quantity

dispersion measure

A measure of the column density of free electrons along a line of sight, causing signal delay.
13 related articles · 3 formulas

Description

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.

History

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.

How it works

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.

In practice

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.

Fun fact

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.

Concept graph →

Formulas

$$\mathrm{DM} = \int n_e \, dl$$
Integrated electron density along the line of sight.
What is in the formula
DMvariableDispersion measure — dispersion measure parsec per cubic centimetre
n_evariableElectron number density — electron number density per cubic metre
lvariablePath length along line of sight — length metre
∫operatorIntegration along the line of sight — integral
$$\mathrm{DM}_{\mathrm{obs}} = \mathrm{DM}_{\mathrm{MW\,ISM}} + \mathrm{DM}_{\mathrm{MW\,halo}} + \mathrm{DM}_{\mathrm{LSS}}(z) + \frac{\mathrm{DM}_{\mathrm{host}}}{1+z}$$
Total dispersion measure is sum of contributions from Milky Way, halo, large-scale structure, and redshifted host.
What is in the formula
DM_obsvariableObserved dispersion measure — dispersion measure parsec per cubic centimetre
DM_MW_ISMvariableDispersion measure from Milky Way interstellar medium — dispersion measure parsec per cubic centimetre
DM_MW_halovariableDispersion measure from Milky Way halo — dispersion measure parsec per cubic centimetre
DM_LSSvariableDispersion measure from large-scale structure — dispersion measure parsec per cubic centimetre
DM_hostvariableDispersion measure from host galaxy — dispersion measure parsec per cubic centimetre
zvariableRedshift of the source — redshift
$$\Delta t = \frac{e^2}{2\pi m_e c} \mathrm{DM} \left(\nu_1^{-2} - \nu_2^{-2}\right)$$
Time delay between frequencies due to plasma dispersion.
What is in the formula
ΔtvariableTime delay between two frequencies — time second
DMvariableDispersion measure (column density of free electrons) — dispersion measure parsec per cubic centimetre
ν_1variableHigher frequency of the signal — frequency hertz
ν_2variableLower frequency of the signal — frequency hertz
econstantThe fundamental charge carried by a single proton or electron. — elementary charge = 1.602176634e-19 coulomb
m_econstantThe rest mass of an electron. — electron mass = 9.1093837015e-31 kilogram
cconstantThe universal speed limit for massless particles and information. — speed of light = 299792458 metre per second

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