Giant impacts stochastically change the internal pressures of terrestrial planets

Pressure is a key parameter in the physics and chemistry of planet formation and evolution. Previous studies have erroneously assumed that internal pressures monotonically increase with the mass of a body. Using smoothed particle hydrodynamics and potential field method calculations, we demonstrate that the hot, rapidly rotating bodies produced by giant impacts can have much lower internal pressures than cool, slowly rotating planets of the same mass. Pressures subsequently increase because of thermal and rotational evolution of the body. Using the Moon-forming impact as an example, we show that the internal pressures after the collision could have been less than half that in present-day Earth. The current pressure profile was not established until Earth cooled and the Moon receded, a process that may take up to tens of millions of years. Our work defines a new paradigm for pressure evolution during accretion of terrestrial planets: stochastic changes driven by impacts

Atmospheric loss in giant impacts depends on pre-impact surface conditions

Earth likely acquired much of its inventory of volatile elements during the main stage of its formation. Some of Earth's proto-atmosphere must therefore have survived the giant impacts, collisions between planet-sized bodies, that dominate the latter phases of accretion. Here we use a suite of 1D hydrodynamic simulations and impedance match calculations to quantify the effect that pre-impact surface conditions (such as atmospheric pressure and presence of an ocean) have on the efficiency of atmospheric and ocean loss from proto-planets during giant impacts. We find that -- in the absence of an ocean -- lighter, hotter, and lower-pressure atmospheres are more easily lost. The presence of an ocean can significantly increase the efficiency of atmospheric loss compared to the no-ocean case, with a rapid transition between low and high loss regimes as the mass ratio of atmosphere to ocean decreases. However, contrary to previous thinking, the presence of an ocean can also reduce atmospheric loss if the ocean is not sufficiently massive, typically less than a few times the atmospheric mass. Volatile loss due to giant impacts is thus highly sensitive to the surface conditions on the colliding bodies. To allow our results to be combined with 3D impact simulations, we have developed scaling laws that relate loss to the ground velocity and surface conditions. Our results demonstrate that the final volatile budgets of planets are critically dependent on the exact timing and sequence of impacts experienced by their precursor planetary embryos, making atmospheric properties a highly stochastic outcome of accretion.Comment: 45 pages, 17 figures, and 5 tables. Accepted to The Planetary Science Journa

Runge-Kutta IMEX schemes for the Horizontally Explicit/Vertically Implicit (HEVI) solution of wave equations

Many operational weather forecasting centres use semi-implicit time-stepping schemes because of their good efficiency. However, as computers become ever more parallel, horizontally explicit solutions of the equations of atmospheric motion might become an attractive alternative due to the additional inter-processor communication of implicit methods. Implicit and explicit (IMEX) time-stepping schemes have long been combined in models of the atmosphere using semi-implicit, split-explicit or HEVI splitting. However, most studies of the accuracy and stability of IMEX schemes have been limited to the parabolic case of advection–diffusion equations. We demonstrate how a number of Runge–Kutta IMEX schemes can be used to solve hyperbolic wave equations either semi-implicitly or HEVI. A new form of HEVI splitting is proposed, UfPreb, which dramatically improves accuracy and stability of simulations of gravity waves in stratified flow. As a consequence it is found that there are HEVI schemes that do not lose accuracy in comparison to semi-implicit ones. The stability limits of a number of variations of trapezoidal implicit and some Runge–Kutta IMEX schemes are found and the schemes are tested on two vertical slice cases using the compressible Boussinesq equations split into various combinations of implicit and explicit terms. Some of the Runge–Kutta schemes are found to be beneficial over trapezoidal, especially since they damp high frequencies without dropping to first-order accuracy. We test schemes that are not formally accurate for stiff systems but in stiff limits (nearly incompressible) and find that they can perform well. The scheme ARK2(2,3,2) performs the best in the tests

The energy budget and figure of Earth during recovery from the Moon-forming giant impact

Quantifying the energy budget of Earth in the first few million years following the Moon-forming giant impact is vital to understanding Earth's initial thermal state and the dynamics of lunar tidal evolution. After the impact, the body was substantially vaporized and rotating rapidly, very different from the planet we know today. The subsequent evolution of Earth's energy budget, as the body cooled and angular momentum was transferred during lunar tidal recession, has not been accurately calculated with all relevant energy components included. Here, we use giant impact simulations and planetary structure models to calculate the energy budget at stages in Earth's evolution. We show that the figure and internal structure of Earth changed substantially during its post-impact evolution and that changes in kinetic, potential, and internal energy were all significant. These changes have important implications for the dynamics of tidal recession and the thermal structure of early Earth