astronomy Astronomy () is a natural science that studies celestial objects and phenomena. It uses mathematics, physics, and chemistry in order to explain their origin and evolution. Objects of interest include planets, moons, stars, nebulae, g ...

, the velocity dispersion (''σ'') is the

statistical dispersion In statistics, dispersion (also called variability, scatter, or spread) is the extent to which a distribution is stretched or squeezed. Common examples of measures of statistical dispersion are the variance, standard deviation, and interquartile ...

of velocities about the

mean There are several kinds of mean in mathematics, especially in statistics. Each mean serves to summarize a given group of data, often to better understand the overall value ( magnitude and sign) of a given data set. For a data set, the '' ar ...

velocity for a group of

astronomical object An astronomical object, celestial object, stellar object or heavenly body is a naturally occurring physical entity, association, or structure that exists in the observable universe. In astronomy, the terms ''object'' and ''body'' are often u ...

s, such as an

open cluster An open cluster is a type of star cluster made of up to a few thousand stars that were formed from the same giant molecular cloud and have roughly the same age. More than 1,100 open clusters have been discovered within the Milky Way galaxy, an ...

globular cluster A globular cluster is a spheroidal conglomeration of stars. Globular clusters are bound together by gravity, with a higher concentration of stars towards their centers. They can contain anywhere from tens of thousands to many millions of membe ...

galaxy A galaxy is a system of stars, stellar remnants, interstellar gas, dust, dark matter, bound together by gravity. The word is derived from the Greek ' (), literally 'milky', a reference to the Milky Way galaxy that contains the Solar System ...

galaxy cluster A galaxy cluster, or a cluster of galaxies, is a structure that consists of anywhere from hundreds to thousands of galaxies that are bound together by gravity, with typical masses ranging from 1014 to 1015 solar masses. They are the second-lar ...

, or

supercluster A supercluster is a large group of smaller galaxy clusters or galaxy groups; they are among the largest known structures in the universe. The Milky Way is part of the Local Group galaxy group (which contains more than 54 galaxies), which in t ...

. By measuring the radial velocities of the group's members through

astronomical spectroscopy Astronomical spectroscopy is the study of astronomy using the techniques of spectroscopy to measure the spectrum of electromagnetic radiation, including visible light, ultraviolet, X-ray, infrared and radio waves that radiate from stars an ...

, the velocity dispersion of that group can be estimated and used to derive the group's mass from the

virial theorem In mechanics, the virial theorem provides a general equation that relates the average over time of the total kinetic energy of a stable system of discrete particles, bound by potential forces, with that of the total potential energy of the system. ...

.Collins Dictionary of Astronomy, 2nd Ed.; Harper Collins Publishers; 2000; pp. 444, 449 Radial velocity is found by measuring the Doppler width of

spectral lines A spectral line is a dark or bright line in an otherwise uniform and continuous spectrum, resulting from emission or absorption of light in a narrow frequency range, compared with the nearby frequencies. Spectral lines are often used to ident ...

of a collection of objects; the more radial velocities one measures, the more accurately one knows their dispersion. A ''central velocity dispersion'' refers to the σ of the interior regions of an extended object, such as a galaxy or cluster. The relationship between velocity dispersion and

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 ...

(or the observed

electromagnetic radiation In physics, electromagnetic radiation (EMR) consists of waves of the electromagnetic (EM) field, which propagate through space and carry momentum and electromagnetic radiant energy. It includes radio waves, microwaves, infrared, (visib ...

emitted by this matter) takes several forms in astronomy based on the object(s) being observed. For instance, the ''M''–''σ'' relation was found for material circling

black holes A black hole is a region of spacetime where gravity is so strong that nothing, including light or other electromagnetic waves, has enough energy to escape it. The theory of general relativity predicts that a sufficiently compact mass can def ...

, the

Faber–Jackson relation The Faber–Jackson relation provided the first empirical power-law relation between the luminosity L and the central stellar velocity dispersion \sigma of elliptical galaxy, and was presented by the astronomers Sandra M. Faber and Robert Earl ...

for elliptical galaxies, and the

Tully–Fisher relation In astronomy, the Tully–Fisher relation (TFR) is an empirical relationship between the mass or intrinsic luminosity of a spiral galaxy and its asymptotic rotation velocity or emission line width. It was first published in 1977 by astronomers ...

for spiral galaxies. For example, the ''σ'' found for objects about the

Milky Way The Milky Way is the galaxy that includes our Solar System, with the name describing the galaxy's appearance from Earth: a hazy band of light seen in the night sky formed from stars that cannot be individually distinguished by the naked eye. ...

supermassive black hole A supermassive black hole (SMBH or sometimes SBH) is the largest type of black hole, with its mass being on the order of hundreds of thousands, or millions to billions of times the mass of the Sun (). Black holes are a class of astronomical ob ...

(SMBH) is about 100 km/s. The

Andromeda Galaxy The Andromeda Galaxy (IPA: ), also known as Messier 31, M31, or NGC 224 and originally the Andromeda Nebula, is a barred spiral galaxy with the diameter of about approximately from Earth and the nearest large galaxy to the Milky Way. The gal ...

( Messier 31) hosts a SMBH about 10 times larger than our own, and has a . Groups and clusters of galaxies have a wider range of velocity dispersions than smaller objects. For example, our own poor group, the Local Group, has a . But ''rich'' clusters of galaxies, such as the

Coma Cluster The Coma Cluster (Abell 1656) is a large cluster of galaxies that contains over 1,000 identified galaxies. Along with the Leo Cluster (Abell 1367), it is one of the two major clusters comprising the Coma Supercluster. It is located in and tak ...

, have a . The dwarf elliptical galaxies within Coma have their own internal velocity dispersion for their stars, which is a , typically. Normal elliptical galaxies, by comparison, have an average . For spiral galaxies, the increase in velocity dispersion in

population I stars During 1944, Walter Baade categorized groups of stars within the Milky Way into stellar populations. In the abstract of the article by Baade, he recognizes that Jan Oort originally conceived this type of classification in 1926: Baade noticed th ...

is a gradual process which likely results from the random

momentum In Newtonian mechanics, momentum (more specifically linear momentum or translational momentum) is the product of the mass and velocity of an object. It is a vector quantity, possessing a magnitude and a direction. If is an object's mass ...

exchanges, known as dynamical friction, between individual stars and large

interstellar media In astronomy, the interstellar medium is the matter and radiation that exist in the space between the star systems in a galaxy. This matter includes gas in ionic, atomic, and molecular form, as well as dust and cosmic rays. It fills interstel ...

(gas and dust clouds) with masses greater than . Face-on spiral galaxies have a central ; slightly more if viewed edge-on.

References

{{reflist Celestial mechanics Galactic astronomy Extragalactic astronomy Equations of astronomy

See also

References