Erosion and accretion by cratering impacts on rocky and icy bodies: Formulation of scaling relations for high-speed ejecta

Numerous small bodies inevitably lead to cratering impacts on large planetary bodies during planet formation and evolution. As a consequence of these small impacts, a fraction of the target material escapes from the gravity of the large body, and a fraction of the impactor material accretes onto the target surface, depending on the impact velocities and angles. Here, we study the mass of the high-speed ejecta that escapes from the target gravity by cratering impacts when material strength is neglected. We perform a large number of cratering impact simulations onto a planar rocky and icy targets using the smoothed particle hydrodynamics method. We show that the escape mass of the target material obtained from our numerical simulations agrees with the prediction of a scaling law under a point-source assumption when v_imp > ~ 10 v_esc, where v_imp is the impact velocity and v_esc is the escape velocity of the target. However, we find that the point-source scaling law overestimates the escape mass up to a factor of ~ 70, depending on the impact angle, when v_imp < ~ 10 v_esc (Figure 1). Using data obtained from numerical simulations, we derive a new scaling law for the escape mass of the target material􏰁. We also derive a scaling law that predicts the accretion mass of the impactor material onto the target surface upon cratering impacts by numerically evaluating the escape mass of the impactor material. Our newly derived scaling laws would be useful for predicting the erosion of the target body and the accretion of the impactor for a variety of cratering impacts that would occur on large rocky and icy planetary bodies during planet formation and collisional evolution from ancient times to today (Figure 2).

 

Figure 1. Schematic illustration of cratering impacts (left) and velocity distribution of the ejecta (right). High- and low-speed ejecta are launched closer to and farther from the impact point, respectively; that is, the escape mass is launched from the vicinity of the impact point (left). Irregular-shaped objects in the left panel indicate ejecta of target and impactor materials (the total amount and their fractions depend on the impact condition). The point-source scaling law is characterized by a unique slope in the velocity distribution, while direct SPH simulations of cratering impacts demonstrated that high-speed ejecta would have a steeper slope for the velocity distribution (the gray line in the right panel). This discrepancy leads to an overestimation in the escape mass when using the point-source scaling law, depending on the considered escape velocity of the target v_esc.

 

Figure 2. Impact angle-averaged scaling laws for rocky (red lines) and icy (blue lines) bodies as a function of v_imp/v_esc. Left: the escape mass of the target material (M_esc,tar) normalized by impactor mass (m_imp). Middle: the accretion mass of the impactor material onto the target surface (M_acc,imp/m_imp). Right: total escape mass (M_esc,tot = M_esc,tar + M_esc,imp in a unit of m_imp; M_esc,tot > 1 indicates a net erosion and vice versa for a net accretion). Examples of typical outcomes of cratering impacts on different solar system bodies under different contexts are indicated by the labels in each panels.