Astronomers do not get a fast radio burst’s distance from its dispersion measure alone. The measure records how much free-electron material the radio pulse crossed, which offers a distance clue but varies with the gas along the route and near the source. The firmer method is to pinpoint the burst, identify its host galaxy, and measure the galaxy’s redshift.
What the radio pulse reveals
A fast radio burst (FRB) is a brief radio signal. As it travels through ionized gas, its lower-frequency radio waves arrive later than its higher-frequency waves. Astronomers measure that frequency-dependent delay and express it as a dispersion measure (DM): the integrated column of free electrons along the line of sight.
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More intervening electrons generally mean a larger DM, so the signal contains information about the material between Earth and the burst. But DM is not a direct distance reading. The electron density varies from one region to another, and gas close to the source can add to the signal. Different combinations of distance and electron distribution can therefore produce similar DMs. For an overview of FRB dispersion, see The Astronomy and Astrophysics Review’s 2019 review of fast radio bursts.
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How astronomers interpret dispersion measure
To estimate how much of an FRB’s DM comes from beyond the Milky Way, researchers first model the contribution of free electrons in our own galaxy. Common Galactic electron-density models include NE2001 and YMW16. The remaining DM is attributed chiefly to the intergalactic medium (IGM) and the source’s host galaxy, though the subtraction and the source environment are uncertain.
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A useful simplified accounting is:
DMexcess = DMIGM + DMhost / (1 + z)
Here, DMexcess is the observed DM after estimating and removing the Milky Way contribution; DMIGM is the intergalactic contribution; DMhost is the host-galaxy and local-source contribution; and z is redshift. The host term is reduced in the observed DM budget by the factor (1 + z). Because the Galactic estimate, intergalactic gas and host environment are not known exactly for an individual burst, the excess DM does not uniquely determine its distance. The components and their uncertainties are discussed in the 2019 FRB review.
When DM is used to estimate redshift
Astronomers can compare an FRB’s DM with the population-level relationship between dispersion measure and redshift, often called the Macquart relation. This can provide a statistical redshift estimate when no host-galaxy redshift is available. It is a model-based inference, not a confirmed measurement of that burst’s host redshift; variations in the gas along the sightline and near the source produce uncertainty. See the 2022 review of FRBs at the dawn of the 2020s and the 2024 analysis of modeling the DM–redshift relation.
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The firmer route: identify the host and measure its redshift
For a more direct distance estimate, astronomers need to localize the burst precisely enough to associate it with a galaxy. They can then observe that host’s spectrum and measure its redshift. Redshift provides the basis for estimating a cosmological distance; it is a different kind of evidence from the burst’s DM.
- Localize the burst: radio observations determine its position on the sky with enough precision to search for a possible host.
- Identify a plausible host: optical or infrared observations look for a galaxy at the burst position. A precise position helps, but does not guarantee that a host will be detected or securely associated.
- Measure the host’s redshift: spectroscopy of the identified galaxy provides the redshift used for a cosmological distance estimate.
FRB 121102 illustrates this chain: radio interferometric follow-up localized the repeating burst, astronomers identified a dwarf-galaxy host, and the host’s measured redshift was z = 0.193, as summarized in Astronomy & Geophysics in 2021. The host redshift is the distance-related measurement; localization made it possible to obtain it.
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Why localization does not always produce a distance
A burst can be localized accurately without a host galaxy being detected. FRB 20210912A had subarcsecond localization and deep optical and infrared follow-up, but the cited study did not identify a host. Its measured DM was 1233.696 ± 0.006 pc cm⁻³. That high DM supports a possible high-redshift interpretation under the Macquart relation, but does not establish a host redshift or a unique distance. These findings are reported in the 2023 study of FRB 20210912A.
By contrast, the European Southern Observatory reported a complex host-galaxy system for FRB 20220610A at redshift z = 1.016 ± 0.002. The burst’s redshift and dispersion were consistent with substantial intervening intergalactic material. This event shows how host spectroscopy can establish redshift while DM helps describe the gas encountered along the way; the value is specific to this burst, not a general property of FRBs. See the ESO’s 2023 release paper.
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What to take from an FRB distance claim
- DM alone: a measured free-electron column and a clue to distance, interpreted with Galactic, intergalactic and host contributions in mind.
- DM-based redshift: a statistical estimate from a population relation, not a confirmed redshift for an individual host.
- Host redshift: a measurement made from an identified host galaxy’s spectrum and the firmer route to a cosmological distance estimate.
- Precise localization: an accurate sky position, not by itself a host identification or redshift measurement.
Even when a host redshift is available, astronomers distinguish that redshift measurement from the cosmological distance inferred from it. For the broader question of how FRB dispersion measures can serve as distance indicators, see the 2019 Physical Review D study.
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