Atmospheric mass-loss from high-velocity giant impacts

Abstract

Using moving mesh hydrodynamic simulations, we determine the shock propagation and resulting ground velocities for a planet hit by a high velocity impactor. We use our results to determine the atmospheric mass loss caused by the resulting ground motion due to the impact shock wave. We find that there are two distinct shock propagation regimes: In the limit in which the impactor is significantly smaller than the target (R i << R t ), the solutions are self-similar and the shock velocity at a fixed point on the target scale as m 2/3 i , where m i is the mass of the impactor. In addition, the ground velocities follow a universal profile given by v g /v i = (14.2x 2 − 25.3x + 11.3)/(x 2 − 2.5x + 1.9) + 2 ln R i /R t , where x = sin (θ/2), θ is the latitude on the target measured from the impact site, and v g and v i are the ground velocity and impact velocity, respectively. In contrast, in the limit in which the impactor is comparable to the size of the target (R i ∼ R t ), we find that shock velocities decline with the mass of the impactor significantly more weakly than m 2/3 i . We use the resulting surface velocity profiles to calculate the atmospheric mass loss for a large range of impactor masses and impact velocities and apply them to the Kepler-36 system and the Moon forming impact. Finally, we present and generalise our results in terms of the v g /v i and the impactor to target size ratio (R i /R t ) such that they can easily be applied to other collision scenarios.

Self Similar Shocks in Atmospheric Mass Loss Due to Planetary Collisions

“…We note that the results obtained in this section are in accord with the numerical simulations presented in [30], which found that for the three dimensional impact problem, the shock decelerates roughly asẊ ∝ m −2/3 (where m is the swept up mass) for γ = 5/3, where the model presented here predicts δ = −0.64. The model here also explains impact experiments, although the translation between the theoretical results and the experimental results is not straightforward.…”

“…What's incredible about the impulsive piston problem is that the relation between the shock velocity and the swept up mass v ∝ m δ holds also in the three dimensional impact problem [30], i.e. a power law with the same exponent δ.…”

“…In this section we demonstrate how the atmospheric mass loss from a giant collision is estimated. The dependence of the mass loss on impactor size and velocity in head on collisions was studied in [30], so in this section we consider the effects of obliquity. For this purpose, we run simulations of collisions between planetary cores and planets.…”

“…A systematic study of atmospheric mass loss for head on collisions has been carried out in [22,30]. The model they developed consists of two phases.…”

Lunar and Martian Silica

“…This simulation is supposed to represent a normal cratering event. We chose the adiabatic index to be 𝛾 = 1.4, since this value best describes the high pressure shock behaviour in silica (Yalinewich & Schlichting 2019). Since we want to resolve the impactor and also follow the shock wave to distances much larger than the impactor radius, we arranged 20,000 mesh generating points in a non-uniform way inside the computational domain.…”