Figure 2.

Compositional difference between the disk and final planet (δf_T, eqn. 2) produced by simulations with γ = 0.3 (left) and γ = 0.4 (right, triangles) and 0.45 (right, squares) versus the predicted mass of the moon that would accrete from each disk (M_M, eqn. 1) scaled to the final planet’s mass (M_P). Note the change in y-axis scales between the two plots. Grey, purple, dark blue, light blue, green, yellow, orange, and red points correspond to v_imp/v_esc = 1.0, 1.1, 1.2, 1.3, 1.4, 1.6, 1.8, and 2.0, respectively. The open square is run 60* from Table 1 that includes pre-impact rotation. Forming an appropriate mass Moon mass requires M_M/M_P > 0.012, the region to the right of the vertical solid line. Constraints on δf_T needed to satisfy Earth-Moon compositional similarities are shown by horizontal lines for oxygen (solid), titanium (dotted), and chromium (dot-dashed), assuming a Mars-composition impactor.