Thursday, February 20, 2014

Jeans Length

Jeans is the name. Sir James Jeans.

What determines the size of the structures that we see in the universe? Stars, galaxies, clusters of galaxies, and the cosmic filaments? A very prominent role is played by Jeans length (or Jeans mass, or Jeans criterion).

Suppose we have a cloud of some kind of self-gravitating matter. This cloud will tend to contract under its own gravity unless some other force - pressure - prevents it. Two numbers turn out to be central: the free fall time, or the time takes for the gravitational attraction to pull the cloud together and time it takes a sound wave to cross the cloud. If the free fall time is less, the cloud will collapse before pressure has a chance to present organized resistance. In practice, this means that clouds smaller than the Jeans size (free fall time greater than time for sound to cross the cloud) won't contract.

In the early universe, the speed of sound is nearly that of light, so that the Jeans size is comparable to the cosmic horizon size. After the universe cools enough for atoms to form by recombination of positive and negative charged particles, the Jeans size plummets abruptly, by many orders of magnitude. Consequently, the largest scale features fragment into much smaller contracting pieces of a trillion solar masses or less - galaxies. Larger structures become fragmented into clusters or superclusters of galaxies.