
In modern models of
physical cosmology
Physical cosmology is a branch of cosmology concerned with the study of cosmological models. A cosmological model, or simply cosmology, provides a description of the largest-scale structures and dynamics of the universe and allows study of fu ...
, 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 pa ...
.
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
The Lambda-CDM, Lambda cold dark matter, or ΛCDM model is a mathematical model of the Big Bang theory with three major components:
# a cosmological constant, denoted by lambda (Λ), associated with dark energy;
# the postulated cold dark ma ...
, propose that dark matter halos and subhalos may contain galaxies.
The dark matter halo of a
galaxy
A galaxy is a Physical system, system of stars, stellar remnants, interstellar medium, interstellar gas, cosmic dust, dust, and dark matter bound together by gravity. The word is derived from the Ancient Greek, Greek ' (), literally 'milky', ...
envelops the
galactic disc
A galactic disc (or galactic disk) is a component of disc galaxies, such as spiral galaxies like the Milky Way and lenticular galaxies. Galactic discs consist of a stellar component (composed of most of the galaxy's stars) and a gaseous compone ...
and extends well beyond the edge of the visible galaxy. Thought to consist of
dark matter
In astronomy, dark matter is an invisible and hypothetical form of matter that does not interact with light or other electromagnetic radiation. Dark matter is implied by gravity, gravitational effects that cannot be explained by general relat ...
, halos have not been observed directly. Their existence is inferred through observations of their effects on the motions of
stars
A star is a luminous spheroid of plasma held together by self-gravity. The nearest star to Earth is the Sun. Many other stars are visible to the naked eye at night; their immense distances from Earth make them appear as fixed points of ...
and gas in galaxies and
gravitational lensing
A gravitational lens is matter, such as a galaxy cluster, cluster of galaxies or a point particle, that bends light from a distant source as it travels toward an observer. The amount of gravitational lensing is described by Albert Einstein's Ge ...
. 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, and
massive compact halo object
A MAssive Compact Halo Object (MACHO) is a kind of astronomy, astronomical body that might explain the apparent presence of dark matter in galactic halos. A MACHO is a body that emits little or no radiation and drifts through interstellar space un ...
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 effect on a spiral galaxy's
rotation curve. 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 speed
In gravitationally bound systems, the orbital speed of an astronomical body or object (e.g. planet, moon, artificial satellite, spacecraft, or star) is the speed at which it orbits around either the barycenter (the combined center of mass) or ...
s of the outer planets decrease with distance from the Sun. However,
observations
Observation in the natural sciences is an act or instance of noticing or perceiving and the acquisition of information from a primary source. In living beings, observation employs the senses. In science, observation can also involve the perceptio ...
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 pa ...
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 as Einstein's theory of gravity, is the differential geometry, geometric theory of gravitation published by Albert Einstein in 1915 and is the current description of grav ...
) 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. The
spherical collapse framework analytically models the formation and growth of such 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
The cuspy halo problem (also known as the core-cusp problem) is a discrepancy between the inferred dark matter density profiles of low-mass galaxies and the density profiles predicted by cosmological N-body simulations. Nearly all simulations form ...
.
Higher resolution computer simulations are better described by the
Einasto profile:
: