Pith. sign in

REVIEW 4 major objections 5 minor 1 cited by

Deriving the Energy Function of Non-repeaters from CHIME/FRB Baseband Data

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

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read Baseband CHIME data put the low-redshift energy-function slope of non-repeaters at -1.66.

desk verdict A worthwhile Vmax update to CHIME baseband data, but the high-redshift slope is not reproducible until Flimit and the actual weighting scheme are specified. read the letter →

arxiv 2504.13705 v1 pith:7RLENF3C submitted 2025-04-18 astro-ph.HE

Wenqi Ma , Zhifu Gao , Biaopeng Li , Jumei Yao , Fayin Wang This is my paper · ORCID
classification astro-ph.HE
keywords fastradioburstsnon-repeatersenergyfunctionvolumetricrateVmaxmethoddispersionmeasureredshiftevolutionbasebanddata
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 aims to establish the energy function and redshift-dependent volumetric rate of non-repeating fast radio bursts from the 116 CHIME/FRB baseband detections that survive its cuts, using the $V_\mathrm{max}$ method without assuming how the rate evolves with redshift. It finds a Schechter-like low-redshift energy function in the bin $0.04

What carries the argument

The load-bearing machinery is the $V_\mathrm{max}$ estimator: for each burst, the largest comoving volume in which it could still be detected, computed from redshift and energy via the fluence limit, with $V_\mathrm{max}$ capped by the upper boundary of the burst's redshift bin. These volumes convert each burst into a number density per unit time, corrected by selection functions for dispersion measure and fluence that are fitted to the ratio of assumed intrinsic distributions to observed ones, and the corrected densities are weighted and rescaled to match the expected number after applying the CHIME injection-test detection efficiency. The energy function is then assumed to be a Schechter function $\phi(\log E)\,d\log E = \phi_\star (E/E_\star)^{\gamma+1} e^{-E/E_\star}\,d\log E$, with parameters estimated by Bayesian nested sampling and uncertainties from Monte Carlo trials.

What would settle it

Recompute the $V_\mathrm{max}$ densities with intrinsic DM and fluence distributions measured directly from a complete, injection-calibrated baseband sample, or from localized events with known host DM; if the low-redshift slope then lies outside $\gamma=-1.66^{+0.33}_{-0.23}$, or the high-redshift slope no longer settles near $-2$, the paper's central claim is falsified.

Watch

Extended reading notes

Core claim

On its own terms, the paper claims that non-repeaters in the CHIME/FRB baseband sample have an energy function that is Schechter-like at low redshift, with $\log \phi_\star = 2.60^{+0.61}_{-0.68}$, $\log E_\star = 40.90^{+0.37}_{-0.45}$, and $\gamma = -1.66^{+0.33}_{-0.23}$ in the bin $0.04<z<0.44$. In the higher bins, fixing the slope at this value gives poor descriptions of the data, and freeing it yields steeper slopes around $\gamma \approx -2$ after dropping the lowest-energy, most uncertain point in each bin. Integrating the energy function over $10^{39}$ to $10^{42}$ erg gives volumetric rates whose redshift evolution is ambiguous, and the paper explicitly notes it cannot rule out either SFRD or SMD evolution with so few high-redshift points.

Load-bearing premise

The corrected number densities assume the true dispersion-measure and fluence distributions of the baseband non-repeaters match the intrinsic distributions adopted from the earlier CHIME catalog analysis (lognormal DM with $\mu_0=506$, $\sigma=0.31$ and fluence power-law index $\alpha=0.41$), together with an unstated CHIME fluence limit in Equation 15.

Editorial extensions

If this is right

  • Low-redshift energy-function fits for non-repeaters should use $\gamma\approx -1.66$ rather than steeper values derived from Catalog 1 lower-limit fluences.
  • If the high-redshift slope is genuinely near $-2$, high-redshift surveys should find proportionally more low-energy non-repeaters than a single Schechter shape anchored at low redshift would predict.
  • The ambiguous rate evolution means that rate-density comparisons alone cannot currently distinguish star-formation-tracking progenitors from old-population progenitors.
  • Fixing the slope in higher redshift bins because of small samples is not adequate; future fits should treat $\gamma$ as free in every redshift bin.

Reading between the lines

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

  • If baseband fluence calibration is trustworthy, applying the same machinery to future baseband catalogs should show whether the $\gamma\approx -2$ high-redshift slope remains once the high-redshift sample grows far beyond 22 sources.
  • A natural external check is to rerun the analysis with intrinsic DM and fluence distributions inferred from localized baseband FRBs with measured host-galaxy DM, which would directly test the main completeness assumption.
  • Extending the same $V_\mathrm{max}$ treatment to repeaters in baseband data could reveal whether the population split seen in pulse properties also appears as a difference in energy-function slopes.
Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

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. The paper uses 116 CHIME/FRB baseband non-repeaters with updated fluence measurements, estimates pseudo-redshifts from dispersion measures via Bayesian analysis, and applies the V_max method to derive the energy function in three redshift bins (0.04-0.44, 0.44-0.94, 0.94-2.50). The authors fit Schechter functions, claiming a low-redshift slope gamma = -1.66 (+0.33, -0.23), a steeper high-redshift slope gamma ~ -2, and an ambiguous volumetric-rate evolution that does not clearly track star-formation or stellar-mass density. Selection functions for DM and fluence are constructed by assuming intrinsic distributions from Hashimoto et al. (2022), and volumetric rates are compared with SFRD and SMD after arbitrary scaling.

Significance. If the central claims held, the paper would provide updated energy-function parameters based on the better-calibrated CHIME baseband fluences, which would be a useful contribution to FRB population studies. The manuscript explicitly attempts to account for selection effects, uses Monte Carlo and nested-sampling error estimates, and compares with SFRD/SMD evolution. However, the load-bearing results currently rest on an unreported detection limit, a weighting scheme that appears to bypass the newly fitted selection functions, and post-hoc exclusions that are not tabulated or justified. These issues mean the claimed energy-function slopes and rate evolution are not yet established from this analysis.

major comments (4)
  1. [Section 2.2, Eq. (15)] The value of Flimit is never specified anywhere in the manuscript. Since d_L,max is obtained from (1+z)E / (4 pi d_L,max^2 Delta nu) >= Flimit, every V_max in Eq. (14), every number density rho_i in Eq. (16), and hence every fitted Schechter parameter in Table 1 depends on this unreported constant. This is not a harmless overall normalization: for a fixed energy, the V_max of low-energy sources is most sensitive to Flimit, so changing Flimit can alter the shape of the energy function, not just its amplitude. Please state the adopted Flimit in physical units and show that the reported gamma values are robust to plausible variations of this threshold.
  2. [Section 2.3, Eq. (17)] The corrected number density is written explicitly with wi(DM) and wi(F) 'derived from T. Hashimoto et al. (2022)', while Section 2 states that the newly fitted s(DM) and s(Fnu) in Eqs. (5)-(6) are 'utilized for correcting the FRB number densities'. These statements are contradictory. If Eq. (17) is literal, the new selection functions are never applied, and the results inherit Hashimoto et al.'s assumed intrinsic DM log-normal and fluence power-law distributions; if the intended relation is w_i = 1/s with the authors' own Eqs. (5)-(6), the manuscript does not say so. Either way, the corrected densities, and therefore the energy-function slopes, are not reproducible from the text as written. Please make the weighting scheme explicit and rerun the analysis with the selection functions derived in this paper.
  3. [Section 3.1, Table 1 and Figure 5] The abstract's claim of a high-redshift slope gamma ~ -2 is not supported by the reported fits: Table 1 fixes gamma = -1.66 for bins 2 and 3, and the 'unfixed' fits shown in Figure 5 are described only qualitatively, with the lowest-energy points in both bins discarded post hoc. No best-fit values, uncertainties, or goodness-of-fit statistics are given for the unfixed fits. Because those low-energy points dominate the high-redshift slope, the exclusion rule must be stated in advance (e.g., a completeness or V_max criterion) and the free-fit parameters must be tabulated, including a test of whether gamma ~ -2 persists when the excluded points are retained or when Flimit is varied.
  4. [Section 2, Eqs. (1)-(3), and Abstract] The abstract states that the V_max method 'allows us to measure redshift evolution without prior assumptions', but the analysis assumes that the intrinsic DM and fluence distributions of the baseband sample are the same as those adopted for CHIME/FRB Catalog 1 by Hashimoto et al. (2022), as encoded in Eqs. (2)-(3). These assumed distributions enter the selection functions and hence the corrected number densities, so the energy-function normalization and slopes are conditional on those priors. Please qualify this claim and demonstrate robustness of the results to alternative choices of the intrinsic DM parameters (mu0, sigma) and fluence index alpha, for example by rerunning the analysis over a grid of these parameters.
minor comments (5)
  1. [Title and Abstract] There are typographical and grammatical errors, including 'Energy F unction' in the title and 'Analyse of the energy function' in the abstract; these should be corrected before resubmission.
  2. [Section 2, Eq. (3)] Equation (3) as typeset, 'P(Fnu) ∝ −α (Fnu/Fnu,0)^{α−1}', appears to have a typographical issue: a power-law probability distribution is usually written P(F) ∝ F^{α−1} (or with a positive coefficient for a decreasing distribution), and the minus sign and placement of alpha are confusing. Please correct the expression.
  3. [Section 2.3, Eq. (16)] The exposure time is given as t_obs = 0.59 yr, attributed to the CHIME/FRB Catalog 1 observation, but the baseband data span 2018 December 9 to 2019 July 1. Please clarify whether this same exposure is appropriate for the baseband subset and whether the subset's live-time fraction is accounted for.
  4. [Section 3.1] The text says the energy functions are poorly constrained in bins 2 and 3 when the slope is fixed, but the main conclusion about the high-redshift slope is then drawn from the unfixed fits. Please make the caveat explicit in the abstract and conclusions, since the high-redshift result is the most uncertain part of the analysis.
  5. [Data availability] The manuscript does not state whether the derived energy-function data points, the fitted selection functions, or the analysis code will be made available. Given the reproducibility issues in Eqs. (15) and (17), a data/code availability statement would be valuable.

Circularity Check

3 steps flagged · score 6.0 of 10

Energy-function gamma values inherit the assumed Hashimoto et al. fluence index and fixed slopes, and the claimed high-z gamma ~ -2 is not traceable to a reported fit.

  1. self definitional [Sec. 2, Eqs. (3), (13), (17); Sec. 3.1, Table 1]
    "The intrinsic fluence distribution is P(Fν)∝−α( Fν/Fν,0 )α−1, (3) ... We use α = 0.41 and Fν,0 = 5.0 Jy ms for deriving intrinsic fluence distribution. ... ρi,scaled =ρi× NFRB/ϵ / Σni=1wi(DM)wi(F )×wi(DM)wi(F ), (17) where wi(DM) and wi(F ) are the weighted functions of DM and fluence derived from T. Hashimoto et al. (2022)."

    The selection correction is defined as s(λ)=P_obs(λ)/P(λ) (Eq. 1) with P(F) fixed to a power law of index α=0.41, and the Vmax estimator is then multiplied by weights built from that same assumed distribution (Eq. 17). Since E=4πd_L^2 F Δν/(1+z) (Eq. 13), at fixed redshift E is proportional to F; hence the corrected energy function is a reweighted copy of the assumed fluence power law. A Schechter fit to such a distribution returns γ approximately α−2 = −1.59, which is the value reported as γ=−1.66 and then fixed for bins 2 and 3. The headline slopes are therefore the input fluence index renamed as an energy-function slope, not an independent measurement.

  2. fitted input called prediction [Sec. 3.1, Table 1 and Fig. 3 caption; Sec. 4]
    "Noted that the slope index of redshift bins 2 and 3 are fixed to −1.66. ... Slope index γ is fixed at -1.66 (consistent with T. Hashimoto et al. (2022)). ... while showing steeper slopes ( γ≈− 2) in higher redshift regions (z > 1)."

    The only tabulated high-redshift slopes are imposed a priori as γ=−1.66 to match Hashimoto et al.; they are not free-fit outputs. The later 'unfixed' fit that reportedly yields γ≈−2 is described after 'the lowest energy point in both redshift bins 2 and 3 are discarded', but no parameters or uncertainties are presented. Thus the abstract/conclusion claim of γ≈−2 at high z is either the fixed input or an unreported post-hoc fit; in both readings the published evidence does not support a derived high-redshift slope.

1 more flagged steps
  1. other [Section 2, after Eq. (6) and Eq. (17)]
    "These selection functions are utilized for correcting the FRB number densities calculated in Section 2.3. ... ρi,scaled =ρi× NFRB/ϵ / Σni=1wi(DM)wi(F )×wi(DM)wi(F ), (17) where wi(DM) and wi(F ) are the weighted functions of DM and fluence derived from T. Hashimoto et al. (2022)."

    The text claims the newly fitted s(DM) and s(Fν) (Eqs. 5–6) are used, but Eq. (17) explicitly uses weights taken from Hashimoto et al. (2022), not from these fits. If the equations are literal, the new baseband selection functions never enter the density correction, and every ρ_i,scaled—hence the whole energy function—is computed with the Catalog-1 correction weights the paper claims to supersede. The 'derived' energy function is then a reweighting of the same data and assumptions, not an independent result.

full rationale

The paper's Vmax calculation is not wholly empty: it uses observed baseband energies and pseudo-redshifts, and the low-redshift gamma is a free fit after correction. However, the corrections that produce every ρ_i,scaled are explicitly built from the assumed intrinsic DM lognormal (µ0=506, σ=0.31) and fluence power law (α=0.41) of Hashimoto et al. (2022), and Eq. 17 applies Hashimoto et al.'s weights rather than the paper's own fitted selection functions. Because E is proportional to F within a redshift bin, the corrected energy function inherits the assumed fluence slope, so the reported γ≈−1.66 is close to α−2=−1.59 by construction. The high-redshift story is weaker still: Table 1 fixes γ=−1.66 for bins 2 and 3, and the later γ≈−2 is asserted after discarding points but with no tabulated fit. The self-citation to W. Q. Ma et al. (2025) for DM_host is minor and not load-bearing, and the missing numerical value of F_limit in Eq. 15 is a separate reproducibility problem rather than circularity. On balance, the central gamma claims substantially reduce to assumed inputs and fixed prior slopes, so partial circularity is present. Score 6.

Assumptions & free parameters 9 free parameters · 6 assumptions · 0 invented entities

The energy function rests on a chain of assumed distributions: intrinsic DM/fluence from Hashimoto, host DM log-normal with chosen parameters, a Schechter model for the energy function, and an unstated detection limit in Vmax. These are not measured in this paper and propagate directly into the reported slopes and volumetric rates.

free parameters (9)
  • Intrinsic DM log-normal parameters = mu0 = 506 pc cm^-3, sigma = 0.31
    Adopted from Hashimoto et al. (2022) to construct the DM selection function in Section 2.
  • Intrinsic fluence power-law parameters = alpha = 0.41, pivot F_nu,0 = 5.0 Jy ms
    Adopted from Hashimoto et al. (2022); sets the fluence selection function and affects corrected densities.
  • DM selection polynomial coefficients = 0.4688, -3.2373, 6.3178
    Fitted in Eq 5 to the ratio of observed baseband DM distribution to the assumed intrinsic log-normal.
  • Fluence selection function parameters = a = 3.7713, b = 0.8810
    Fitted in Eq 6 to the fluence ratio; directly enters the weight factors used to correct number densities.
  • Host DM log-normal parameters = mu_host = 65.0, sigma_host = 1.00
    Chosen as 'reasonable' from literature including the authors' Ma et al. (2025); determines pseudo-redshifts and hence energies and Vmax.
  • Schechter normalization log phi* = 2.60, 2.47, 1.61 (bins 1, 2, 3)
    Fitted with bilby/Dynesty and reported in Table 1.
  • Schechter break energy log E* = 40.90, 41.16, 41.65 (bins 1, 2, 3)
    Fitted with bilby/Dynesty and reported in Table 1.
  • Schechter slope gamma = bin 1 free: -1.66+0.33-0.23; bins 2,3 fixed to -1.66
    The slope parameter is fitted in bin 1 and fixed in bins 2 and 3 in Table 1; the later unfixed fits are shown without tabulated values.
  • CHIME detection fluence limit Flimit = not stated
    Appears in Eq 15 to compute Vmax but no numeric value or source is given; all volumetric rates depend on it.
assumptions (6)
  • domain assumption Macquart relation and Planck18 cosmology describe the DMIGM-redshift relation (Eqs 8-9).
    Used in Bayesian redshift estimation; if f_IGM or the electron distribution is wrong, redshifts and energies are biased.
  • domain assumption Host galaxy DM follows a log-normal distribution with mu=65, sigma=1.0 (Eq 10).
    Adopted from literature; central to P(z|DMex) and to the energy estimates.
  • ad hoc to paper The intrinsic DM and fluence distributions of the baseband sample equal those used for Catalog 1 (Eqs 2-3).
    Not measured for this sample; the selection functions in Eqs 5-6 are fitted to this assumption.
  • standard math Vmax method with survey time 0.59 yr and sky fraction 0.003 gives unbiased rates (Eqs 14-16).
    Standard Schmidt estimator; assumes a known detection limit and uniform source distribution within bins.
  • domain assumption The energy function follows a Schechter function (Eq 19).
    This functional form is assumed and fitted; no alternative shapes are tested.
  • ad hoc to paper Slope gamma for bins 2 and 3 is fixed to the bin-1/Hashimoto value -1.66 (Table 1), and the lowest energy points are later discarded.
    Post-hoc model choice that directly affects the claimed high-redshift slope.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Deriving the Energy Function of Non-repeaters from CHIME/FRB Baseband Data." pith.science (2026). https://pith.science/paper/7RLENF3C

@misc{pith2026250413705,
  author       = {Pith},
  title        = {Pith review of: Deriving the Energy Function of Non-repeaters from CHIME/FRB Baseband Data},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/7RLENF3C}},
  note         = {Machine review of arXiv:2504.13705}
}
abstract

Fast radio bursts (FRBs) are radio pulses that originate from cosmological distance. Over 800 FRB sources with thousands of bursts have been detected, yet their origins remain unknown. Analyse of the energy function and the redshift evolution of volumetric rate could provide crucial insights into FRB progenitors. In this paper, we present the energy functions of non-repeaters selected from the CHIME/FRB baseband data using the $V_\mathrm{max}$ method. The $V_\mathrm{max}$ method allows us to measure redshift evolution without prior assumptions. We observed Schechter-like shapes in the energy function at low redshift region, while high redshift regions show a relatively small slope ($\gamma\approx -2$). The redshift evolution of volumetric rates shows an ambiguous trend, indicating that the population of non-repeaters is still not well understood. In the future, more samples and accurate measurements are needed to clarify these trends.

Figures

Figures reproduced from arXiv: 2504.13705 by the authors.

Figure 1
Figure 1. The dispersion measure (top) and fluence (bottom) histograms of baseband data and corrected selection functions. The observed and intrinsic data distributions are shown in the left-hand panels with histogram and red solid line, respectively. The derived selection functions are presented in the right-hand panels, and the selection functions from T. Hashimoto et al. (2022) are also shown as green dashed lines [PITH_F… view at source ↗
Figure 2
Figure 2. The relationship between isotropic-equivalent energy and pseudo-redshift is shown. The redshift values are estimated using the Bayesian method, while the energy values are calculated using Equation 13. Redshift subbox boundaries: z=0.04, 0.44, 0.94, 2.50; Sample size: Bin 1:54, Bin 2:40, Bin 3:22. The boundaries of the redshift bins are indicated by vertical red lines. The colors correspond to the observed fluence v… view at source ↗
Figure 3
Figure 3. The energy function data for redshift bin 1 (red dots), bin 2 (green dots), and redshift bin 3 (blue dots). The solid lines are represented the best-estimated energy function of three redshift bins, colored by red, green, and blue too. Noted that the slope index of redshift bins 2 and 3 are fixed to −1.66. 3. RESULTS 3.1. Energy function The energy functions are derived in three redshift bins. We assume that the ene… view at source ↗
Figures from the paper (2 more)
Figure 4
Figure 4. Figure 4: Corner plots of energy function parameters for three redshift bins. The parameter estimations of bin 2 and 3 are performed by fixing slope index to the best estimated value of redshift bin 1 (γ = −1.66). According the trend of data points in redshift bins 2 and 3, it i…
Figure 5
Figure 5. Figure 5: Left panel: the energy function data point and the corrected energy functions (dashed lines). Right Panel: the volumetric rate of non-repeaters as a function of redshift. The purple dots with error bars correspond to the volumetric rates derived from each redshift bin.…

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. A Unified Volumetric Rate-Energy Relation from Magnetar Radio Bursts to Fast Radio Bursts

    astro-ph.HE 2025-07 conditional novelty 6.0 of 10

    The volumetric rate of radio bursts from magnetar SGR 1935+2154, repeating FRB 20180916B, and non-repeating CHIME FRBs follows a single power law R ∝ E^-1.31 from 10^29 to 10^42 erg.

Reference graph

Works this paper leans on

34 extracted references · 3 canonical work pages · cited by 1 Pith paper

  1. [1]

    2019, Astrophys

    Ashton, G., et al. 2019, Astrophys. J. Suppl., 241,

    work page 2019

  2. [2]

    2020a, MNRAS, 494,

    https://arxiv.org/abs/1804.04101 Hashimoto, T., Goto, T., Wang, T.-W., et al. 2020a, MNRAS, 494,

    arXiv

  3. [7]

    C., et al

    https://arxiv.org/abs/2106.04352 CHIME/FRB Collaboration, Amiri, M., Andersen, B. C., et al. 2024, ApJ, 969,

    arXiv 2024

  4. [22]

    M., Mickaliger, M

    https://arxiv.org/abs/2106.04356 Rajwade, K. M., Mickaliger, M. B., Stappers, B. W., et al. 2020, MNRAS, 495,

    arXiv 2020

  5. [23]

    G., Cordes, J

    https://arxiv.org/abs/1112.2706 Spitler, L. G., Cordes, J. M., Hessels, J. W. T., et al. 2014, ApJ, 790,

    arXiv 2014

  6. [27]

    https://arxiv.org/abs/1811.02042 Avni, Y., & Bahcall, J. N. 1980, ApJ, 235, 694 Bannister, K. W., Shannon, R. M., Macquart, J. P., et al. 2017, ApJL, 841, L12, doi: 10.3847/2041-8213/aa71ff Bhandari, S., Sadler, E. M., Prochaska, J. X., et al. 2020, ApJL, 895, L37. https://arxiv.org/abs/2005.13160 Bhandari, S., Heintz, K. E., Aggarwal, K., et al. 2022, AJ, 163,

    arXiv 1980

  7. [29]

    2023, Reviews of Modern Physics, 95, 035005

    https://arxiv.org/abs/1610.09448 Zhang, B. 2023, Reviews of Modern Physics, 95, 035005. https://arxiv.org/abs/2212.03972 Zhang, G. Q., Yu, H., He, J. H., & Wang, F. Y. 2020, ApJ, 900,

    arXiv 2023

  8. [31]

    M., Manchester, R

    https://arxiv.org/abs/1909.00849 Yao, J. M., Manchester, R. N., & Wang, N. 2017, ApJ, 835,

    arXiv 1909

Show all 34 references
  1. [39]

    2020, ApJL, 898, L29

    https://arxiv.org/abs/1606.07887 Mereghetti, S., Savchenko, V., Ferrigno, C., et al. 2020, ApJL, 898, L29. https://arxiv.org/abs/2005.06335 Mo, J.-F., Zhu, W., Wang, Y., Tang, L., & Feng, L.-L. 2023, MNRAS, 518,

    2020 arXiv

  2. [49]

    https://arxiv.org/abs/2011.14494

    2011 arXiv

  3. [54]

    C., et al

    https://arxiv.org/abs/2005.10324 CHIME/FRB Collaboration, Amiri, M., Andersen, B. C., et al. 2020b, Nature, 582,

    2005 arXiv

  4. [59]

    H., Jia, X

    https://arxiv.org/abs/2005.10828 Chen, J. H., Jia, X. D., Dong, X. F., & Wang, F. Y. 2024, ApJL, 973, L54, doi: 10.3847/2041-8213/ad7b39 CHIME/FRB Collaboration, Andersen, B. C., Bandura, K. M., et al. 2020a, Nature, 587,

    2005 arXiv

  5. [69]

    D., Ravi, V., Belov, K

    https://arxiv.org/abs/2108.01282 Bochenek, C. D., Ravi, V., Belov, K. V., et al. 2020, Nature, 587,

    2020 arXiv

  6. [101]

    G., Scholz, P., Hessels, J

    https://arxiv.org/abs/1404.2934 11 Spitler, L. G., Scholz, P., Hessels, J. W. T., et al. 2016, Nature, 531,

    2016 arXiv

  7. [105]

    M., Smith, B

    https://arxiv.org/abs/2207.14316 Shull, J. M., Smith, B. D., & Danforth, C. W. 2012, ApJ, 759,

    2012 arXiv

  8. [145]

    W., Lang, D., & Goodman, J

    https://arxiv.org/abs/2311.00111 Foreman-Mackey, D., Hogg, D. W., Lang, D., & Goodman, J. 2013, PASP, 125,

    2013 arXiv

  9. [170]

    C., & Zhang, B

    https://arxiv.org/abs/2007.13935 Zhang, R. C., & Zhang, B. 2022, ApJL, 924, L14. https://arxiv.org/abs/2109.07558 Zhang, Z. J., Yan, K., Li, C. M., Zhang, G. Q., & Wang, F. Y. 2021, ApJ, 906,

    2007 arXiv

  10. [202]

    2021, Nature Astronomy, 5,

    https://arxiv.org/abs/1603.00581 Tavani, M., Casentini, C., Ursi, A., et al. 2021, Nature Astronomy, 5,

    2021 arXiv

  11. [306]

    https://arxiv.org/abs/1202.3665 Gajjar, V., Siemion, A. P. V., Price, D. C., et al. 2018, ApJ, 863,

    2018 arXiv

  12. [351]

    C., et al

    https://arxiv.org/abs/2001.10275 CHIME/FRB Collaboration, Amiri, M., Andersen, B. C., et al. 2021, ApJS, 257,

    2001 arXiv

  13. [372]

    1968, ApJ, 151, 393 Shannon, R

    https://arxiv.org/abs/2005.11178 Schmidt, M. 1968, ApJ, 151, 393 Shannon, R. M., Macquart, J. P., Bannister, K. W., et al. 2018, Nature, 562, 386, doi: 10.1038/s41586-018-0588-y Shin, K., Masui, K. W., Bhardwaj, M., et al. 2023, ApJ, 944,

    2005 arXiv

  14. [378]

    M., P´ erez, E., et al

    https://arxiv.org/abs/2005.11071 L´ opez Fern´ andez, R., Gonz´ alez Delgado, R. M., P´ erez, E., et al. 2018, A&A, 615, A27. https://arxiv.org/abs/1802.10118 Lorimer, D. R., Bailes, M., McLaughlin, M. A., Narkevic, D. J., & Crawford, F. 2007, Science, 318,

    2005

  15. [391]

    2017, ApJ, 840,

    https://arxiv.org/abs/2005.13161 Madau, P., & Fragos, T. 2017, ApJ, 840,

    2005 arXiv

  16. [401]

    P., Bassa, C

    https://arxiv.org/abs/2005.12164 Tendulkar, S. P., Bassa, C. G., Cordes, J. M., et al. 2017, ApJL, 834, L7. https://arxiv.org/abs/1701.01100 Wu, Q., & Wang, F.-Y. 2024, Chinese Physics Letters, 41, 119801, doi: 10.1088/0256-307X/41/11/119801 Yamasaki, S., & Totani, T. 2020, ApJ, 888,

    2005 arXiv

  17. [505]

    2020, A&A, 641, A6

    https://arxiv.org/abs/2012.08348 Planck Collaboration, Aghanim, N., Akrami, Y., et al. 2020, A&A, 641, A6. https://arxiv.org/abs/1807.06209 Pleunis, Z., Good, D. C., Kaspi, V. M., et al. 2021, ApJ, 923,

    2012 arXiv

  18. [539]

    2021, Nature, 596,

    https://arxiv.org/abs/2210.14052 Pastor-Marazuela, I., Connor, L., van Leeuwen, J., et al. 2021, Nature, 596,

    2021 arXiv

  19. [665]

    Q., Gao, Z

    https://arxiv.org/abs/2003.04848 Ma, W. Q., Gao, Z. F., Li, B. P., et al. 2025, ApJ, 981, 24, doi: 10.3847/1538-4357/adaf19 Macquart, J. P., Prochaska, J. X., McQuinn, M., et al. 2020, Nature, 581,

    2003 arXiv

  20. [777]

    2020, MNRAS, 494,

    https://arxiv.org/abs/0709.4301 Luo, R., Men, Y., Lee, K., et al. 2020, MNRAS, 494,

    2020 arXiv

  21. [891]

    W., Prochaska, J

    https://arxiv.org/abs/1704.03459 James, C. W., Prochaska, J. X., Macquart, J. P., et al. 2022a, MNRAS, 510, L18. https://arxiv.org/abs/2101.07998 James, C. W., Prochaska, J. X., Macquart, J. P., et al. 2022b, MNRAS, 509, 4775, doi: 10.1093/mnras/stab3051 Li, C. K., Lin, L., Xi...

    arXiv

  22. [928]

    2021, Nature Astronomy, 5,

    https://arxiv.org/abs/1907.06619 Ridnaia, A., Svinkin, D., Frederiks, D., et al. 2021, Nature Astronomy, 5,

    1907 arXiv

  23. [1961]

    2019, Statistics and Computing, 29,

    https://arxiv.org/abs/2201.03574 Higson, E., Handley, W., Hobson, M., & Lasenby, A. 2019, Statistics and Computing, 29,

    2019 arXiv

  24. [2886]

    https://arxiv.org/abs/2004.02079 Hashimoto, T., Goto, T., On, A. Y. L., et al. 2020b, MNRAS, 498,

    2004 arXiv

  25. [3551]

    2019, Nature Astronomy, 3,

    https://arxiv.org/abs/2003.03596 Ravi, V. 2019, Nature Astronomy, 3,

    2003 arXiv

  26. [3927]

    H., et al

    https://arxiv.org/abs/2008.09621 Hashimoto, T., Goto, T., Chen, B. H., et al. 2022, MNRAS, 511,

    2008 arXiv

Pith tools

Reviewed August 16, 2026 · model on record in the stance chip above.