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Cosmological Parameter Estimate from Persistent Radio Sources of Fast Radio Bursts

T0 review · 4 major / 5 minor · reviewed 2026-08-16 · deepseek-v4-flash

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Pith's one-line read A proposed method uses the Yang relation between FRB rotation measure and persistent radio source luminosity to break the H0–Ωb–fIGM degeneracy, yielding H0 = 75 ± 30 km/s/Mpc from six observed systems.

desk verdict Nice idea, but Eq. 6 doesn't eliminate H0 as claimed, making the two-stage calibration circular; the paper needs a real fix and a baseline before the result means anything. read the letter →

arxiv 2504.13132 v2 pith:XMHG64CG submitted 2025-04-17 astro-ph.CO astro-ph.HE

Zi-Liang Zhang , Bing Zhang This is my paper · ORCID
classification astro-ph.COastro-ph.HE
keywords fastradioburstspersistentsourcesHubbleconstantYangrelationrotationmeasuredispersioncosmologicalparametersMCMCanalysis
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper proposes a way to measure the Hubble constant $H_0$ by pairing fast radio bursts with their persistent radio sources. The key input is the Yang relation, $L_\nu \propto |\mathrm{RM}|$, which lets the observed rotation measure of an FRB stand in for the luminosity of its persistent radio counterpart. The authors show that this relation breaks the degeneracy among $H_0$, $\Omega_b$, and $f_{\mathrm{IGM}}$ that normally plagues dispersion-measure-only analyses, and they extract $H_0 = 75\pm 30~\mathrm{km\,s^{-1}\,Mpc^{-1}}$ from six observed systems. The result matters because it offers an independent, late-universe probe of the Hubble tension.

What carries the argument

The load-bearing object is the Yang relation $$L_\nu = \frac{64\$pi^{3}$}{27 m_e $c^{2}$} \zeta_e \gamma_{\rm th}^2 $R^{2}$ |\mathrm{RM}_{\rm src}|,$$ which links the synchrotron luminosity of a persistent radio source to the rotation measure of its FRB. The argument runs through two coupled equations: Equation 6 uses dispersion measure to calibrate the nuisance product $\zeta_e \gamma_{\rm th}^2 R^2$, and Equation 2 then converts RM and flux into a distance that depends on $H_0$. The two-stage MCMC chains these together so that the DM-based calibration supplies the prior that breaks the otherwise circular $H_0$–$\zeta_e \gamma_{\rm th}^2 R^2$ degeneracy.

What would settle it

Measure the nebular radius $R$ directly with very long baseline interferometry for a dozen or more PRSs, compute the implied product $\zeta_e \gamma_{\rm th}^2 R^2$ for each, and compare the spread and redshift trend against the single log-normal assumed here; a redshift drift or a scatter much larger than the assumed width would falsify the calibration.

Watch

Extended reading notes

Core claim

On the paper's own terms, the central claim is that the Yang relation turns persistent radio sources into standard candles: once the product $\zeta_e \gamma_{\rm th}^2 R^2$, the factor connecting PRS luminosity to rotation measure, is calibrated from dispersion measures, the same relation gives a distance and hence $H_0$ from flux, redshift, and RM alone. A two-stage MCMC first fits Equation 6 to DM data to constrain the product, then uses that posterior as a prior in Equation 2 to infer $H_0$. With a mock sample the method recovers the injected value ($75\pm 15$), and with the six observed PRSs it gives $75\pm 30~\mathrm{km\,s^{-1}\,Mpc^{-1}}$, insensitive to the choice of Galactic electron density model.

Load-bearing premise

The method assumes that the product of the electron fraction, the square of the thermal Lorentz factor, and the square of the source radius is drawn from one universal log-normal distribution across all persistent radio sources; if this product changes with redshift or host environment, the dispersion-measure calibration is biased and the Hubble constant inherits that bias.

Editorial extensions

If this is right

  • If the Yang relation holds, PRS systems become standard candles: RM, flux, and redshift give a distance without relying on the DM-only degeneracy.
  • With the six observed PRSs the method returns $H_0 = 75 \pm 30~\mathrm{km\,s^{-1}\,Mpc^{-1}}$, and the mock-sample recovery ($75 \pm 15$) shows the pipeline is unbiased at least for the assumed population.
  • A larger PRS sample, together with a full Bayesian treatment of all DM components, will tighten the constraint substantially.
  • Calibrating $\zeta_e \gamma_{\rm th}^2 R^2$ against an independent distance anchor in the same host galaxy—analogous to Type Ia supernova calibration—would remove the DM-based steps entirely.
  • The method extends to any persistent radio source with the same emission mechanism and a measured RM, not just sources already tied to FRBs.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • Beyond the paper, the same two-stage design should also constrain $\Omega_b$ and $f_{\mathrm{IGM}}$ simultaneously, since the first-stage fit to Equation 6 depends on both; a large PRS sample could turn the method into a baryon census rather than just an $H_0$ probe.
  • Beyond the paper, if the product $\zeta_e \gamma_{\rm th}^2 R^2$ correlates with host-galaxy star formation, that correlation could be measured and used as an additional distance calibrator instead of being treated as scatter.
  • Beyond the paper, a concrete test is to generate mock PRS catalogs with redshift-evolving $\zeta_e \gamma_{\rm th}^2 R^2$ and check how many sources are needed to detect the evolution; with the current six sources, the universal log-normal prior is essentially unconstrained.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

4 major / 5 minor

Summary. This paper proposes a new method to measure the Hubble constant using persistent radio sources (PRSs) associated with fast radio bursts. The method exploits the Yang relation Lν∝|RM|, which gives the PRS luminosity from its rotation measure up to a nuisance product ζeγth²R². The authors combine this with dispersion-measure data: a first-stage MCMC fits the combination of DM_host+DM_src and ζeγth²R² from an equation that is supposed to be H0-free, and a second-stage MCMC uses the resulting posterior as a prior in the luminosity-distance relation to infer H0. The pipeline is tested on ~50 mock PRSs and then applied to six observed systems (four confirmed plus two candidate PRSs), giving H0=75±30 km/s/Mpc. The paper also presents a mock population synthesis and discusses future improvements.

Significance. The proposed probe is timely and, if the derivation is correct, would provide an independent H0 measurement that does not rely on Type Ia supernovae or the CMB. The authors make several good practical choices: they treat DM_host+DM_src as a free parameter rather than fixing it at ~100 pc/cm³, they check insensitivity to the Milky Way electron-density model, and they explicitly acknowledge the remaining H0–ζR² degeneracy. The main weakness is that the printed central equations are inconsistent: Equation (6) claims to have eliminated H0 but still contains H0^4 inside the square root, and Equation (2) has a suspicious coefficient. Because the mock test is generated with the same equations, it cannot validate the physical calibration. The idea is worth pursuing, but the manuscript needs a corrected derivation and a rerun of the numerical results before the claims can be accepted.

major comments (4)
  1. [2.1, Eq. (6)] The printed Equation (6) is not the result of eliminating H0 from Equation (5) using Equation (2), because H0^4 still appears inside the square root. After a correct substitution the Hubble constant should cancel completely, leaving a relation among DM_ex, z, Fν, RM_obs, ζeγth²R², Ωm (with Ωb h² and fIGM fixed). As written, Sec. 3, step 3 fits Equation (6) without any prior or fixed value for H0, so the first-stage posterior for ζeγth²R² is either H0-dependent or undefined. The claimed H0-independent calibration of ζeγth²R², which is the basis of the two-stage decoupling, is therefore not demonstrated. If the H0 in Equation (6) is meant to be a shorthand for the right-hand side of Equation (2), that substitution must be displayed explicitly and the resulting H0-free equation used in the MCMC.
  2. [2.1, Eq. (2)] Equation (2) appears to have a dimensional error in its coefficient. Combining Equation (1) with Lν = 4πDL²Fν/(1+z) and DL = c(1+z)/H0 ∫ dz/E gives |RM_obs| = 27 m_e c^4 Fν [∫ dz/E]^2 / [16π² ζeγth²R² H0²(1+z)], i.e., a factor m_e c^4 in the numerator, not 1/m_e as printed. Because the mock sample is generated using the same Equation (2), the mock test cannot detect this normalization error, while the quoted H0=75±30 from the observed sample depends directly on it. Please verify the coefficients in Equations (2) and (6) and rerun the analysis if the factor is corrected.
  3. [3, steps 1-4] The mock test is an internal consistency check rather than a validation of the method. The mock sample is generated from the same Yang relation, the same DM decomposition, the same log-normal distributions for ζeγth²(R/0.01pc)² and DM_host+DM_src, and the same fiducial H0=73.04 that are used in the recovery, so obtaining H0=75±15 only shows that the pipeline can invert its own input. The key physical assumption that ζeγth²R² is a universal log-normal variable with fixed scatter is not tested by this procedure. The paper should state this limitation explicitly and, if possible, include a stress test in which the assumed ζeγth²R² distribution is incorrect (e.g., redshift evolution or environmental dependence) to quantify the resulting bias on H0.
  4. [3, observational sample] The observational constraint is not reproducible as printed because the paper gives no table of the six systems with their z, DM, Fν, and RM values. In addition, two of the six are candidate PRSs from Ibik et al. (2024) whose association with FRBs is not yet confirmed; including them without a separate treatment or an association-probability model can bias the central value H0=75±30. Please include the data table and either exclude the candidates from the main result or model their unknown association probability.
minor comments (5)
  1. [2.1, below Eq. (1)] The text 'RM_src = (1+z)^2 RM_obs^2' should read 'RM_src = (1+z)^2 RM_obs'; the square on RM_obs is either a typo or dimensionally incorrect.
  2. [2.1, Eq. (7)] The citation for σ_MW should be to the Galactic electron density models (Cordes & Lazio 2002; Yao et al. 2017), not to Manchester et al. (2005), which is a pulsar catalogue.
  3. [4, second bullet] The claim that the Yang relation 'unravels degeneracies among H0, Ωb, and fIGM' is stronger than what is implemented, since Ωb h² and fIGM are fixed in the fits; please rephrase to describe the degeneracy that is actually broken (H0 versus ζR²).
  4. [3, second-stage MCMC] The first-stage posterior is marginalized over ζeγth²R² before being used as a prior in the second stage; this discards correlations with Ωm and DM_host+DM_src. Please either propagate the full joint posterior or discuss why the correlation is negligible.
  5. [Title] The title contains a typo: 'F ast Radio Bursts' should be 'Fast Radio Bursts'.

Circularity Check

1 steps flagged · score 7.0 of 10

Equation 6 claims to eliminate H0 but retains H0^4, so the first-stage calibration of ζeγth²R² is H0-dependent and the second-stage H0 fit double-counts the same data.

  1. self definitional [Section 2.1, Eq. (6), including the derivation sentence 'By eliminating H0 from Equation 5 using Equation 2...']
    "By eliminating H0 from Equation 5 using Equation 2 and substituting the result into Equation 4, we derive: DMex = [mec2 f2IGM χ2 Ω2b H4 0 / (12G2m2p) × ζeγ2 R2 (1+z)|RMobs|/Fν]^{1/2} × [∫0z (1+z′)/E(z′) dz′]/[∫0z 1/E(z′) dz′] + (DMhost + DMsrc)/(1+z). (6)"

    The text says H0 was eliminated, yet Eq. (6) still contains H0^4. Substituting Eq. (2) into Eq. (5) gives H0^2 proportional to I²/[ζeγth²R²|RMobs|(1+z)/Fν], which makes all H0 dependence cancel; the printed Eq. (6) is therefore not the promised elimination. As printed, the first-stage fit of ζeγth²R² from DMex requires assuming or marginalizing over H0, so the resulting ζ posterior is conditioned on H0. Feeding that posterior into Eq. (2) to recover H0 from the same DM/Fν/RM data re-imports the assumed H0 and double-counts the same measurements; the claimed independent constraint that would break the H0–ζR² degeneracy is not demonstrated.

full rationale

The central claim is that the Yang relation helps break the H0–Ωb–fIGM degeneracy of DM-only FRB cosmology, permitting a two-stage estimate of H0. The load-bearing step is Eq. (6), which is introduced as the result of eliminating H0 between Eq. (2) and Eq. (5). As printed, Eq. (6) contains H0^4 inside the radical, so no elimination has occurred. If one performs the substitution correctly, H0 cancels; if one does not, the first-stage calibration of ζeγth²R² is explicitly H0-dependent and the second stage reuses that H0-dependent information to 'measure' H0. The paper itself concedes in the final section that 'a degeneracy remains between ζeγ2thR2 and H0 (Figure 3)', which is in tension with the abstract's claim that the relation unravels these degeneracies. The Yang relation itself is a same-group result, but it is supported by external observational papers (e.g., Bruni et al. 2024, 2025), so I do not treat that citation as the circular element. The mock recovery is also not the issue; it only checks internal consistency. The circularity is specific to the printed derivation of Eq. (6) and its use in the two-stage MCMC, giving score 7: the H0 estimate is partially reduced by construction, but the paper does not rely on a pure self-citation chain and the method could in principle be repaired by correctly eliminating H0.

Assumptions & free parameters 4 free parameters · 6 assumptions · 0 invented entities

The central claim rests on calibrating the Yang relation product and the host/source DM term, both of which are free parameters in the MCMC. The mock population functions and the assumed f_IGM value are additional domain assumptions. No new physical entities are introduced.

free parameters (4)
  • zeta_e gamma_th^2 (R/0.01 pc)^2 = posterior around 1 (mock used median ~0.86)
    Fitted in the first-stage MCMC via Eq. 6 using DM data, with a log-normal prior (mu=0, sigma=0.5). This product calibrates the Yang relation and is the central nuisance parameter.
  • DM_host + DM_src = posterior within (0, 1500) pc cm^-3
    Treated as a free parameter with uniform prior in the first-stage MCMC. It absorbs host galaxy and local source plasma contributions, which are poorly known for PRS-associated FRBs.
  • Omega_m = posterior around 0.34
    Gaussian prior Omega_m = 0.34 +/- 0.03. It enters E(z) and is marginalized over in the MCMC.
  • H0 (target) = 75 +/- 30 km/s/Mpc (observed), 75 +/- 15 km/s/Mpc (mock)
    Uniform prior (0, 140) in the second-stage MCMC. This is the cosmological parameter the paper aims to constrain.
assumptions (6)
  • domain assumption Yang relation: L_nu = 64 pi^3 / (27 m_e c^2) * zeta_e gamma_th^2 R^2 * |RM_src|.
    Physical model from Yang et al. (2020); the paper assumes this relation holds for all PRSs with a universal product parameter.
  • domain assumption RM_src = (1+z)^2 RM_obs; Milky Way and IGM RM contributions are negligible.
    Section 2.1 footnote 2. The observed RM is assumed to originate in the FRB source environment.
  • domain assumption The IGM DM formula, Eq. 5, with electron fraction chi = 7/8 and f_IGM = 0.83.
    Standard formula from Deng & Zhang (2014); f_IGM is fixed to 0.83 following Fukugita et al. (1998).
  • domain assumption PRS-associated FRBs trace the cosmic star formation history, and their luminosity function is a power law Phi(L) proportional to L^-1.3.
    Section 2.2. Used to generate mock samples; the paper states the analysis is not critically dependent on these forms.
  • standard math LambdaCDM with E(z) = sqrt(Omega_m (1+z)^3 + 1 - Omega_m).
    Assumed cosmological model in both equations.
  • ad hoc to paper DM_host + DM_src is drawn from a log-normal distribution (mu=6, sigma=0.6) in the mock and given a uniform prior in the fit.
    Adopted to represent the large host/source DM values of PRS-associated FRBs; not independently constrained.

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Pith. "Pith review of Cosmological Parameter Estimate from Persistent Radio Sources of Fast Radio Bursts." pith.science (2026). https://pith.science/paper/XMHG64CG

@misc{pith2026250413132,
  author       = {Pith},
  title        = {Pith review of: Cosmological Parameter Estimate from Persistent Radio Sources of Fast Radio Bursts},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/XMHG64CG}},
  note         = {Machine review of arXiv:2504.13132}
}
abstract

We introduce a novel method to constrain the Hubble constant ($H_0$) by combining fast radio bursts (FRBs) and their persistent radio sources (PRSs) through the observationally validated Yang relation, $ L_{\nu} \propto | \mathrm{RM} | $, which links PRS luminosity to the rotation measure (RM) of the associated FRB. Using a mock sample of PRSs, we demonstrate that the Yang relation can help to unravel the degeneracies among $H_0$, baryon density parameter $\Omega_b$, and baryon fraction in the intergalactic medium $f_{\mathrm{IGM}}$ in the traditional approach of using dispersion measure only to perform cosmological analyses. Our method employs a two-stage Markov Chain Monte Carlo (MCMC) analysis to constrain $H_0$. Using the available data of six observed PRS systems, we obtain a preliminary constraint of $H_0 = 75 \pm 30~\mathrm{km\,s^{-1}\,Mpc^{-1}}$. We briefly discuss possible refinements of the method by reducing residual degeneracies and systematic uncertainties using future data and physical modeling. Our results indicate that the Yang relation can potentially become a new probe for performing FRB cosmology.

Figures

Figures reproduced from arXiv: 2504.13132 by the authors.

Figure 1
Figure 1. Observed and simulated PRS population. Main panel: Luminosity-redshift distribution for mock (grey/blue) and observed PRSs (orange). The red curve indicates the de￾tection threshold. Upper/right panels: Intrinsic redshift dis￾tribution Ψ(z) and luminosity function Φ(Lν) (grey), com￾pared to detected mock PRSs (blue). 2.2. PRS redshift and luminosity distribution To validate our methodology, we employ Monte Carlo sim… view at source ↗
Figure 2
Figure 2. Posterior distributions from MCMC analyses of Equation 6. The contour plot is smoothed using kernel den￾sity estimation. Blue, orange, and green solid lines corre￾spond to fitting results for detected mock PRSs and real PRSs analyzed using the YMW16 model and the NE2001 model, respectively. In each contour set, 1σ, 2σ, and 3σ con￾fidence regions appear from innermost to outermost. Blue dashed lines indicate the medi… view at source ↗
Figure 3
Figure 3. Posterior distributions from MCMC anal￾yses of Equation 2. The posterior distribution of lg ζeγ 2 th(R/0.01 pc)2 in [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗

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Forward citations

Cited by 2 Pith papers

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  1. Constraints on Primordial Black Hole Dressed by Dark Matter Halo from Microlensing Effect of Fast Radio Bursts

    astro-ph.CO 2026-07 conditional novelty 5.0 of 10

    A new conversion formula turns monochromatic bare-PBH microlensing bounds into extended-mass dressed-PBH bounds, and a 10^5-FRB forecast places f_PBH near 10^-4.

  2. Calibrating $\rm{DM_{IGM}}-z$ relation using host galaxies of FRBs

    astro-ph.GA 2025-07 reject novelty 5.0 of 10

    A claimed tight sSFR-DM_exc correlation is used to calibrate the DM_IGM-z relation, but the improvement is evaluated on the same data used to fit the model.

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