Download Billiards and planet formation

Billiards and planet formation
Volker Hoffmann, Simon Grimm, Ben Moore & Joachim Stadel
Institute for Computational Science, University of Zurich.
Rocky Earth-like planets are thought to be the end result of a vast number of gravitational
interactions and collisions between smaller bodies. We have developed the world’s fastest simulation
code for simulating the formation of planets, GENGA, which runs entirely on the graphics processing
cards. This speeds up the calculation by an order of magnitude, allowing us to study the statistics of
the formation of planetary systems1. Our simulations result in several terrestrial planets around each
star we simulate. However, in this study2 we find that practically identical initial conditions result in a
wide array of final planetary configurations. If a single planetary building block is moved by less than
one millimetre, then a completely different set of planets results - this timescale for chaotic
divergence decreases with increasing particle number. If our solar system had contained one extra
molecule then the Earth may not have formed.
This behaviour is rather like billiards. If two balls collide we can calculate the outcome with some
uncertainty, but this uncertainty becomes larger as more collisions take place. Furthermore, a tiny
change in the angle or speed of the first collision can lead to a completely different final
configuration. This chaotic behaviour does not mean the billiards behave randomly. It is theoretically
possible to calculate the outcome, but practically impossible since our computers are not accurate
enough to make the calculation. In fact, no computer will ever be powerful enough to simulate
exactly the outcome of even 9 collisions - just the gravitational attraction of anyone standing next to
the table will influence the outcome3.
In order to design our solar system, the positions and velocities of over 1057 atoms would need to
accurately specified. This highly chaotic behaviour questions the predictability of different scenarios
for the formation and evolution of our solar system and planetary systems in general. However,
multiple realisations of the same initial conditions can be used to predict certain global statistics. For
example, we find that the same simulations including giant planets like Jupiter tend to generate
fewer but higher mass planets than simulations without. This prediction can be tested with
forthcoming observational programs. By extracting outliers in the observations, we cautiously predict
that Kepler-10, Kepler-9, 61 Vir, HD 134060, and HD 51608 may host as yet undetected giant planets.
For further information contact:
Volker Hoffmann, [email protected] or Prof. Dr. Ben Moore, [email protected]
1. https://bitbucket.org/sigrimm/genga, “The GENGA Code”, http://arxiv.org/abs/1404.2324
2. “Chaos in terrestrial planet formation”, http://arxiv.org/abs/1508.00917
3. Michael Berry, 1967 “Regular and irregular motion” Topics in Non-linear Mechanics,
Am.Inst.Ph.Conf.Proc No. 46, 16-120
Fig 1. A cartoon showing the development of our solar system over time.
Fig 2. The Earth photographed from the Moon by the Apollo astronauts.