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.
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 σ = 61±8 km/s. But rich clusters of galaxies, such as the Coma Cluster, have a σ ≈ 1,000 km/s. The dwarf elliptical galaxies in Coma have their own, internal, velocity dispersion for their stars, which is a σ ≲ 80 km/s, typically. Normal elliptical galaxies, by comparison, have an average σ ≈ 200 km/s.
For spiral galaxies, the increase in velocity dispersion in population I stars is a gradual process which likely results from the random momentum exchanges, known as dynamical friction, between individual stars and large interstellar gas and dust clouds with masses ≳ 105 M☉. Face-on spiral galaxies have a central σ ≲ 90 km/s; slightly more if viewed edge-on.
- M–σ relation – for material circling supermassive black holes
- Faber–Jackson relation – for elliptical galaxies
- Tully–Fisher relation – for spiral galaxies
- Collins Dictionary of Astronomy, 2nd Ed.; Harper Collins Publishers; 2000; pp.444,449
- Gebhardt, Karl; Bender, Ralf; Bower, Gary; Dressler, Alan; Faber, S. M.; Filippenko, Alexei V.; Green, Richard; Grillmair, Carl; Ho, Luis C.; Kormendy, John; Lauer, Tod R.; Magorrian, John; Pinkney, Jason; Richstone, Douglas; Tremaine, Scott (June 2000). "A Relationship between Nuclear Black Hole Mass and Galaxy Velocity Dispersion" (PDF). The Astrophysical Journal. Chicago, Illinois, USA: The University of Chicago Press. 539 (1): L13–L16. arXiv: . Bibcode:2000ApJ...539L..13G. doi:10.1086/312840. Retrieved March 10, 2010.
- van den Bergh, Sidney (1999). "The local group of galaxies". The Astronomy and Astrophysics Review. Springer. 9 (3-4): 273–318 (1999). Bibcode:1999A&ARv...9..273V. doi:10.1007/s001590050019. Retrieved March 10, 2012.
- Struble, Mitchell F.; Rood, Herbert J. (November 1999). "A Compilation of Redshifts and Velocity Dispersions for ACO Clusters" (PDF). The Astrophysical Journal Supplement Series. Chicago, Illinois, USA: The University of Chicago Press. 125 (1): 35–71. Bibcode:1999ApJS..125...35S. doi:10.1086/313274. Retrieved March 10, 2012.
- Kourkchi, E.; Khosroshahi, H. G.; Carter, D.; Karick, A. M.; Mármol-Queraltó, E.; Chiboucas, K.; Tully, R. B.; Mobasher, B.; Guzmán, R.; Matković, A.; Gruel, N. (March 2012). "Dwarf galaxies in the Coma cluster – I. Velocity dispersion measurements". Monthly Notices of the Royal Astronomical Society. Wiley Online Library. 420 (4): 2819–2834. arXiv: . Bibcode:2012MNRAS.420.2819K. doi:10.1111/j.1365-2966.2011.19899.x.
- Forbes, Duncan A.; Ponman, Trevor J. (November 1999). "On the relationship between age and dynamics in elliptical galaxies" (PDF). Monthly Notices of the Royal Astronomical Society. 309 (3): 623–628. arXiv: . Bibcode:1999MNRAS.309..623F. doi:10.1046/j.1365-8711.1999.02868.x. Retrieved March 10, 2012.
- Spitzer, Lyman Jr.; Schwarzschild, Martin (July 1953). "The Possible Influence of Interstellar Clouds on Stellar Velocities. II." (PDF). Astrophysical Journal. 118: 106. Bibcode:1953ApJ...118..106S. doi:10.1086/145730. Retrieved March 10, 2012.
- Bershady, Matthew A.; Martinsson, Thomas P. K.; Verheijen, Marc A. W.; Westfall, Kyle B.; Andersen, David R.; Swaters, Rob A. (October 2011). "Galaxy Disks are Submaximal". The Astrophysical Journal Letters. 739 (2): L47. arXiv: . Bibcode:2011ApJ...739L..47B. doi:10.1088/2041-8205/739/2/L47.