Dark Matter

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DARK MATTER

Despite the enormous amount of progress made during the last century in physics and astronomy, scientists still cannot identify over 90 percent of the overall composition of the universe. Indeed, what has been learned is that the visible matter forming planets, stars, and galaxies only makes up a relatively small fraction of the total mass-energy of the universe. In the past, this unseen component was called the missing matter or missing mass of the universe. However, many different astronomical observations have confirmed its presence. Most of the mass of the universe is not missing, it is just dark, and what it is remains unknown.

Observational Evidence

The presence of dark matter was suggested by Fritz Zwicky in 1933. Typical velocities v of galaxies in a cluster of galaxies can be related to the total mass M and size R of the system through the simple Newtonian relation

?² ?G_NM/R

where G_N is Newton's constant. Measurements of velocities of galaxies in the Coma and Virgo clusters of galaxies indicated that there was significantly more matter than could be accounted for by the individual light-producing galaxies. This discrepancy is often accounted for by computing a mass-to-light ratio. A mass-to-light ratio is the mass of the system divided by the luminosity of the system and is usually expressed in solar units (i.e., it is compared to the mass and luminosity of the Sun). In the solar neighborhood, the mass-to-light ratio is about 2 M_?/L_? The solar neighborhood, however, is not typical of either the galaxy or the universe as a whole. In the bright central parts of galaxies, the ratio is (10–20) h₀. For the Coma cluster, this ratio is about 400 h₀, indicating that there is significantly more matter on the large scales associated with clusters of galaxies than in galaxies themselves. Both of the mass-to-light ratios above carry an uncertainty as a result of the very large distance to other galaxies or clusters. The uncertainty is qualified by the Hubble parameter H (see discussion below). The quantity h₀ is a scaled value of the present Hubble parameter and is given by h₀ = H₀/100 km Mpc^-1 s^-1. The present value of the scaled parameter is h₀ = 0.71 ± 0.07.

There are several modern astronomical techniques for establishing the existence of dark matter. The same Newtonian relation expressed above can be applied to measurements of the rotation velocities of the disks of spiral galaxies. Rotation velocities can be determined from the Doppler shifts of 21-cm hydrogen lines in the far outer reaches of spiral galaxies. At radii far beyond the point where most of the light is concentrated, one would expect that the velocities diminish as ?? 1/?R Instead, one finds the following surprising result: the velocities remain constant at large radii, producing what are called flat rotation curves and indicating that the mass of galaxies continues to increase as M ? R . This provides direct evidence for the presence of dark matter.

Additional evidence is available from X-ray observations of elliptical galaxies and clusters of galaxies. The X rays are emitted by the hot hydrogen gas surrounding these systems. The atoms in a gas, with a temperature of order 10⁶ K, have velocities that would enable them to escape the system unless there was a sufficient amount of dark matter to gravitationally bind the gas to the system.

It is also possible to infer the presence of dark matter in clusters of galaxies through gravitational lensing. The large mass associated with clusters causes the trajectories of light from background galaxies to be bent. The degree of bending is related to the amount of dark matter in the cluster.

There is also a strong theoretical argument for dark matter arising from the theory of structure formation. Galaxies and clusters of galaxies are thought to have grown from primordial density fluctuations produced in the very early universe. These fluctuations begin to grow as a result of gravitational collapse that occurs when the universe becomes dominated by nonrelativistic matter. Without dark matter and, more importantly, without nonbaryonic dark matter (see below), there is not enough time for these perturbations to grow into the structures observed today.

The Density of Matter in the Universe

It is often convenient to relate the overall density of matter in the universe to a critical density ?_c that is given in terms of Newton's constant and the Hubble parameter H : The ratio ? = ?/?_c is called the cosmological density parameter and is related to the overall spatial geometry of the universe. If ? > 1, the universe is closed and finite in spatial extent; if ? < 1, the universe is open and infinite; and if ? = 1, the universe is spatially flat and infinite. The universe is observed to be expanding so that the distances to far-away objects are increasing. Furthermore, the expansion is uniform so that the increase in distance can be related to a common scale factor for the universe a (t ). The Hubble parameter expresses the rate of change of the scale factor and determines the velocities of distant objects: where a? is the time rate of change of a, v is the velocity of a distant object, and d is the distance to that object. This is known as Hubble's law.

Tghe density parameter may have several different types of contributions. Ordinary matter made up of neutrons and protons is referred to as baryonic matter. (Baryons are a class of particles composed of three quarks or three antiquarks. Neutrons and protons are the lightest-and longest-lived baryons.) Other forms of matter that may contribute to ? can be collectively called nonbaryonic dark matter. The energy densities of both baryonic and nonbaryonic matter scale with the expansion of the universe in such a way that the density decreases inversely with the volume expansion, ?_m ? a_-3.

Baryonic Dark Matter

The total amount of baryonic matter can be determined from the observations of the light element abundances D, ³He, ⁴He, and ⁷Li. These elements were produced within the first 3 minutes after the Big Bang. In particular, the abundance of deuterium is particularly sensitive to the baryon density. The value of the baryon density ?_b is commonly expressed relative to the critical density. Therefore, one can define ?_b = ?_b/?_c. A firm upper limit to the quantity is 0.03. By the same token, Big Bang nucleosynthesis also requires that The detailed spectrum of microwave background fluctuations can also determine the baryon density. Current estimates yield However, the observed baryon density is much smaller. By adding up the densities of baryons in stars (both living and dead) as well as the observed gas, it has only been possible to find a fraction There is still the possibility that baryons contribute to some of the dark matter, particularly on the scale of galaxies. In general, baryons make poor dark matter candidates since they are typically associated with luminous objects such as stars or X-ray-producing gas. However, it is possible that dark baryons reside in the dead remnants of stars, such as black holes, neutron stars, or white dwarfs. Gravitational microlensing has been useful in limiting the amount of dark matter in these forms.

Particle Dark Matter

The data so far indicate that most of the dark matter in the universe is nonbaryonic. Various techniques, which include the study of the dynamics of galaxies and clusters, show that the total density of matter is roughly ?matter ? 0.3 - 0.5. The difference between this density and the baryon density yields the nonbaryonic component to the density of the universe. Fortunately, there are many potential candidates for dark matter in the well-studied models of particle physics.

From the standpoint of the Standard Model of particle physics, the simplest candidate for dark matter would be a neutrino. Originally, the theory of electroweak interactions was constructed so that the neutrino was massless. Recent data on solar neutrinos, and neutrinos produced by cosmic-ray collisions in the atmosphere, strongly indicate that neutrinos of different types oscillate and thereby have mass. As such, they could, in principle, contribute to the dark matter.

Even a small neutrino mass can make a large contribution to the overall density of matter. If m_? is the mass of neutrino, then so long as m_? < 1 MeV, its contribution to the density parameter is = m_?/(94 eV). However, a neutrino-dominated universe is strongly disfavored by the observed large-scale structure of the universe. Light neutrinos remain relativistic until relatively late times. By the time they come to dominate the mass density of the universe, they have traveled across immense distances, erasing the possibility of the growth of structures on smaller scales. Thus, a neutrino-dominated universe inevitably produces too much large-scale structure. Furthermore, it appears that the oscillation data require neutrino masses that are too small to make a dominating contribution to the overall mass density.

In contrast to light neutrinos, which are typically labeled hot dark matter because of their relativistic velocities, an ideal dark matter candidate should be almost at rest with respect to the cosmic expansion. These cold dark matter candidates lead to the formation of smaller structures (galaxy size and smaller) first and fit the observations reasonably well.

Beyond the Standard Model of particle physics there are many particle candidates for cold dark matter. One of the best-studied candidates is found in an extension of the Standard Model based on supersymmetry. Supersymmetry is a symmetry that relates particles of different spin (an internal quantum number assigned to all particles). The supersymmetric Standard Model contains many new particles and predicts that one of these will be stable. This new stable particle is normally a neutralino (it is the supersymmetric partner of the photon and Z gauge boson) and may have a mass of order 100 times the mass of the proton. Another potential candidate is called the axion, and it arises in a theoretical solution to what is known in particle physics as the strong CP problem. Fortunately (or not), many other particle candidates are found in theories extending the Standard Model.

Dark Energy

It is also possible that there is a component of ? for which the energy density is constant (with respect to the expansion of the universe). This is called the cosmological constant ?. It was originally introduced by Albert Einstein in order to cancel the expansion he found in his cosmological models. When the expansion of the universe was observed, he described the introduction of the cosmological constant as his biggest blunder. Nevertheless, its potential contribution must be considered.

The total density parameter has been established to be very close to unity by microwave background experiments, which indicate that ?total = 1.03 ± 0.06. As mentioned above, it appears that the contribution of ? due to matter (both baryonic and nonbaryonic) is approximately 0.3–0.5. The difference between ?total and ?matter has been called dark energy. The existence of dark energy has also been suggested by recent supernovae observations, which detect that the universe may be accelerating (i.e., its expansion rate is increasing). The cosmological constant could play the role of dark energy as could any smoothly distributed energy associated with the vacuum.