Dark matter halo

A dark matter halo is a fundamental unit of structure in modern physical cosmology. It is defined as a hypothetical region that has decoupled from the expansion of the universe. Within this region, matter is held together by the force of gravity. These halos are not just empty spaces; they act as containers for cosmic structures. A single halo may contain several smaller clumps of dark matter called subhalos. These subhalos are also gravitationally bound to the larger host. Modern models, such as the Lambda Cold Dark Matter (ΛCDM) model, suggest that both halos and subhalos can contain entire galaxies.

The process of halo formation is a key part of how the universe organized itself. In the early universe, there were small variations in density. These density perturbations grew over time as the universe expanded. Once a region reached a critical density, it stopped expanding and began to collapse. This process is often studied using the spherical collapse framework. As these halos form, they continue to grow in mass and size. They do this through two main methods: accretion or merging. Accretion involves pulling in material from the immediate neighborhood. Merging occurs when two separate halos collide and combine into one.

Scientists use different mathematical models to describe the density of these halos. One common model is the pseudo-isothermal halo. This model uses a central density and a core radius to fit rotation data. However, this model is only an approximation because its mass does not stay finite at infinite distances. A more famous model is the NFW profile, named after researchers Navarro, Frenk, and White. The NFW profile is considered "universal" because it describes halos across four orders of magnitude. This includes everything from small individual galaxies to massive galaxy clusters. Another model, the Einasto profile, uses an extra parameter to better match high-resolution computer simulations.

We know these halos exist because of their gravitational effects on visible matter. In a spiral galaxy, the rotation curve shows how fast stars and gas move at different distances from the center. If only visible matter existed, the rotation speed would decrease as you move further out. This is similar to how outer planets orbit the Sun more slowly than inner planets. However, radio observations of the 21 cm Hydrogen line show that rotation curves actually flatten out. This means stars at the edge of a galaxy move just as fast as those closer in. This observation was a major clue. It suggests a massive, invisible halo is providing extra gravity to keep those outer stars in orbit.

The history of this discovery involves several important scientists. In 1970, Ken Freeman proposed the existence of undetected mass. He noticed that the expected decline in velocity was missing in galaxies like NGC 300 and M33. Later, in 1978, A. Bosma also studied these rotation curves. These findings suggested that either dark matter exists or our understanding of gravity, such as general relativity, is incomplete. Since then, the dark matter hypothesis has been reinforced by many studies. We now use complex numerical simulations to understand how cold dark matter (CDM) forms these structures. CDM is special because it lacks the thermal and radiative pressures that prevent normal matter from collapsing.

Dark matter halos are not always perfect spheres. In fact, the collapse of matter in the universe is usually aspherical. Early simulations showed that halos are often substantially flattened. Most researchers describe the shapes of these halos as ellipsoids. These are three-dimensional shapes defined by the different lengths of their axes. The shape of a halo can also be influenced by its spin, or angular momentum. Asymmetric collapse in an expanding universe produces objects with significant spin. Simulations show that the distribution of this spin follows a log-normal distribution. This means that halos in denser regions of the universe tend to have higher spin.

Our own Milky Way galaxy provides a clear example of how these systems work. The visible disk of our galaxy is embedded within a much larger, roughly spherical dark matter halo. This halo likely contains between $10^{11}$ and $10^{12}$ solar masses of dark matter. In fact, it is believed that about 95% of our galaxy is composed of dark matter. The luminous matter we can see, like stars and gas, makes up only about 5%. Dark matter is unique because it does not interact with energy or normal matter in any way except through gravity. This invisible structure is what holds our entire galaxy together.