astronomy Astronomy is a natural science that studies celestial objects and the phenomena that occur in the cosmos. It uses mathematics, physics, and chemistry in order to explain their origin and their overall evolution. Objects of interest includ ...

, the velocity dispersion (''σ'') is the statistical dispersion of velocities about the

mean A mean is a quantity representing the "center" of a collection of numbers and is intermediate to the extreme values of the set of numbers. There are several kinds of means (or "measures of central tendency") in mathematics, especially in statist ...

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 within the observable universe. In astronomy, the terms ''object'' and ''body'' are of ...

s, such as an

open cluster An open cluster is a type of star cluster made of tens 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, and ...

globular cluster A globular cluster is a spheroidal conglomeration of stars that is bound together by gravity, with a higher concentration of stars towards its center. It can contain anywhere from tens of thousands to many millions of member stars, all orbiting ...

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', ...

, galaxy cluster, or supercluster. By measuring the radial velocities of the group's members through astronomical spectroscopy, the velocity dispersion of that group can be estimated and used to derive the group's mass from the virial theorem.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 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 pa ...

(or the observed

electromagnetic radiation In physics, electromagnetic radiation (EMR) is a self-propagating wave of the electromagnetic field that carries momentum and radiant energy through space. It encompasses a broad spectrum, classified by frequency or its inverse, wavelength ...

emitted by this matter) takes several forms – specific correlations – in astronomy based on the object(s) being observed. Notably, the ''M''–''σ'' relation applies for material orbiting many black holes, the Faber–Jackson relation for elliptical galaxies, and the Tully–Fisher relation for spiral galaxies. For example, the ''σ'' found for objects about the

Milky Way The Milky Way or Milky Way Galaxy is the galaxy that includes the Solar System, with the name describing the #Appearance, galaxy's appearance from Earth: a hazy band of light seen in the night sky formed from stars in other arms of the galax ...

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 ...

(SMBH) is about 100 km/s, which provides an approximation of the mass of this SMBH. The Andromeda Galaxy ( Messier 31) hosts a SMBH about 10 times larger than our own, and has a . Groups and clusters of galaxies have more disparate (contrasting in degree) velocity dispersions than smaller objects. For example, while our own poor group, the Local Group, has a , ''rich'' clusters of galaxies, such as the Coma Cluster, have a . The dwarf elliptical galaxies within Coma, as with all galaxies, 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 is a gradual process which likely results from the near-random incidence of

momentum In Newtonian mechanics, momentum (: momenta or momentums; 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. ...

exchanges, specifically dynamical friction, between individual stars and large interstellar media (gas and dust clouds) with masses greater than . Face-on spiral galaxies have a central ; slightly more if viewed edge-on.

References

{{reflist Concepts in astrophysics Celestial mechanics Equations of astronomy Extragalactic astronomy Galactic astronomy

See also

References