The key properties of disk galaxies, which are also commonly called spiral galaxies, are that they are very thin, rotate rapidly, and often show spiral structure. One of the main challenges to galaxy formation is the great number of thin disk galaxies in the local universe. The problem is that disks are very fragile, and mergers with other galaxies can quickly destroy thin disks.
Olin Eggen, Donald Lynden-Bell, and Allan Sandage in 1962, proposed a theory that disk galaxies form through a monolithic collapse of a large gas cloud. As the cloud collapses the gas settles into a rapidly rotating disk. Known as a top-down formation scenario, this theory is quite simple yet no longer widely accepted because observations of the early universe strongly suggest that objects grow from bottom-up (i.e. smaller objects merging to form larger ones). It was first proposed by Leonard Searle and Robert Zinn that galaxies form by the coalescence of smaller progenitors.
More recent theories include the clustering of dark matter halos in the bottom-up process. Essentially early on in the universe galaxies were composed mostly of gas and dark matter, and thus, there were fewer stars. As a galaxy gained mass (by accreting smaller galaxies) the dark matter stays mostly on the outer parts of the galaxy. This is because the dark matter can only interact gravitationally, and thus will not dissipate. The gas, however, can quickly contract, and as it does so it rotates faster, until the final result is a very thin, very rapidly rotating disk.
Astronomers do not currently know what process stops the contraction. In fact, theories of disk galaxy formation are not successful at producing the rotation speed and size of disk galaxies. It has been suggested that the radiation from bright newly formed stars, or from an active galactic nuclei can slow the contraction of a forming disk. It has also been suggested that the dark matter halo can pull the galaxy, thus stopping disk contraction.
In recent years, a great deal of focus has been put on understanding merger events in the evolution of galaxies. Our own galaxy (the Milky Way) has a tiny satellite galaxy (the Sagittarius Dwarf Elliptical Galaxy) which is currently gradually being ripped up and “eaten” by the Milky Way. It is thought these kinds of events may be quite common in the evolution of large galaxies. The Sagittarius dwarf galaxy is orbiting our galaxy at almost a right angle to the disk. It is currently passing through the disk; stars are being stripped off of it with each pass and joining the halo of our galaxy. There are other examples of these minor accretion events, and it is likely a continual process for many galaxies. Such mergers provide “new” gas, stars, and dark matter to galaxies. Evidence for this process is often observable as warps or streams coming out of galaxies.
The Lambda-CDM model of galaxy formation underestimates the number of thin disk galaxies in the universe. The reason is that these galaxy formation models predict a large number of mergers. If disk galaxies merge with another galaxy of comparable mass (at least 15 percent of its mass) the merger will likely destroy, or at a minimum greatly disrupt the disk, yet the resulting galaxy is not expected to be a disk galaxy. While this remains an unsolved problem for astronomers, it does not necessarily mean that the Lambda-CDM model is completely wrong, but rather that it requires further refinement to accurately reproduce the population of galaxies in the universe.