The opening lines from R. Brent Tully’s “Lighthouses in the Shoals of Dark Halos“:
In the imaginary world of simulations, researchers have a well developed picture of the collapse of matter into halos. Overtime, small halos are absorbed into larger units. Collapsed regions filled with substructure can be defined by hundreds or thousands of particles. Halos can be identified with precision within those simulations
In the real world, most galaxies are observed to lie in groups or clusters. However, membership may be so limited that the structure is ill defined.
The first line is certainly arresting, especially for a theoretician! It sounds like we’re off with the fairies, making our own universes, while the real world lies waiting. But the point Tully is making is actually more subtle, and more interesting. By page 3 he cites an N-body paper to reinforce a conclusion drawn from the simple analytic model of Bertschinger (1985), so He obviously believes that simulations aren’t complete fiction.
The point he is making is that simulators are perfect observers. We know where every particle is and where it is going. So if we want to group galaxies into clusters and calculate the virial radius, then we can. We can follow a galaxy for a few billion years and see if it escapes the group or collides with another galaxy.
The real universe, unfortunately, isn’t that easy. We can only see things that, for whatever reason, have been lit up bright enough to be visible from astronomical distances. We cannot watch a galaxy for a few billion years to see how it turns out.
So we need to be smart. Instead of the virial radius, Tully considers the radius of 2nd turnaround. Think of a perfectly smooth, expanding universe. Then make a little bit of it a bit denser, and watch gravity make it collapse. At some outer point, the inwards pull of gravity will have caused the outwards expansion of the universe to stall – this is the first turnaround. The matter inside falls into the centre of the overdense lump, overshoots and sloshes outwards. The maximum radius reached by this material marks the second turnaround. This radius we can observe – the density will step down as we move out past this radius. With this radius in hand, we can test (and confirm) a prediction of self-similar collapse models: the mass within this radius, divided by the radius cubed, will be constant across the population of clusters.
The general moral of the story, I think, is that there is more to astronomy than just theory and observation. It sometimes takes considerable cleverness to think of a way to test a model. Often the most direct ideas are swamped by complications. This missing link between theory and observation must be bridged from both sides. Theoreticians will be tempted to idealise the telescope. Observers can (and have) oversimplify models, testing non sequiturs.
But that, in the end, is the fun of astrophysics. You didn’t think that the universe would be easy, did you?
Leave a Reply