Galaxy groups and clusters

The galaxies of HCG 87, about four hundred million light-years distant. The large edge-on spiral, the fuzzy elliptical galaxy immediately to its right, and the spiral near the top of the image are members of the group, while the small spiral galaxy exactly in the middle is a more distant background galaxy. Credit: NASA/ESA.

Galaxy groups and clusters are the largest gravitationally-bound objects. They form the densest part of the large scale structure of the Universe. In models for the gravitational formation of structure with cold dark matter, the smallest structures collapse first and eventually build the largest structures, clusters of galaxies. Clusters are then formed relatively recently between 10 billion years ago and now. Groups and clusters may contain from ten to thousands of galaxies. The clusters themselves are often associated with larger groups called superclusters.

Groups of galaxies

Groups of galaxies are the smallest aggregates of galaxies. They typically contain fewer than 50 galaxies in a diameter of 1 to 2 megaparsecs (Mpc) (see 1 E22 m for distance comparisons). Their mass is approximately 10¹³ solar masses. The spread of velocities for the individual galaxies is about 150 km/s. However, this definition should be used as a guide only, as larger and more massive galaxy systems are sometimes classified as galaxy groups.

The group which contains our own galaxy, the Milky Way, is called the Local Group, and contains more than 40 galaxies.

Clusters of galaxies

Clusters are larger than groups, although there is no sharp dividing line between the two. When observed visually, clusters appear to be collections of galaxies held together by mutual gravitational attraction. However, their velocities are too large for them to remain gravitationally bound by their mutual attractions, implying the presence of either an additional invisible mass component, or an additional attractive force besides gravity. X-ray studies have revealed the presence of large amounts of intergalactic gas known as the intracluster medium. This gas is very hot, between 10⁷K and 10⁸K, and hence emits X-rays in the form of bremsstrahlung and atomic line emission. The total mass of the gas is greater than that of the galaxies by roughly a factor of two. However this is still not enough mass to keep the galaxies in the cluster. Since this gas is in approximate hydrostatic equilibrium with the overall cluster gravitational field, the total mass distribution can be determined. It turns out the total mass deduced from this measurement is approximately six times larger than the mass of the galaxies or the hot gas. The missing component is known as dark matter and its nature is unknown. In a typical cluster perhaps only 5% of the total mass is in the form of galaxies, maybe 10% in the form of hot X-ray emitting gas and the remainder is dark matter.

Clusters typically have the following properties.

• They contain 50 to 1000 galaxies, hot X-ray emitting gas and large amounts of dark matter
• The distribution of these three components is approximately the same in the cluster.
• They have total masses of 10¹⁴ to 10¹⁵ solar masses.
• They typically have a diameter from 2 to 10 Mpc (see 1 E23 m for distance comparisons).
• The spread of velocities for the individual galaxies is about 800-1000 km/s.

Notable galaxy clusters in the relatively nearby universe include the Virgo cluster, Hercules Cluster, and the Coma Cluster. A very large aggregation of galaxies known as the Great Attractor, dominated by the Norma cluster, is massive enough to affect the local expansion of the universe (Hubble flow).

In the last few decades, they are also found to be relevant sites of particle acceleration, a feature which has been discovered by the observing non-thermal diffuse radio emissions as Radio Halos and Radio Relics.

Note: clusters of galaxies should not be confused with star clusters such as galactic clusters and open clusters, which are structures within galaxies, as well as globular clusters, which typically orbit galaxies.

Superclusters

Main article: Supercluster

Groups, clusters and some isolated galaxies form even larger structures, the superclusters. At the very largest scales of the visible universe, matter is gathered into filaments and walls surrounding vast voids. This structure resembles a foam.

Observational methods

Clusters of galaxies have been found in surveys by a number of observational techniques and have been studied in detail using many methods:

• Optical or infrared: The individual galaxies of clusters can be studied through optical or infrared imaging and spectroscopy. Galaxy clusters are found by optical or infrared telescopes by searching for overdensities, and then confirmed by finding several galaxies at a similar redshift. Infrared searches are more useful for finding more distant (higher redshift) clusters.
• X-ray: The hot plasma emits X-rays which can be detected by X-ray telescopes. The cluster gas can be studied using both X-ray imaging and X-ray spectroscopy. Clusters are quite prominent in X-ray surveys and along with AGN are the brightest X-ray emitting extragalactic objects.
• Radio: A number of diffuse structures emitting at radio frequencies have been found in clusters. Groups of radio sources (which may include diffuse structures or AGN have been used as tracers of cluster location. At high redshift imaging around individual radio sources (in this case AGN) has been used to detect proto-clusters (clusters in the process of forming).
• Sunyaev-Zel'dovich effect: The hot electrons in the intracluster medium scatter radiation from the cosmic microwave background through inverse Compton scattering. This produces a "shadow" in the observed cosmic microwave background at some radio frequencies.
• Gravitational Lensing: Clusters of galaxies contain enough matter to distort the observed orientations of galaxies behind them. The observed distortions can be used to model the distribution of dark matter in the cluster.

Temperature and Density

Clusters of galaxies are the most recent and most massive objects to have arisen in the hierarchical structure formation of the Universe and the study of clusters tells one about the way galaxies form and evolve. Clusters have two important properties: their masses are large enough to retain any energetic gas ejected from member galaxies and the thermal energy of the gas within the cluster is observable within the X-Ray bandpass. The observed state of gas within a cluster is determined by a combination of shock heating during accretion, radiative cooling, and thermal feedback triggered by that cooling. The density, temperature, and substructure of the intracluster X-Ray gas therefore represents the entire thermal history of cluster formation. To better understand this thermal history one needs to study the entropy of the gas because entropy is the quantity most directly changed by increasing or decreasing the thermal energy of intracluster gas.

Entropy

In astrophysics, what is referred to as "entropy" is actually the adiabatic constant derived as follows.

Using the first law of thermodynamics for a quasi-static, infinitesimal process for a hydrostatic system

Failed to parse (Missing texvc executable; please see math/README to configure.): dQ = dU-dW.

For an ideal gas in this special case, the internal energy, U, is only a function of T; therefore the partial derivative of heat capacity with respect to T is identically the same as the full derivative, yielding through some manipulation

Failed to parse (Missing texvc executable; please see math/README to configure.): dQ = C_{V} dT+P dV.

Further manipulation using the differential version of the ideal gas law, the previous equation, and assuming constant pressure, one finds

Failed to parse (Missing texvc executable; please see math/README to configure.): dQ = C_{P} dT-V dP.

For an adiabatic process Failed to parse (Missing texvc executable; please see math/README to configure.): dQ=0

and recalling Failed to parse (Missing texvc executable; please see math/README to configure.): \gamma = \frac{C_{P}}{C_{V}}

, one finds

Failed to parse (Missing texvc executable; please see math/README to configure.): \frac{V dP = C_{P} dT}{P dV = -C_{V} dT}

Failed to parse (Missing texvc executable; please see math/README to configure.): \frac{dP}{P} = -\frac{dV}{V}\gamma

One can solve this simple differential equation to find

Failed to parse (Missing texvc executable; please see math/README to configure.): PV^{\gamma} = constant = K

This equation is known as an expression for the adiabatic constant, K, also called the adiabat. From the ideal gas equation one also knows

Failed to parse (Missing texvc executable; please see math/README to configure.): P=\frac{\rho k_{B}T}{\mu m_{H}},

where Failed to parse (Missing texvc executable; please see math/README to configure.): k_{B}

is Boltzmann's constant.

Substituting this into the above equation along with Failed to parse (Missing texvc executable; please see math/README to configure.): V=[grams]/\rho

and Failed to parse (Missing texvc executable; please see math/README to configure.): \gamma = 5/3
for an ideal monoatomic gas one finds

Failed to parse (Missing texvc executable; please see math/README to configure.): K = \frac{k_{B}T}{\mu m_{H} \rho^{2/3}},

where Failed to parse (Missing texvc executable; please see math/README to configure.): \mu

is the mean molecular weight of the gas or plasma; and Failed to parse (Missing texvc executable; please see math/README to configure.): m_{H}
is the mass of the Hydrogen atom, which is extremely close to the mass of the proton, Failed to parse (Missing texvc executable; please see math/README to configure.): m_{p}

, the quantity more often used in astrophysical theory of galaxy clusters. This is what astrophysicists refer to as "entropy" and has units of [keV cm²]. This quantity relates to the thermodynamic entropy as

Failed to parse (Missing texvc executable; please see math/README to configure.): S = k_{B}\, ln \Omega + S_{0}

where Failed to parse (Missing texvc executable; please see math/README to configure.): \Omega , the density of states in statistical theory, takes on the value of K as defined above.

See also

• Fossil group
• List of galaxy clusters
• Large-scale structure of the cosmos
• Timeline of galaxies, clusters of galaxies, and large-scale structure
• Intracluster mediumar:مجموعات وعناقيد المجرات

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