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A velocity dispersion (σ, sometimes shortened to dispersion) is the statistical dispersion of velocities of a group of objects. It is a quality of interest in open clusters, globular clusters, galaxies, galaxy clusters, and superclusters. Radial velocity can be determined by Doppler shift and the width of the affected spectral lines can determine dispersion across a group, which, with the virial theorem, can determine the group's mass. Statistical dispersion characterizes the "spread" of a distribution function and the standard deviation of a sample set is one measure of statistical dispersion.
Velocity dispersion can also be of interest regarding fluid and dust, e.g., within clouds and stars.
The term dispersion is also used in optics, spectroscopy, and radio astronomy (or any type of wave such as sound waves) to indicate some type of spreading out. Common cases disperse based upon wavelength or frequency (chromatic dispersion). One such case is a spreading out in time due to differences in wave-speed. Another is a spreading out in direction, such as by dispersers in refractive spectroscopes, which, in the case of a prism, is a consequence of the wave-speed dispersion. Such dispersion is also the source of chromatic aberration in lenses. Within electromagnetic radiation, low frequencies (long wavelengths) show the most dispersion and the largest variation by frequency, radio being most affected, e.g., a short pulse's arrival time varies by frequency, with the lowest frequency latest. This has a significant effect on the radio pulses from pulsars: the lower the frequency, the later the pulse reaches us. The dispersive delay is the time that some particular frequency of a signal has been delayed and a dispersion measure is a measure used regarding radio signal to quantify the effect.