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IMPACTS / PLANETARY COLLISIONS

Collisions among planetary objects are at times wild and destructive events. However, we have also seen evidence for cases in which collisions are extremely gentle. The term 'planetary collisions' is in fact overly generic, since it applies to a really huge variety of different types of impactors, targets, collision velocities and collision geometries. For example, planetary collisions can involve comets activated by hits from boulder-sized projectiles, mutual collisions of asteroid-sized objects, dwarf-planets, moons, moons and planets, two planets, stars and so on.

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Such impacts are triggered by many different dynamical channels: random collisions, hierarchical systems, gravitational capture, chaotic evolution and so on. In the last couple of decades, planetary collisions are studied through sophisticated computer simulations that try to capture the physics involved. One of the main methods is called smooth particle hydrodynamics, or SPH. In this method, we arrange millions of tiny particles to represent each planetary object in the computer. Our goal is to approximate all the forces (including gravity) between fluid elements in the simulation, by solving an appropriate set of mathematical equations. Obviously, we cannot reach the ultimate resolution of atom-sized particles. Instead, we can use far fewer particles and effectively smooth over the gaps between them, which is what SPH is all about.

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I have found that being able to simulate collisions, constitutes as an incredibly powerful tool, that enables a lot of very interesting science. Collaborating with a team of German researchers led by Christoph Schaefer from the university of Tübingen, I participate in developing various tools and implementations, applying them to a novel SPH computer code which utilizes graphical processing units (GPUs). GPUs are electronic circuits designed with a highly parallel structure. They are composed of thousands of cores, that can handle thousands of threads simultaneously, and are thus designed to work out problems much faster than regular central processing units.

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Here are some examples of different collision simulations.

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GAS GIANT COLLISIONS:

When it comes to collisions, one might argue that bigger is better. I personally like all types of collisions, but I can certainly see why extremely energetic collisions might be more interesting to some. For example here is a simulation that mimics the impact that might have titled Uranus on its side, spinning unlike all the other planets in the Solar system.

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The above animation shows an SPH simulations of a collision between Uranus and a terretrial-like planet, about 4 times as massive as the Earth. Here the color scheme shows different materials. The impacting planet, as well as the core of Uranus, are composed of pure rock (blue). This rocky core underlies a thick water layer (white), underlying an outermost envelope of hydrogen and helium in Solar proportions (red). Here I implemented a new equation of state for the hydrogen-helium mixture to work with our SPH code.

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SUPER-EARTHS AND EXO-MOON FORMATION:

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Our Solar system consists of only two types of planets. Terrestrial planets and gas giant planets. Nevertheless, we have now discovered thousands of exo-Solar planets which are nothing like those seen in the Solar system. A very frequent type of planet is called a super-terrestrial or super-Earth planet. Such a planet is several times more massive than the Earth, yet is composed of similar materials. One of the interesting ideas regarding super-Earth planets is that giant impacts among them may lead to the formation of exo-Solar moons like our own moon, also believed to have been formed by a giant impact. Being more massive, however, we may be led to believe that exomoons around super-Earth planets can also be larger than our own moon. Nevertheless, we have not yet been able to detect them. Our instruments are not yet sensitive enough, but perhaps that would change in the next decade. My colleagues and I have put this theory to the test, examining just how large they might get.

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The above animation shows a collision between a terrestrial planet and a super-terrestrial planet, both composed of an iron core underlying a rocky mantle. The numerical resolution is one million particles. The rendered top-view animation is semi-transparent, the colors denoting different densities.

 

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This example results in a relatively rare outcome. The smaller planet grazes the larger planet and emerges intact, stripped of some of its mass. On its next close approach of the larger planet, the two objects might merge, and if it remains sufficiently far, it might even survive from being tidally stripped, remaining in orbit as a captured moon. We have simulated examples of both potential scenarios.

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A much more frequent collision outcome is the formation of a debris disc surrounding the merged planet.

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​​In the above animation two super-Earth planets collide and merge, forming a debris disc. The animation is semi-transparent and so disc particles are only partially visible here (see the denser clumps). Eventually an exomoon may emerge slowly by coagulating from the disc. This formation process is however much longer than the collision timescale featured above, and therefore it cannot be resolved by the SPH simulation, being too computationally expensive. In order to model longer timescales, one can hand over the results from SPH simulations like these, to less computationally expensive codes. For example, N-body codes only consider the gravitational forces between particles, and are thus easier to carry out for longer periods. Additionally, clumps of particles may be considered as single gravitating fragments, and so during the hand over clumps of physically connected particles may identified, saving additional computation time. A nice example of such hand over is featured below.

 

 

 

MOON FORMATION THROUGH SPH/N-BODY HANDOVER: 

The following example is merely a visually enjoyable demonstration of how the hand over from SPH to N-body code works. I caution that it was never meant to be physically plausible, for reasons which I will not go into here. The simulation features the so-called canonical 'giant impact' scenario that is considered by many to have formed the Earth's moon. It has ran for several hours, then truncated abruptly and switched to an N-body code called REBOUND, which I modified further to interface with our SPH code and track additional important properties.

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​The initial SPH color scheme denotes the particles' energies, while the N-body color scheme shows the fraction of impactor material in the simulation fragments. When handledling these hand overs in a more physically plausible manner, I have used this setup previously in order to obtain end-to-end formation and lower limit mass estimates of moons. For example, the technique was used in order to follow the formation of exomoons from debris discs of super-Earth collisions, successfully calculating their final size, composition and orbit.

 

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MOON-MOON COLLISIONS IN THE GRAVITATIONAL POTENTIAL OF A NEARBY PLANET: 

On of the ideas regarding the formation of our moons, or moons in general, is that they can also form gradually by multiple smaller collisions rather than one large giant impact. This idea applies equally to dwarf planets. When such smaller collisions take place near a host planet, the material has to escape the larger gravitational potential of the planet. Depending on the distance from the planet, this could lead to various interesting outcomes. This scenario is completely plausible, especially in the early stages of planet formation (that is, when planetary systems are in the process of forming).

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This animation starts when two small moons collide. The colors denote temperature variations. Debris formed in the collision are affected by the gravitational potential of the planet, which is accounted for in this simulation by a single gravitating point mass (the large blue sphere in the center of the image is simply increased to the Earth's size for the display). In other words, the planet is not resolved by an assemblage of SPH particles, just a single particle, but its gravitational tag on all the other particles is calculated. I stop this animation when particles temporarily stop accreting onto the planet. Note that here the planet is a 'sink' particle, which grows in mass by accumulating regular particles passing within some effective accretion radius. A moon can further coagulate from the debris disc that was resulted in the collision, and this process can be tracked by subsequent N-body dynamical simulations. In a new collaboration with DLR planetary physics department in Berlin headed by Doris Breuer, we lay out a collaborative framework to follow not merely the formation of the moon, but also its internal evolution and the solidification of its crust.  Note that some of the fragments in the movie are irregularly shaped. That's because this simulation includes their internal strength properties. Below there are some more explanations about that.

 

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SMALL BODIES:

Unlike large moons or planets, in which the dominating forces are those from self-gravitation, smaller objects are dominated by the electrostatic forces. In other words, they are held together by their intrinsic material strength, as a pebble does, or as the human body does, and not merely by gravity. Accordingly, small planetary bodies often have highly irregular shapes, and only when the gravitational forces become comparable, objects tend to transition toward a spherical shape. This idea is supported by numerous examples of objects observed in our Solar system. The transition size is about a few hundred kilometers, although one cannot be too precise since the composition is important, as different materials have different strengths. And so is the temperature.

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Additionally, small bodies are often not consolidated pieces of material - instead they have porosity. To read more about porosity see the link below regarding planetary interiors.

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So when we model collisions between small bodies using SPH, we must account for both material strength and porosity, in addition to other complicated physical behaviors such as damage caused by fracture during collisions. This adds a new layer of complication to the regular SPH method, which many codes do not posses. The code that I used here in the aforementioned examples also fully supports small body collisions, hence making it one of the most state-of-the-art codes in the SPH community.

 

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The example below features several animations of collisions between two elliptic spheroids, each one a few tens of kilometers in diameter. They are all colliding at the same velocity (~ 4 m/s) but at different angles and with different material strengths.

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In the above animation the material strength is high, and the two objects conjoin to form an undeformed pair, also known as a 'contact binary'. This one is a perfect contact binary. Conversely, using very low internal strength and the same impact angle, the resulting contact binary is highly deformed.

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We can play around with different parameters to get different outcomes. For example, if the impact angle is sufficiently high such that the two object graze each other near the edges, and the material strength is intermediate between the two former cases, then they can crater each other before rolling one on top of the other as they come to a stop.

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Of course they may also bounce and rebound to collide again at a lower velocity, etc. Numerous possibilities exist.

 

 

These animations are actually not generic study cases, but instead various models for the formation of the contact binary Arrokoth. Arrokoth is the most distant Solar system object ever explored by a spacecraft, and the only one of its kind ever seen, with hardly any discernible deformation or significant contact 'neck'. Here is what it really looks like.

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I led the impact section on a paper that was published in Nature journal. The paper dealt with the formation of Arrokoth. A suite of simulations demonstrated that numerous model realizations can achieve both the small deformation and exact rotation period of the contact binary for various velocities, impact angles and material densities, constituting for a rather robust model.

 

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In am currently also working with collaborators from Monash university in Australia in order to develop an even more robust model that features two categorical types of collisions that may occur. The first type is similar to the original Nature paper, and the second type is brand new, and yields even better outcomes. Here's an example of a much more recent simulation.

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