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Dispersion measure (DM) is a measure of the dispersion of a signal, i.e., the phenomenon of the duration of a short signal growing longer as it travels. Electromagnetic radiation is slowed by the material it is passing through, generally, the longer the wavelength, the more it is slowed, so the shorter wavelengths of the signal are received earlier than longer wavelengths that were sent at the same time, and dispersion measure is a measure of how much delay results from additional wavelength. The concept is used in radio astronomy for transients consisting of very short pulses, such as those of pulsars (i.e., the pulsar dispersion measure) and more recently, it is used for fast radio bursts (FRBs). The dispersion measure is scaled to match a column density of free electrons that would cause the dispersion, using conventional units tailored to astronomy: pc cm-3.
t2-t1
DM = ———————————————
kDM (ν2-2-ν1-2)
Used with a typical interstellar medium (ISM) electron density, the dispersion measure yields an estimate of the distance to the source. Such an estimate that far exceeds the span of the Milky Way is evidence that a source is extragalactic. In such cases, a model of the sources of dispersion can be attempted:
DMobserved = DMMW + DMIGM + DMhost galaxy
Observing the dispersion and measuring it requires a clearly-defined transient in the radio signal and radio pulses are very useful for offering data regarding distances and electron density.
A dispersion correction is a correction (using the DM) to the timing of a received EMR transient (e.g., pulsar pulse) due to the affects of this dispersion. This a necessary part of the analysis of pulsar-timing-array data.
Dispersion measure is effectively an alternate quantification of Thomson optical depth, calibrated to match the electron column density along the line of sight. Thus dispersion measures of FRBs, which travel cosmological distances, offer a means of testing and refinement of cosmological models.