An analytical model of crater count equilibrium

TL;DR

This paper introduces an analytical model explaining how cratered surfaces reach equilibrium through processes like cookie-cutting, ejecta-blanketing, and sandblasting, with applications to lunar regions.

Contribution

The paper presents a novel analytical model that integrates multiple physical processes to describe crater count equilibrium on planetary surfaces.

Findings

Power law of equilibrium slope is independent of production function slope when steeper.

Model successfully fits empirical data from lunar regions.

Degradation parameterization aligns with observed crater distributions.

Abstract

Crater count equilibrium occurs when new craters form at the same rate that old craters are erased, such that the total number of observable impacts remains constant. Despite substantial efforts to understand this process, there remain many unsolved problems. Here, we propose an analytical model that describes how a heavily cratered surface reaches a state of crater count equilibrium. The proposed model formulates three physical processes contributing to crater count equilibrium: cookie-cutting (simple, geometric overlap), ejecta-blanketing, and sandblasting (diffusive erosion). These three processes are modeled using a degradation parameter that describes the efficiency for a new crater to erase old craters. The flexibility of our newly developed model allows us to represent the processes that underlie crater count equilibrium problems. The results show that when the slope of the production function is steeper than that of the equilibrium state, the power law of the equilibrium slope is independent of that of the production function slope. We apply our model to the cratering conditions in the Sinus Medii region and at the Apollo 15 landing site on the Moon and demonstrate that a consistent degradation parameterization can successfully be determined based on the empirical results of these regions. Further developments of this model will enable us to better understand the surface evolution of airless bodies due to impact bombardment.