Velocity dispersion

In astronomy, the velocity dispersion (σ) is the statistical dispersion of velocities about the mean velocity for a group of objects, such as an open cluster, globular cluster, galaxy, galaxy cluster, or supercluster. By measuring the radial velocities of its members, the velocity dispersion of a cluster can be estimated and used to derive the cluster's mass from the virial theorem. 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 (or the observed electromagnetic radiation 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, 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's supermassive black hole (SMBH) is about 75 km/s. The Andromeda Galaxy (Messier 31) hosts a SMBH about 10 times larger than our own, and has a σ ≈ 160 km/s.

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