According to modern models of
physical cosmology, a dark matter halo is a basic unit of
cosmological structure. It is a hypothetical region that has decoupled from
cosmic expansion and contains gravitationally bound
matter
In classical physics and general chemistry, matter is any substance that has mass and takes up space by having volume. All everyday objects that can be touched are ultimately composed of atoms, which are made up of interacting subatomic part ...
.
A single dark matter halo may contain multiple
virialized clumps of dark matter bound together by gravity, known as subhalos.
Modern cosmological models, such as
ΛCDM, propose that dark matter halos and subhalos may contain galaxies.
The dark matter halo of a
galaxy envelops the
galactic disc and extends well beyond the edge of the visible galaxy. Thought to consist of
dark matter
Dark matter is a hypothetical form of matter thought to account for approximately 85% of the matter in the universe. Dark matter is called "dark" because it does not appear to interact with the electromagnetic field, which means it does not ...
, halos have not been observed directly. Their existence is inferred through observations of their effects on the motions of
stars and gas in galaxies and
gravitational lensing. Dark matter halos play a key role in current models of
galaxy formation and evolution. Theories that attempt to explain the nature of dark matter halos with varying degrees of success include
cold dark matter (CDM),
warm dark matter
Warm dark matter (WDM) is a hypothesized form of dark matter that has properties intermediate between those of hot dark matter and cold dark matter, causing structure formation to occur bottom-up from above their free-streaming scale, and top-down ...
, and
massive compact halo object
A massive astrophysical compact halo object (MACHO) is a kind of astronomical body that might explain the apparent presence of dark matter in galaxy halos. A MACHO is a body that emits little or no radiation and drifts through interstellar space ...
s (MACHOs).
Rotation curves as evidence of a dark matter halo
The presence of dark matter (DM) in the halo is inferred from its
gravitational
In physics, gravity () is a fundamental interaction which causes mutual attraction between all things with mass or energy. Gravity is, by far, the weakest of the four fundamental interactions, approximately 1038 times weaker than the str ...
effect on a spiral galaxy's
rotation curve
The rotation curve of a disc galaxy (also called a velocity curve) is a plot of the orbital speeds of visible stars or gas in that galaxy versus their radial distance from that galaxy's centre. It is typically rendered graphically as a plot, an ...
. Without large amounts of mass throughout the (roughly spherical) halo, the rotational velocity of the galaxy would decrease at large distances from the galactic center, just as the
orbital speeds of the outer planets decrease with distance from the Sun. However,
observations of spiral galaxies, particularly
radio observations of
line emission from neutral atomic hydrogen (known, in astronomical parlance, as 21 cm
Hydrogen line, H one, and H I line), show that the rotation curve of most spiral galaxies flattens out, meaning that rotational velocities do not decrease with distance from the galactic center. The absence of any visible
matter
In classical physics and general chemistry, matter is any substance that has mass and takes up space by having volume. All everyday objects that can be touched are ultimately composed of atoms, which are made up of interacting subatomic part ...
to account for these observations implies either that unobserved (dark) matter, first proposed by
Ken Freeman in 1970, exist, or that the theory of motion under gravity (
general relativity
General relativity, also known as the general theory of relativity and Einstein's theory of gravity, is the geometric theory of gravitation published by Albert Einstein in 1915 and is the current description of gravitation in modern physics ...
) is incomplete. Freeman noticed that the expected decline in velocity was not present in NGC 300 nor M33, and considered an undetected mass to explain it. The DM Hypothesis has been reinforced by several studies.
Formation and structure of dark matter halos
The formation of dark matter halos is believed to have played a major role in the early formation of galaxies. During initial galactic formation, the temperature of the baryonic matter should have still been much too high for it to form gravitationally self-bound objects, thus requiring the prior formation of dark matter structure to add additional gravitational interactions. The current hypothesis for this is based on cold dark matter (CDM) and its formation into structure early in the universe.
The hypothesis for CDM structure formation begins with density perturbations in the Universe that grow linearly until they reach a critical density, after which they would stop expanding and collapse to form gravitationally bound dark matter halos. These halos would continue to grow in mass (and size), either through accretion of material from their immediate neighborhood, or by
merging with other halos. Numerical simulations of CDM structure formation have been found to proceed as follows: A small volume with small perturbations initially expands with the expansion of the Universe. As time proceeds, small-scale perturbations grow and collapse to form small halos. At a later stage, these small halos merge to form a single virialized dark matter halo with an ellipsoidal shape, which reveals some substructure in the form of dark matter sub-halos.
The use of CDM overcomes issues associated with the normal baryonic matter because it removes most of the thermal and radiative pressures that were preventing the collapse of the baryonic matter. The fact that the dark matter is cold compared to the baryonic matter allows the DM to form these initial, gravitationally bound clumps. Once these subhalos formed, their gravitational interaction with baryonic matter is enough to overcome the thermal energy, and allow it to collapse into the first stars and galaxies. Simulations of this early galaxy formation matches the structure observed by galactic surveys as well as observation of the Cosmic Microwave Background.
Density profiles
A commonly used model for galactic dark matter halos is the pseudo-isothermal halo:
:
where
denotes the finite central density and
the core radius. This provides a good fit to most rotation curve data. However, it cannot be a complete description, as the enclosed mass fails to converge to a finite value as the radius tends to infinity. The isothermal model is, at best, an approximation. Many effects may cause deviations from the profile predicted by this simple model. For example, (i) collapse may never reach an equilibrium state in the outer region of a dark matter halo, (ii) non-radial motion may be important, and (iii) mergers associated with the (hierarchical) formation of a halo may render the spherical-collapse model invalid.
Numerical simulations of structure formation in an expanding universe lead to the empirical
NFW (Navarro-Frenk-White) profile:
:
where
is a scale radius,
is a characteristic (dimensionless) density, and
=
is the critical density for closure. The NFW profile is called 'universal' because it works for a large variety of halo masses, spanning four orders of magnitude, from individual galaxies to the halos of galaxy clusters. This profile has a finite gravitational potential even though the integrated mass still diverges logarithmically. It has become conventional to refer to the mass of a halo at a fiducial point that encloses an overdensity 200 times greater than the critical density of the universe, though mathematically the profile extends beyond this notational point. It was later deduced that the density profile depends on the environment, with the NFW appropriate only for isolated halos. NFW halos generally provide a worse description of galaxy data than does the pseudo-isothermal profile, leading to the
cuspy halo problem.
Higher resolution computer simulations are better described by the
Einasto profile:
: