A measure of the column density of free electrons along a line of sight, causing signal delay.Dispersion measure (DM) is a quantity in astrophysics that measures the total number of free electrons along a line of sight, integrated from the observer to a distant source. It is defined as the integral of the electron number density over the path length. Because free electrons slow down radio waves, a higher DM causes a frequency-dependent delay in the arrival time of a signal, with lower frequencies arriving later than higher ones.
The concept of dispersion measure was introduced in the mid-20th century with the discovery of pulsars in 1967. Astronomers quickly realized that the observed frequency-dependent delays in pulsar signals could be used to infer the electron content of the interstellar medium.
When a radio pulse travels through ionized gas, the group velocity of the wave depends on frequency: lower frequencies are delayed more. By measuring the arrival times of a pulse at multiple frequencies, astronomers can calculate the DM. This delay is proportional to the DM divided by the square of the frequency, allowing a direct estimate of the electron column density along the line of sight.
Dispersion measure is used to study the interstellar and intergalactic medium, to estimate distances to pulsars and fast radio bursts, and to probe the electron density distribution in the Milky Way and beyond.
The dispersion measure of a fast radio burst can be used to estimate the distance to the source, with a typical value of a few hundred pc/cm³ indicating a source at cosmological distances.
| DM | variable | Dispersion measure — dispersion measure parsec per cubic centimetre |
| n_e | variable | Electron number density — electron number density per cubic metre |
| l | variable | Path length along line of sight — length metre |
| ∫ | operator | Integration along the line of sight — integral |
| DM_obs | variable | Observed dispersion measure — dispersion measure parsec per cubic centimetre |
| DM_MW_ISM | variable | Dispersion measure from Milky Way interstellar medium — dispersion measure parsec per cubic centimetre |
| DM_MW_halo | variable | Dispersion measure from Milky Way halo — dispersion measure parsec per cubic centimetre |
| DM_LSS | variable | Dispersion measure from large-scale structure — dispersion measure parsec per cubic centimetre |
| DM_host | variable | Dispersion measure from host galaxy — dispersion measure parsec per cubic centimetre |
| z | variable | Redshift of the source — redshift |
| Δt | variable | Time delay between two frequencies — time second |
| DM | variable | Dispersion measure (column density of free electrons) — dispersion measure parsec per cubic centimetre |
| ν_1 | variable | Higher frequency of the signal — frequency hertz |
| ν_2 | variable | Lower frequency of the signal — frequency hertz |
| e | constant | The fundamental charge carried by a single proton or electron. — elementary charge = 1.602176634e-19 coulomb |
| m_e | constant | The rest mass of an electron. — electron mass = 9.1093837015e-31 kilogram |
| c | constant | The universal speed limit for massless particles and information. — speed of light = 299792458 metre per second |





