Velocity dispersion
Statistical spread of velocities in astronomical groups.
Velocity dispersion (σ) is the statistical dispersion of velocities about the mean velocity for a group of astronomical objects, such as open clusters, globular clusters, galaxies, galaxy clusters, or superclusters. It is estimated by measuring radial velocities through astronomical spectroscopy and is used to derive a group's mass via the virial theorem.
- field
- Astronomy
- known_for
- Measuring mass of astronomical objects via velocity spread
- related_concepts
- M–σ relation, Faber–Jackson relation, Tully–Fisher relation
Lore & Background
Velocity dispersion is determined by measuring the Doppler width of spectral lines from a collection of objects; more radial velocity measurements yield a more accurate 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 takes several forms: the M–σ relation for material orbiting 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 is about 100 km/s, providing an approximation of its mass.
Reader's Guide
Velocity dispersion is a key observable in astrophysics, enabling mass estimates of galaxies, clusters, and supermassive black holes. Groups and clusters of galaxies have more disparate velocity dispersions than smaller objects: the Local Group has σ = 61±8 km/s, while rich clusters like the Coma Cluster have σ ≈ 1,000 km/s. Dwarf elliptical galaxies within Coma have internal σ ≲ 80 km/s, while normal elliptical galaxies average σ ≈ 200 km/s. For spiral galaxies, the increase in velocity dispersion in population I stars results from dynamical friction between stars and large interstellar clouds. Face-on spiral galaxies have central σ ≲ 90 km/s; slightly more if viewed edge-on. These measurements underpin fundamental scaling relations that link galaxy properties to their dark matter halos and black hole masses.
Did You Know?
- Velocity dispersion is estimated by measuring the Doppler width of spectral lines.
- The Milky Way's supermassive black hole has a velocity dispersion of about 100 km/s.
- The Coma Cluster has a velocity dispersion of about 1,000 km/s.
- Face-on spiral galaxies have a central velocity dispersion of less than or equal to 90 km/s.
Frequently Asked Questions
What is Velocity dispersion?
It is the statistical spread of individual velocities around the mean motion of a group of astronomical bodies. Rather than describing one speed, it captures how scattered the motions are within a collection like a cluster or galaxy.
How do astronomers actually measure Velocity dispersion?
They use spectroscopy to obtain the radial velocity of each member in a group, then compute the standard deviation of those values about the mean. That resulting spread is the quantity denoted σ.
Why is Velocity dispersion important in astronomy?
It provides a practical route to estimating the total mass of a system by feeding the observed velocity spread into the virial theorem. Without this measurement, pinning down the mass of vast structures like galaxy clusters would be far more difficult.
What other concepts is Velocity dispersion connected to?
It anchors several well-known scaling relations, including the M–σ relation, the Faber–Jackson relation, and the Tully–Fisher relation. These tie the velocity spread to other observable properties such as luminosity or rotational speed.
What kinds of objects does Velocity dispersion apply to?
It is used across a broad hierarchy of groupings, from open and globular clusters through individual galaxies, galaxy clusters, and even superclusters. Essentially any gravitationally associated collection of objects can have a velocity dispersion measured.
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