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Astronomers estimate a fast radio burst’s distance by combining its radio dispersion with information about the galaxy it came from. The pulse’s dispersion measure (DM) reveals the total column of free electrons along the line of sight, which provides a useful but uncertain distance clue. When researchers can pinpoint the burst, identify its host galaxy, and measure that galaxy’s redshift, they can make a firmer cosmological distance estimate.
What a fast radio burst’s dispersion tells astronomers
Radio waves at lower frequencies travel more slowly through ionized gas than higher-frequency waves. As a result, the lower-frequency parts of an FRB pulse arrive later. Astronomers measure this frequency-dependent delay and express the inferred integrated free-electron column as the burst’s dispersion measure, or DM.
More intervening ionized material generally produces a larger DM, so the measurement can indicate that a burst has traveled through more gas. But DM is not a direct measurement of distance: the amount and distribution of free electrons vary from one line of sight and source environment to another. A given DM therefore does not map to one unique distance. The review “Fast radio bursts” (2019) discusses this interpretation and its uncertainties.
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The observed DM includes electrons in several regions between the source and Earth. Researchers estimate the Milky Way’s contribution with Galactic electron-density models such as NE2001 or YMW16. After accounting for that foreground, the remaining excess is attributed mainly to the intergalactic medium (IGM) and the FRB’s host galaxy and local environment.
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A useful conceptual budget is:
DMexcess = DMIGM + DMhost/(1 + z)
Here, z is the source redshift. The host contribution is reduced by the factor (1 + z) when expressed in the observed DM budget. Because the Galactic subtraction is model-based and the host’s local electron contribution can vary, the excess DM still carries uncertainty. See the review “Fast radio bursts” (2019) for the DM components and the review “Fast radio bursts at the dawn of the 2020s” (2022) for the broader distance context.
Why a host-galaxy redshift is the firmer distance route
To obtain a host redshift, astronomers first need to localize an FRB accurately enough to associate it with a galaxy. They can then observe that galaxy’s spectrum and measure its redshift. Redshift provides the basis for a cosmological distance estimate; unlike a DM-only inference, it is tied to an identified host.
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Localization and redshift are separate steps. A precise sky position does not itself provide a redshift, and a host may remain undetected even after extensive follow-up. The radio localization and host-identification process is described in Astronomy & Geophysics’ 2021 review, “Fast radio bursts.”
Example: FRB 121102
Interferometric follow-up with the VLA localized the repeating FRB 121102. Astronomers identified a dwarf-galaxy host and measured its redshift as z = 0.193. This illustrates how accurate radio localization can lead to a host-based redshift and a firmer distance estimate. The event is summarized in Astronomy & Geophysics (2021).
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Example: FRB 20220610A
The European Southern Observatory’s 2023 release paper reports a complex host-galaxy system for FRB 20220610A at redshift 1.016 ± 0.002. The burst’s redshift and dispersion are consistent with substantial intervening intergalactic material. This is a particular event result, not a universal conversion between DM and distance. See the ESO release paper.
When a host redshift is unavailable: the Macquart relation
Astronomers can use the statistical relationship between FRB dispersion and redshift—often called the Macquart relation—to estimate redshift when no host redshift is available. It is a population-level relation: the IGM contribution tends to increase with distance, but variation in intervening gas and in the source’s host environment produces scatter. A DM-based redshift estimate is therefore not a confirmed host redshift or a precise one-burst ruler.
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Modeling choices matter when interpreting this relation. The 2024 study “Modeling the dispersion measure—redshift relation for fast radio bursts” examines how the relation is modeled. Work on using FRB dispersion measures as distance measures also addresses the method’s constraints: Physical Review D (2019).
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Why localization alone may not settle the distance
Even subarcsecond localization may not reveal a host galaxy, and without a host redshift the distance interpretation remains less certain. In a 2023 study, FRB 20210912A was localized to subarcsecond precision and observed in 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. The high DM supports a possible high-redshift interpretation under the Macquart relation, but neither the host nor that distance interpretation was established by the study. See Bhandari et al. (2023).
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How to read an FRB distance claim
| Evidence available | What it establishes | What remains uncertain |
|---|---|---|
| Measured DM | The integrated free-electron column inferred from the pulse’s frequency-dependent delay. | The source’s unique distance; Galactic, intergalactic, and host contributions must be modeled or constrained. |
| Precise localization, but no identified host | The FRB’s position on the sky is well constrained. | A host-galaxy redshift and firm host-based distance may still be unavailable. |
| Localized burst with identified host and measured redshift | A host redshift that supports a cosmological distance estimate. | The interpretation still depends on cosmological distance conventions, but it is not merely a DM-based redshift inference. |
| DM interpreted through the Macquart relation | A statistical redshift estimate based on the population relationship between dispersion and redshift. | The estimate has scatter and is not a confirmed redshift for an identified host. |
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