A user on the forum asked me what I meant by the word ‘random’ in my previous blog post. A statistician could explain this more precisely, but I’ll give my understanding of it in an astronomy context.
A random process is one in which a variety of alternatives could occur, but beforehand we cannot know which alternative actually will occur. The alternatives need not be equally likely, and the probabilities of each alternative happening (the probability density function) may be known very well. If we repeat the process many times, the number of times each alternative occurs will be very close to the probabilities we might already know. But we don’t know which alternative will actually happen each time the process occurs.
A random system is one which arises as a result of random processes. Everything has some element of randomness in it, nothing is perfectly ordered, but some things have a lot more order to them than others. The chair you are probably sitting on while reading this is a highly ordered system. Even though the atoms in it are jiggling around randomly to some extent, their overall motions are generally very ordered. The random motions of the atoms are not very large compared with the order that was instilled in the chair when it’s materials were constructed, whether that was by metal cooling in a mould or wood slowly forming in a tree.
The motions of stars in a spiral galaxy disk have a lot of order to them, as they are mostly formed by relatively gentle physical processes that maintain information about the history of the system. The galaxy started rotating long ago, and the stars which formed in it are still rotating today. In an elliptical galaxy some process has happened, for example a merger of two galaxies, which disturbs that order. The random process at work is the multiple close interactions of pairs of stars. The motion of two stars after they have passed close by one another is very dependent on the exact values of their motion before the interaction. If each of those stars then interacts with other stars we quickly get to a state where we could never know the stars’ initial motions well enough to predict their motions at a later time. This is an example of a chaotic system, and it can even occur for three objects interacting through gravity, never mind the billions of stars in a typical galaxy. There are many alternative paths the stars could travel along, and beforehand we don’t know which paths the individual stars will take. Despite this, we can go part way to determining what the result will be overall, a big fuzzy ball. The stars in elliptical galaxies are not moving totally randomly, there are certain ranges of orbits that are more populated than they should be for a truly random system. This order is a ‘memory’ of the initial motions of the stars in the merging galaxies. However, most of the stars’ movements are dominated by random motions.