Tue, 2010-05-04 4:47pm — Tiaan

When we look at objects in the sky, out there in the solar system, galaxy and universe, we often see a pattern where numerous smaller or lighter items are scattered in a disk-shaped formation and are orbiting around something larger or heavier. For example, there are planetary rings, such as the prominent ones found around Saturn’s equator, which consist of things like dust, ice, rocks and moonlets. Then there is our Solar System: the Sun with the planets orbiting within a relatively flat disk around it — and the planets are thought to have formed from a protoplanetary disk. Also, at a larger scale we have, for example, the spiral galaxy with a central bulge and a rotating disk of stars around it (defining its galactic plane). So, rotating disks of celestial objects are quite common and repeated at every size scale; but how do they get to have that specific shape? Scientific explanations go along the lines of: the process starts with a cold cloud of gas and dust, the cloud collapses under gravity, and “conservation of angular momentum causes any small net rotation of the cloud to increase, forcing the material into a rotating disk”. But what does that really mean? Even astronomers say: “it’s so hard to explain in simple words”.

To get a hands-on feel for how these disk-shaped structures might form from objects under the influence of gravity, I wrote a simulation using Unity 3D to visualize the process. Even by ignoring the detail of general relativity and just using a crude implementation of Newton’s law of universal gravitation, the simulation produces a structure that has a heavy core with lighter objects swirling in a disk around it. In the real Universe, the process is much more complex when taking things like gas pressure, electromagnetic forces and the speed of light into account, but I think the simulation illustrates the basic concept of a disk forming from conservation-of-angular-momentum quite nicely. The code is released as open source under the MIT License, and it can be downloaded as either a Unity Package or ZIP file. If you have the Unity Web Player installed, you can view an interactive version of the simulation in your browser by clicking here or on the animated image above (it works better in Firefox than Internet Explorer). Or you can watch a time-lapse video of the simulation from YouTube, shown below:

So what is it that we see in the simulation? Well, we begin with a cloud of debris where each object is randomly positioned in space. The mass of each object is also determined randomly and this is represented by its color: lighter objects have greenish colors and heavier objects have orangey colors. Initially the objects don’t move or rotate by themselves, which is something one might associate with a “low-temperature cloud”. The initial stationary state of the cloud is depicted below.

Once the simulation has started, the cloud collapses under gravity; the objects collide and clump together. Within the first 15 to 30 seconds or so, a sphere-shaped blob forms roughly at the center, as seen in the next screenshot. The resulting ball of debris rotates slowly due to the small net-rotation from all the interacting objects.

The individual objects keep wiggling to find more comfortable positions for each object’s shape, size and weight. Some of the heavier objects bury themselves deeper inside the core and some of the lighter objects bubble to the outer regions. As a result of the overall shift of mass towards the center, the sphere’s rotation speeds up — angular momentum is preserved. (Think of the analogy with the ice skater spinning faster when contracting arms or legs.) The objects that are located near the sphere’s equator generally move faster than the ones towards the poles, and, as the rotation speeds up, the lighter objects start to dislodge at the equator. And so, after about 1 or 2 minutes, the disk starts to form:

The process continues, causing more material to be flung out from the equator. After about 5 to 15 minutes, a nice accretion-disk has formed, as seen in the last two images (first a face-on view, then an edge-on view).

This simulation helped me to get a better understanding of how the disk-shaped celestial objects might be formed if left to forces such as gravity. But don’t read too much into the simulation, since, after all, is was written using a physics engine developed primarily for games rather than for astrophysical research — space debris might not always look and behave exactly like they do in this simulation. Despite its shortcomings, I hope the simulation would benefit others.