eulerian) hydrocode 2, and was improved to include an elastic-plastic constitutive model, fragmentation models 3, various Equations of State (EoS), and multiple materials. Recently a modified acoustic fluidization model, a strength model, and a porosity compaction model 4 were also included. The first step in the simulation is to create the geologic column around the Copernicus crater, which we divided into two layers to represent the lunar crust and mantle. The EoS of the lunar crust was approximated by granite with a depth of 30 km, and the mantle by dunite. The parameters can be found in below in Tables S1 and S2. Table S1: Model parameters used for best fitting isale models of Copernicus crater. Because of the small number of equations of state for geologic materials the lunar mantle and basalt layer were represented by dunite, while the lunar crust was represented by granite. NATURE GEOSCIENCE 1

2 Parameter Description Value Number of high resolution cells in x-direction 400 Number of high resolution cells in y-direction 600 Cell size in x-direction 100 m Cell size in y-direction 100 m Surface temperature 250 K Gravitational acceleration 1.63 m/s 2 Projectile diameter 7 km Projectile material type Dunite Crustal thickness 30 km Crustal material type Granite Mantle material type Dunite

3 Table S2: Material input parameter used for best fitting isale models of Copernicus crater. Parameter Description Granite Dunite Poisson ratio a Cohesion, strength at P=0 (intact) a 10 MPa 10 MPa Cohesion (damaged) a 0.01 MPa 0.01 MPa Von Mises plastic limit a 2500 MPa 3500 MPa Coefficient of internal friction (intact) a Coefficient of internal fiction (damaged) a Melt Temperature a 1673 K 1373 K Specific Heat Capacity a 1000 J/kg/K 1000 J/kg/K Thermal Softening Parameter a Simon!! parameter for melt temperature. vs. pressure b Simon!! parameter for melt temperature. vs. pressure b Acoustic fluidization viscosity scaling parameter! c! 4 10!! 4 10!! Acoustic fluidization decay time scaling parameter! c! Equation of state ANEOS (granite d ) ANEOS (dunite e ) a See Collins et al. 3 (and references therein) for a description of the strength-model parameters. b See Wünnemann et al. 5 (and references therein) for a description of the Simon!! and!! parameters and their implementation in isale. c See Wünnemann and Ivanov 6 (and references therein) for details regarding the acoustic fluidization parameters!! and!!. d See Pierazzo and Melosh 7 e See Benz et al. 8 For further description of the ANEOS equation of state see Melosh 9 and references therein.

4 Further Description of Fig 1 Model of the formation of Copernicus Crater Model for the formation of Copernicus crater following the impact of a 7 km diameter dunite asteroid at 10 km/sec. All figures are in cylindrical co-ordinates with the origin centered on the point of impact. Details of model input parameters can be found in the SOM. (Top) 60 seconds after initial impact, a thin layer of impactor material (red) lines the transient crater. (Middle) 700 seconds after initial impact, the crater has finished collapsing. During collapse the impactor material (red) is concentrated in the central peak of the crater. The black lines originally horizontal with a 1 km vertical spacing connect massless tracers. These lines show the uplift of crustal material (grey) and minimal uplift of mantle material (brown). Completely overturned lines represent material that has been excavated. Thus, the maximum depth of excavation is between 6-7 km. (Bottom) The solid black line is the modeled crater profile 700 seconds after the initial impact. The modeled crater has a rim-to-floor depth of 4.5 km, a central peak height of 0.5 km, and a rim-to-rim diameter of ~89 km. The grey dashed line is an axisymmetric profile for Copernicus crater derived from (Lunar Orbiter Laser Altimeter) LOLA topography as described in the SOM (maybe put LOLA citation from SOM here). The LOLA derived profile has a rim-to-floor depth of ~3.6 km, a central peak height of 0.46 km, and a rim-to-rim diameter of 97 km. The black dashed line acts as a guide to the eye showing the rim position of a crater with the nominal Copernicus rim-rim diameter of 93 km (8). Considering the 100 m resolution of the modeled crater and the averaging of non-axisymmetric features in the LOLA derived crater profile, we believe the modeled crater is an excellent fit of Copernicus crater. Note that the scale of the axes is different for each panel The axisymmetric profile of Copernicus crater is fit using Lunar Orbiter Laser Altimeter (LOLA) Gridded Data Records (GDR), which is has a resolution of 1024 pixel/degree or ~0.03 km/pixel 10. PRODUCT_VERSION_ID = "V1.05"

5 DATA_SET_ID = "LRO-L-LOLA-4-GDR-V1.0" PRODUCT_ID = "LDEM_1024_00N_15N_150_180" We created axisymmetric crater profiles by assuming a central-point of Copernicus and calculating a radius for each pixel position. We found the average topography of radial bins from! to! +!", where!" = 200 m. The mid-point of Copernicus crater is poorly constrained so we searched parameter space in the central region of the crater, changing the assumed central point in increments of degree or ~760 m. We then chose the center-point of N, W that minimized the rim-rim diameter giving a value of 96.6 km. Further Description of Figure 2: Model for the formation of Copernicus crater, 700 seconds after a 7km diameter dunite asteroid impacted at 14 km/sec. The figure is in cylindrical co-ordinates with the origin centered on the point of impact. Details of model input parameters can be found in the SOM. Projectile material (red) has been almost completely vaporized leaving very little projectile material in the crater. The black lines were originally horizontal with a 1 km vertical spacing connect massless tracers. These lines show the uplift of crustal material (grey) and minimal uplift of mantle material (brown). Similarly to Figure 1 the maximum depth of excavation is 6-7 km. This crater has a rim-to-rim diameter of 94 km, a rim-to-floor depth of 5.2 km, and a peak ring height of 0.95 km at a radius of 6 km. Lunar impact velocity distribution The left figure compares the lunar impact velocity distribution from our work to that of Marchi et al. 11. Note the close similarities of the two distributions. On the right we also plot our data in cumulative form to make it easier to read off the percentage of impacts below a given impact velocity. The dashed line in the right-hand figure indicates the fraction of impacts at or below 12 km/sec.

6 SOM References: 1. Bjork RJ. Analysis of the formation of Meteor Crater, Arizona: A preliminary report. J Geophys Res 1961, 66: Amsden AA, Ruppel HM, Hirt CW. SALE: A Simplified ALE Computer Program for Fluid Flow at All Speeds. Los Alamos, N. M.: Los Alamos National Laboratory; Report No.: LA Collins GC, Melosh HJ, Ivanov BA. Damage and deformation in numerical impact simulations. Meteoritics and Planet Sci 2004, 39: Collins GC, Melosh HJ, Wünnemann K. Improvements to the e-a porous compaction model for simulating impacts into high- porosity solar system objects. Int J Impact Eng 2011, 38: Wünnemann K, Collins GS, Osinski GR. Numerical modeling of impact melt production in porous rocks. Earth and Planetary Science Letters 2008, 269: Wünnemann K, Ivanov BA. Numerical modeling of the impact crater depth- diameter dependence in an acoustically fluidized target. Planetary and Space Science 2003, 51: Pierazzo E, Melosh HJ. Melt production in oblique impacts. Icarus 2000, 145: Benz W, Cameron AGW, Melosh HJ. The Origin of the Moon and the Single Impact Hypothesis III. Icarus 1989, 81:

7 9. Melosh HJ. A Hydrocode Equation of State for SiO2. Meteoritics and Planetary Sciences 2007, 42: Smith DE, Zuber MT, Jackson GB, Neumann GA, Riris H, Sun X, et al. The Lunar Orbiter Laser Altimeter Investigation on the Lunar Reconnaissance Orbiter Mission. Space Science Reviews 2009, 150: Marchi S, Mottola S, Cremonese G, Massironi M, Martellato E. A new chronology for the Moon and Mercury. Ap J 2009, 137: