Modeling of Collisional Outcomes Based on Impact Simulations of Mars-sized Bodies

We investigate the outcomes of collisions between Mars-sized bodies through smooth particle hydrodynamics (SPH) simulations, focusing on the transitions among ``merging'', ``hit-and-run'', and catastrophic disruption. By systematically varying impact velocity, angle, and mass ratio, we characterize the dependence of collision outcomes on geometric and energetic parameters. A new analytic model is developed using characteristic energies -- particularly the energy deposited in overlapping regions of the colliding bodies -- to accurately describe the mass of the largest and second-largest remnants. The model successfully reproduces simulation results across a broad range of impact conditions and improves on previous models by better capturing the transitions between ``merging'', ``hit-and-run'', and disruption. We also derive outcome formulas averaged over impact-parameter-weighted angular distributions, enabling more realistic applications to integrated modeling of planet formation. The model further shows consistency with outcomes from dust aggregate collision simulations, highlighting its utility for modeling collisional processes not only for large planetesimals but also for smaller bodies.