Formation of planetary atmospheres: Analytical estimation of vapor production via planetary impacts

TL;DR

This study develops an analytical model for shock-induced vaporization during planetary impacts, aiding understanding of planetary atmosphere formation by accurately estimating vapor production from impact simulations.

Contribution

It introduces a simplified analytical approach to estimate shock internal energy and pressure, matching simulation results and applicable to impact velocities near the sound speed.

Findings

Analytical solutions accurately reproduce iSALE simulation results.

The model is valid for impact angles up to about 60 degrees.

Application to Earth-sized planets estimates atmospheric vaporization effectively.

Abstract

To investigate impact vaporization for planetary atmosphere formation, we have studied the thermodynamic state generated by the shock wave due to a high-velocity impact, called the shock field. We have carried out iSALE simulations for high-velocity vertical impacts using ANEOS for an equation-of-state (EoS) model. To understand the shock fields obtained from simulations, we have investigated the contribution of the thermal and cold terms in the EoS model on the Hugoniot curves. Although the thermal and cold terms are important for the pressure, the internal energy is mainly determined by the thermal term. We thus assume a simple EoS determined by the thermal term and then analytically derive the shock internal-energy field, which reproduces the results of simulations well. Using the analytical solution of internal energy and the Hugoniot curve, we have derived the shock pressure field analytically as well. The analytical solutions for internal energy and pressure are valid even for impact velocities as low as the sound speed. The solution is good for the vertical direction or within the angles of about 60 degrees. We have applied the solution to impact vaporization for the formation of planetary atmospheres. This gives good estimation of reformation of the planetary atmospheres of Earth sized planet.