Circumstellar Chaos

So my latest fascination (albeit maybe not what I’ll actually be working on) is the interesting world of chaos theory.

Chaos theory, while no longer “fashionable” as a scientific paradigm, is a fascinating piece of science, unfurling a whole world of complexity from simple Newtonian Mechanics. Many pop science authors in the past have touted chaos theory as some kind of scientific panacea, holding the answer to everything. I however, despite my penchant for flagrant speculation, like to be slightly more pragmatic about things…

Chaos theory describes the evolution of dynamic systems. A system, with a specific set of initial conditions, evolves over time to give a certain outcome. These systems are so sensitive that the initial conditions make them quite deterministic, defining the end result regardless of how random the system appears to be. This in turn gives rise to “attractors” — or certain repeating patterns that are dynamically stable. Entire systems end up revolving (metaphorically speaking) around these oases of stability, hence the term “attractor”.

That sounds a bit abstract, doesn’t it? How about if you look at it in a simpler context. Imaging you have a big wooden salad bowl and a small rubber ball. Place the ball anywhere within the ball and let gravity do it’s thing. The ball will immediately roll towards the centre, regardless where in the bowl you place it. Having the lowest gravitational potential, the centre of the bowl is the most stable point in the system, and so the ball will always be “attracted” to it. Nature likes low energy states. Consequently, you can start the ball in any location in the bowl, you can even throw it in any direction, and it will always head back towards the centre. That, in essence, is a Lorenz Attractor. In this butterfly-looking diagram to the right, the attractor is in the centre where the lines reapeatedly cross over.

So, a chaotic system (as I’ve already mentioned) can be defined as a system whose state evolves over time, and is highly sensitive to initial conditions. This is also quite a good description of a circumstellar environment. Circumstellar shells, like the one I’m studying, evolve with time, both physically and chemically. Much of the way they work can be explained by fluid dynamics, just like the weather. They contain regions of smooth, laminar flow as well as shocks and turbulent regions. The interesting part is, if a circumstellar environment is indeed a chaotic system, then it will be fully deterministic, meaning based on the initial conditions it should be possible to accurately predict the chemical evolution of the system. For instance, there’s a lot of conjecture over how certain compounds form in stellar outflows. Take PAHs for instance. We know they form, we can see their telltale signatures, and yet no one’s been able to decisively say how. People have tried building models and proposing possible mechanisms, but the models often seem to show that chemicals don’t spend long enough in the right environments to evolve the way they should.

However, if it could be proven that lorenz attractors exist in circumstellar environments, then they could be responsible for concentrating certain key intermediates long enough for them to react together. The reacted products will thus have different parameters to the initial reagents. They will have different mass, and probably be more strongly affected by stellar winds. Thus, a lorenz attractor in a stellar outflow might provide a physical mechanism to catalyse chemical transformations.

After all, if SOHO can get a picture of a coronal mass ejection like this one, showing little globules of solar stuff (caused by turbulence) — then logically the same could be true for any main sequence star. By the by, those little globules of hot plasma are actually larger than our whole planet…

I like the concept of chaos theory. How plausible is it’s application to astrochemistry, though?
As the book I’m reading so eloquently puts it:
“…one must remain cautious about such studies for it is quite easy to misinterpret [these] ideas by an imprecise application of techniques which have thus far only been successful tested in well-controlled laboratory situations. However, if new insights into difficult areas are obtained using this approach, which amount to more than putting common sense into fancy mathematical language, then a great deal has been achieved.”

About Invader Xan

Molecular astrophysicist, usually found writing frenziedly, staring at the sky, or drinking mojitos.
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