Velocity dispersion

Velocity dispersion (σ) quantifies how much the velocities of individual members within an astronomical system—such as star clusters, galaxies, or galaxy clusters—vary around the group’s average velocity. Astronomers estimate this value by measuring the radial velocities of many members using spectroscopy, which reveals the Doppler broadening of spectral lines. The more radial velocities collected, the more precise the dispersion measurement becomes. A central velocity dispersion specifically refers to the σ measured in the inner regions of an extended object like a galaxy or cluster.

The dispersion is not merely a kinematic statistic; it is a fundamental tool for determining mass via the virial theorem. The relationship between velocity dispersion and matter (or its emitted radiation) manifests in several key empirical correlations. For supermassive black holes, the M–σ relation links the black hole’s mass to the dispersion of surrounding material. For example, the Milky Way’s supermassive black hole has an associated σ of about 100 km/s, which approximates the black hole’s mass. The Andromeda Galaxy hosts a black hole roughly ten times larger, with a correspondingly higher dispersion. For elliptical galaxies, the Faber–Jackson relation applies, while spiral galaxies follow the Tully–Fisher relation.

Velocity dispersion values vary dramatically with scale. Rich galaxy clusters, like the Coma Cluster, exhibit much larger dispersions than poor groups such as the Local Group. Within the Coma Cluster, dwarf elliptical galaxies have their own internal stellar dispersions, typically lower than those of normal elliptical galaxies. In spiral galaxies, the velocity dispersion of population I stars increases gradually due to dynamical friction—random momentum exchanges between stars and massive interstellar gas or dust clouds. Face-on spiral galaxies show a central dispersion that is slightly lower than when viewed edge-on.