Our solar system used to be a much more violent place, with proto-planets colliding in cataclysmic giant impacts that helped create the worlds we see today.

We study these dramatic events with 3D smoothed particle hydrodynamics (SPH) simulations, at 100–1000 times higher resolution than the current standard using our newly developed code SWIFT and a powerful supercomputer. This unprecedented detail allows us to study exciting topics like the tilt and strange internal structure of Uranus, the formation of Saturn’s rings from colliding moons, atmospheric erosion from giant impacts, and the collision that is thought to have formed the Moon.

This mp4 animation shows a cross-section of how one of these high-resolution collisions transpires. The colours represent different materials for the particles (rock, ice, or atmosphere).

–   Saturn's rings   –

   ApJ 2023 Paper

Results from NASA's Cassini mission showed that Saturn’s spectacular rings were significantly younger than expected, being no more than a few 100 Myr old, which would be roughly 5% of the age of the Solar System. This was inferred from the fact that the rings are still made predominantly from ice despite becoming increasingly polluted over time by incoming dust. One possible explanation for the rings' youth is that they may be debris from collisions in a previous generation of icy moons.

Another line of evidence supporting this hypothesis is the low orbital inclination of Saturn's moon, Rhea. Just like the Moon's orbital distance from Earth is increasing by about 4 cm/year, Rhea's orbit is also being increased by tidal forces and is currently almost 9 Saturn radii away. In the last few 100 Myr, Rhea should have passed through an evection resonance and had its orbital inclination excited to a value much higher than it currently has. This suggests that Rhea did not pass through this resonance and is young, like Saturn's rings, and may have formed following a dramatic collision.

We have run high-resolution simulations to study the orbits and composition of the ejected debris when a proto-Rhea is smashed into another icy moon. Not only do we find that enough material to form the observed ring system is sent inside Saturn's Roche radius, where the rings reside today just over 1 Saturn radius above Saturn's surface, but it is also ice-rich just like Saturn's rings. Furthermore, some debris is placed onto a collision course with other icy moons currently present between the orbital radius of Rhea and the rings. This would provoke a chain reaction of impacts leading to more icy material being made available to form the rings we see today.

This animation presents a rendering of a 2 km/s impact between two icy moons with masses like the present-day moons Rhea and Dione. White and brown represent ice and rock respectively. The collision is assumed to have occurred 7 Saturn radii away from Saturn, and the first 9 hours after impact are shown. Over 30 million particles were used in the hydrodynamical simulation underpinning this animation.

–   The Moon-forming collision   –

   ApJL 2022 Paper

With sufficiently high numerical resolution, the canonical Moon-forming collision, where a Mars-sized body called Theia strikes the proto-Earth, can lead to a Moon-like body being immediately placed into orbit around Earth. This alternative scenario for lunar origin opens up new options for the Moon's initial orbit and internal properties. For example, the orbiting body has a centre that is predominantly made of material from Theia, and might not be fully molten, while the outermost regions are very hot and can be made of more proto-Earth material. How that composition gradient would evolve over the history of the Moon is yet to be determined. However, it could help explain why the isotope ratios in lunar rocks returned by the Apollo astronauts are similar to those of Earth's mantle. This contrasts with previous lower resolution simulations where a disk of debris was created by the collision, but no large orbiting bodies. In that case, the Moon would form over tens to hundreds of years by the gradual accumulation of this material and no initial composition gradient would be expected.

For small changes in the impact angle or speed, the outcome of the collision can differ significantly. However, even if a Moon-like satellite is placed onto an orbit that goes too close to Earth to be expected to survive, the material stripped off the body can gravitationally torque the remainder of the satellite onto a stable wider orbit, above the Roche radius. The animation below shows one such case of a Moon-like object eventually being flung into an orbit where it can survive destruction by Earth's gravity.

   MNRAS 2021 Paper

We used our initial conditions code WoMa to investigate how the spin of Theia, the hypothesised impactor in the Moon-forming collision, affected the resulting collision. Just by changing Theia’s initial spin, the collision can result in anything from a merger, a hit-and-run, or even a clump surviving in orbit, as illustrated by the 5 scenarios shown in this figure.

The l_Th labels show the rotational angular momentum of Theia as a fraction of the maximum it could have before becoming unstable. Negative values mean that Theia’s spin angular momentum was in the opposite direction to the orbital angular momentum - these two cases produce mergers. The non-spinning Theia and the slowly co-rotating Theia produce orbiting clumps that are roughly the mass of the Moon and with a similar mass of iron core. With our 10⁷-particle simulations, we have enough resolution to measure a spatial gradient in the material forming these proto-Moons. In the centre they are dominated by matter originating in Theia, but towards their surface they are composed of roughly equal amounts of Theia and proto-Earth.

–   Atmospheric erosion   –

   ApJ 2020 Paper, ApJ 2020 Letter

The Earth’s atmosphere has a complicated history of being built up and eroded, and exoplanets around other stars show a huge variety of atmospheres from very thick to very thin. Giant impacts might play a key role in this evolution, but the low density of atmospheres and the complex messiness of impacts makes it a challenging problem to study, so previous studies have primarily focused on 1D models or thick atmospheres, often also limited to only head-on collisions.

We ran 3D simulations of over 300 collisions onto terrestrial planets hosting thin(ish) atmospheres for the first time spanning a wide range of angles and speeds, as well as different masses and compositions. This lets us examine the mechanisms of how giant impacts erode atmospheres and how much is lost in each case. The animations below show the first few hours of four 10⁸-particle simulations with a mix of head-on, grazing, slow, and fast scenarios.

In spite of the complicated details and the great differences between scenarios, we found that a simple scaling law can be used to estimate the erosion from any collision in this regime, as illustrated by this crowded figure with the results from many dissimilar scenarios overlapping on the same line. This makes it possible to predict the loss from other impacts in the context of large-scale models of planet formation.

–   High-resolution simulations and convergence   –

   MNRAS 2019 Paper

Any simulation has limitations. One of the most important tests for a model to be useful is that the answer to your chosen question stays the same when the resolution improves. If not, then regardless of how simple or sophisticated the simulation might be, the results won’t be reliable.

We found that giant impact simulations using the current standard of 10⁵ (top panel) or 10⁶ particles can fail to converge even on bulk outcomes like the rotation period, and get the answer wrong by several hours in this example.

Using SWIFT, we ran simulations with over 10⁷ and 10⁸ (bottom panel) particles and confirmed that these do converge on the large-scale results reliably. Studying finer details like the composition of ejected debris may require even higher resolution.

–   Knocking over an ice giant   –

   ApJ 2018 Paper

Uranus is an odd planet. It spins on its side, with an obliquity of 98° and its major moons orbiting in the same tilted plane. This was most likely caused by a giant impact, which might also help explain other mysteries such as the planet’s extremely cold exterior and strange magnetic field.

We ran the first Uranus impact simulations since the original study in 1992 to study a wide variety of scenarios and the possible consequences of this violent event for the planet. As well as confirming that the impact could knock over Uranus’ spin, we found that with a grazing collision the impactor could form a thin shell around the planet’s ice layer, possibly preventing convection and trapping the interior heat to help explain the freezing outer temperatures.

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—   Simulations and initial conditions   —

The supercomputers we use run on as much electricity as a small town, so it’s important that we use them effectively. As well as running simulations of planets to learn about them, we also work on the code development behind the scenes. This includes big projects like the SWIFT code in collaboration with other astronomers and computer scientists, alongside smaller topics more specific to planetary science.

–   SWIFT   –

   www.swiftsim.com  
SWIFT (SPH With Inter-dependent Fine-grained Tasking) is a hydrodynamics and gravity code for astrophysics and cosmology in open development, designed from the ground up to run fast and scale well on shared/distributed-memory architectures (supercomputers).

A supercomputer is basically a large number of normal computers working together in “parallel”. For the past decade, instead of getting faster, supercomputers are getting more parallel. This makes it ever more important to share the work evenly between every part of the computer so that no processors are sitting idle and wasting time.

SWIFT’s various careful approaches to these challenges have allowed us to run planetary impact simulations with 1000 times more particles than before, and cosmological simulations of galaxy formation over 30 times faster.

Find out everything about SWIFT and give the code a try with the examples and documentation at www.swiftsim.com.

–   Placing particles in spherical shells   –

   MNRAS 2019 Paper    Python: pip install seagen    Github: github.com/jkeger/seagen

The SPH method we use requires arranging many millions of tiny particles to represent each planet in the computer. The spherical symmetry and sharp boundaries between layers in planets makes it helpful to place particles in nested spherical shells. If some particles are a bit too close or a bit too far away from each other, then our model planet won’t be perfectly stable. In that case, we’d need to run an extra simulation to let it “relax” and for any wobbling to settle down before the impact, using up valuable time on a supercomputer. So we have to arrange these particles carefully.

However, it is impossible to place an arbitrary number of particles equally spaced on a sphere – a long-standing problem in mathematics and other fields, such as chemistry for how atoms arrange themselves in molecules.

We developed a new scheme (and public python module) for placing particles almost perfectly by dividing the sphere into equal, roughly square regions, then stretching particles slightly away from the poles. This “stretched equal-area” (SEA) method ensures that all particles have an SPH density within 1% of the right value.

The figures show an example SEA arrangement of 100 particles on a single shell and of 100,000 particles in nested shells to build up a simple model of an Earth-like planet.

–   WoMa: making profiles and spinning planets   –

   MNRAS 2021 Paper    Python: pip install woma    Github: github.com/srbonilla/WoMa   
Before we can arrange any particles, we first need interior models for our planets. Many objects in astronomy are roughly spherical, but rotation is also common and can be very important in giant impacts.

We developed a fast method (and open-source python module) to make models of multi-layered spinning or static bodies in hydrostatic equilibrium, and to convert them into particle representations using a modified version of SEAGen.

Rotating planets have occasionally been studied with particle simulations, but typically the initial conditions had to be made by incrementally spinning up a spherical planet with multiple settling simulations. This can be slow and also makes it impossible to know the precise properties of the final planet until the end of the process. WoMa avoids any extra simulation and also allows us to control everything directly.

–   Other planetary science from the ICC   –

Other planetary research at the ICC in Durham has involved determining the distribution and abundance of water ice on the Moon, Mars and Mercury, studying the argon abundance in the lunar exosphere and using planetary neutron spectroscopy to constrain the lifetime for free neutrons. See http://icc.dur.ac.uk/index.php?content=Research/Topics/O13 for more details.

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