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REVIEW 4 major objections 7 minor 84 references

The Event Rate and Luminosity Function of Fermi/GBM Gamma-Ray Bursts

T0 review · 4 major / 7 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read This paper claims that the Fermi/GBM gamma-ray burst event rate exceeds the star formation rate at low redshift, and that this excess is driven by faint and medium bursts, while bright bursts trace star formation closely.

desk verdict New Fermi/GBM c- analysis with a bright/medium/faint split, but the missing normalization makes the SFR comparison untestable as printed. read the letter →

arxiv 2507.16595 v1 pith:GNJOYALQ submitted 2025-07-22 astro-ph.HE

Yang Liu , Zhi-Bin Zhang , Xiao-Fei Dong , Long-Biao Li , Xiu-Yun Du This is my paper
classification astro-ph.HE PACS 98.70.Rz
keywords gamma-rayburstseventrateluminosityfunctionstarformationLynden-Bellc-methodFermi/GBMevolutionlow-redshiftexcess
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 claims that the cosmic event rate of Fermi/GBM gamma-ray bursts is not a single star-formation-tracing population: the total rate exceeds the star formation rate (SFR) at low redshift and matches it at high redshift, regardless of detector energy band or flux threshold. The excess is carried by faint and medium bursts, while bright bursts follow the SFR closely. If correct, GRB-based measurements of star formation at low redshift must separate bursts by luminosity, and faint or medium GRBs likely have a different physical origin or an efficiency that evolves with cosmic time. The claim is established non-parametrically with the Lynden-Bell c$^-$ method on 115 bursts with measured redshifts and bolometric luminosities.

What carries the argument

The analysis rests on Lynden-Bell's c$^-$ method (Lynden-Bell 1971) with the $\tau$ statistic of Efron & Petrosian (1992). First, each burst's luminosity is de-evolved to $L_0 = L/(1+z)^k$, where $k$ is chosen by the $\tau$ test to make luminosity and redshift uncorrelated (k values of about 3.3 to 3.9 for flux-limited samples, but about 0.13 for the bright subsample). The c$^-$ method then builds cumulative luminosity and redshift distributions as products over truncated sets of bursts, and the event rate follows as $\rho(z) = \frac{d\phi(z)}{dz} (1+z) \left(\frac{dV(z)}{dz}\right)^{-1}$. The resulting $\rho(z)$ is compared in absolute value with a fitted SFR history; the paper also applies the same machinery under different flux limits and completeness cuts to show the excess is stable.

What would settle it

A direct calibration of the absolute GRB rate from the survey exposure and sky coverage of the 115 Fermi/GBM bursts, or from a volume-limited sample, would settle the claim; if, once normalized, the low-redshift excess vanishes, the central conclusion fails.

Watch

Extended reading notes

Core claim

This paper's central discovery is that the low-redshift excess of the gamma-ray burst (GRB) rate over the star formation rate (SFR), previously reported for Swift long GRBs, persists in the Fermi/GBM sample and is not an artifact of energy band, flux threshold, or sample completeness. Splitting the sample at two break fluxes in the cumulative flux distribution (about $2.05\times 10^{-6}$ and $2.91\times 10^{-7}$ erg cm$^{-2}$ s$^{-1}$) into 34 bright, 65 medium, and 16 faint GRBs, the authors find that the bright subsample's event rate matches the SFR within the stated uncertainties, while the medium and faint subsamples exceed it at $z<1$. They therefore conclude that bright, high-luminosity GRBs are likely produced by the core-collapse of massive stars, whereas the faint and medium events responsible for the excess may constitute a different population. The result is stated as independent of energy bands because the same behavior appears for Fermi/GBM and Swift/BAT data.

Load-bearing premise

The Lynden-Bell c$^-$ method determines the event rate $\rho(z)$ only up to an overall normalization constant, and the paper does not specify how that constant is fixed before the GRB rate is plotted on the same absolute axis as the star formation rate.

Editorial extensions

If this is right

  • GRB-based measurements of the cosmic star formation history should use the bright subsample instead of the full population, since faint and medium bursts inflate the rate at $z<1$.
  • Population models of long GRBs must treat bright and faint bursts as distinct classes with different luminosity functions and possibly different progenitors.
  • The low-redshift excess is not an artifact of detector energy band, flux threshold, or sample completeness, so any explanation must be physical.
  • If bright GRBs trace star formation while faint ones do not, then counts of all long GRBs will systematically overestimate the star formation rate at low redshift.

Reading between the lines

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

  • Because the c- method fixes the rate only up to an overall constant, the paper's 'exceeds' statement is strictly about the shape of the rate history; the missing calibration is an open issue the paper does not address.
  • A natural testable extension is to repeat the same bright/medium/faint split on the larger Swift/BAT sample to see whether its bright subsample also matches the SFR; the paper only compares total rates across satellites.
  • If the faint/medium excess is real, it points to a luminosity-dependent efficiency or an additional progenitor channel such as delayed mergers, which the paper mentions as a possibility but does not model quantitatively.
  • The near-zero luminosity-evolution index for bright bursts implies that a volume-limited bright sample could pin down the local GRB rate and simultaneously resolve the normalization ambiguity of the c- method.
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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 / 7 minor

Summary. The paper analyzes 115 Fermi/GBM GRBs with measured redshifts and peak fluxes, applying a power-law luminosity-evolution correction with the tau-statistic and then Lynden-Bell's c- method to derive the cumulative luminosity function and the event rate rho(z). The derived rate is compared with an empirical SFR fit, and the authors report that the GRB rate exceeds the SFR at low redshift but agrees at high redshift, independent of flux cuts. They then fit a triple power-law to the cumulative flux distribution, split the sample into bright, medium, and faint bursts, and claim that the bright subsample follows the SFR while the medium and faint subsamples show the low-redshift excess, suggesting different progenitors.

Significance. If established, the luminosity-dependent behavior of the GRB rate relative to the SFR would be an important constraint on GRB progenitor models, particularly the claim that only bright, high-luminosity bursts track core-collapse star formation. The use of the non-parametric Lynden-Bell method and the exploration of multiple flux thresholds are strengths, as is the comparison with earlier Swift results. However, the headline quantitative comparison with the SFR is currently not supported because the absolute normalization of rho(z) is never specified, and the analysis mixes short and long GRBs. The paper is therefore of interest but requires substantial clarification before the central claims can be evaluated.

major comments (4)
  1. [Section 3, Eqs. (4)-(6) and Figures 2, 3, 7] The c- method as implemented yields rho(z) only up to an overall multiplicative constant, because phi(z_i) is a product of rank counts; with no truncation it reduces to the sample rank. The text never states how this constant is fixed (no exposure time, sky coverage, detection efficiency, or local-rate calibration is given), yet Figures 2, 3, and 7 plot rho(z) on the same absolute axis as the SFR in Msun yr^-1 Mpc^-3. Without specifying C = N_obs/(T_exp Omega_sky epsilon) or an equivalent calibration, the statement that the GRB rate 'exceeds the SFR' at low redshift is not justified: the apparent excess could be a shape effect produced by an arbitrary vertical offset, and the same ambiguity affects the bright/medium/faint comparison in Figure 7.
  2. [Section 2 and Section 4.3] The sample is described as containing 11 short GRBs and 104 long GRBs, but all 115 events are used together in the event-rate calculations of Sections 4.1-4.3. Short GRBs are merger-related and have a different redshift-delay distribution from long GRBs; including them could produce or enhance the low-redshift excess attributed to faint and medium bursts. The claim that bright GRBs trace core-collapse star formation requires repeating the analysis with short GRBs excluded or demonstrating explicitly that the short-burst subsample does not drive the result.
  3. [Section 3, Eqs. (1)-(2)] The truncation boundaries zmax_i and Lmin_0,i are defined only verbally as detectability limits. No formula is given for converting the stated flux thresholds (Flim,1 through Flim,5) into these limits, and the energy band of the flux measurements is not specified in this context. These boundaries define the sets J_i and J'_i and therefore enter every M_j in Eq. (5); without an operational prescription the c- method is not reproducible and the resulting rho(z) cannot be independently checked. Please provide the exact conversion and list the cutoff values used for each subsample.
  4. [Section 4.3] The conclusion that 'the bright GRB rate matches the SFR well' is based on visual inspection of Figure 7 without error bars on the step functions or a goodness-of-fit statistic. This is particularly important because the evolution-correction index k for the bright subsample is 0.13, very different from the medium (3.89) and faint (3.5) values; the shape of rho(z) is partly determined by the k chosen to make tau approximately zero, so a quantitative comparison with the SFR curve (e.g., chi-squared or KS statistic) is needed before the claim can be accepted.
minor comments (7)
  1. [Throughout] The manuscript contains numerous typographical and grammatical errors ('paied', 'consitute', 'di ffernt', 'indepedent', 'generaly', 'energiea', 'Univese', 'simliar'); a thorough language edit is needed.
  2. [Section 2] The K-correction factor used to compute bolometric luminosity is listed in Table 1 but its definition is not given; please state the formula and the energy band of the peak flux to which it applies.
  3. [Section 4.1] The SFR compilation is described as 17 binned data points, but the individual points and their uncertainties are not shown; adding a table or plot of the compiled SFR data would allow the reader to reproduce the fit.
  4. [Section 4.3] The two-dimensional K-S test is mentioned in the text but the test statistic and p-values are not reported; please provide them so the claim that faint and medium GRBs are identically distributed can be evaluated.
  5. [Figures 2, 3, and 7] The vertical axis is labeled 'Event Rate (Msun yr^-1 Mpc^-3)', which is the unit of the SFR; the GRB event rate should be in units such as Gpc^-3 yr^-1 or be explicitly normalized. Please relabel the axis and clarify what quantity is plotted.
  6. [Section 4.3] The uncertainty on the break flux F_b,1 is 1.69 x 10^-6 erg cm^-2 s^-1, comparable to the value itself; the robustness of the bright/medium split to this uncertainty should be discussed.
  7. [References] The citation 'Rong, D. H. et al. 2025' appears in the text but is not listed in the references; please add it or correct the citation.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the event-rate shape is a non-parametric transform of the data with an external SFR comparison; the absolute-normalization ambiguity is a correctness concern, not a circular reduction.

full rationale

The derivation of ρ(z) follows the standard Lynden-Bell c− method (Eqs. 4–6): φ(z) is a cumulative product of inverse-censored counts and ρ(z) is its derivative times the comoving volume factor. The result is a non-parametric transformation of the observed (z, L) data, not a quantity defined to equal the SFR. The comparison with SFR in Figures 2, 3 and 7 uses external data (Hopkins 2004; Thompson et al. 2006; Li 2008; Bouwens et al. 2011), so the central 'excess at low z' claim is an empirical shape comparison. The k values are fitted by the τ-statistic to remove luminosity–redshift covariance; this is a standard modeling step, not a fit of the predicted rate to the SFR. The bright/medium/faint split is obtained by a TPL fit to the cumulative flux distribution of the same sample, but the subsequent event rates are computed independently from the (z, L) data of each subgroup; the conclusion that faint/medium rates exceed SFR while bright matches is a measured outcome, not built into the grouping. Self-citations to Dong et al. (2022) are used for context and interpretation ('proposed by D22'), but the paper performs its own random-subsample completeness test and its own flux-cut comparisons, so the argument does not reduce to a self-citation. The main legitimate concern is that Eq. (6) fixes ρ(z) only up to an overall normalization and the paper never states the exposure/sky-coverage/efficiency constant used to place the curves on an absolute SFR axis; this makes the 'exceeds/matches' language quantitatively underdetermined. That is a correctness/falsifiability problem, not a circular reduction, because the shape of the excess is still data-derived and independent of the vertical offset. No equation in the paper is identical to the claimed conclusion by construction.

Assumptions & free parameters 5 free parameters · 5 assumptions · 0 invented entities

The central claim depends on four fitted quantities: the evolution index k (six values), the TPL break fluxes, the SFR comparison fit, and an unstated normalization of the event rate. The c- method and cosmology are standard inputs. No new physical entities are introduced.

free parameters (5)
  • Luminosity evolution index k = 3.29, 3.85, 3.83, 3.93, 3.69, 3.83 for the six samples
    Fitted via τ-statistic to make de-evolved luminosity and redshift independent (Eq. 3); the derived event rate ρ(z) depends directly on k through L0 = L/(1+z)^k.
  • TPL break fluxes Fb,1 and Fb,2 = Fb,1 = (2.05 ± 1.69)×10^-6, Fb,2 = (2.91 ± 0.17)×10^-7 erg cm^-2 s^-1
    Fitted to the cumulative peak-flux distribution (χ2ν≈1.51) and used to split the sample into bright, medium, and faint GRBs; the paper's conclusion that bright GRBs follow the SFR depends on this split.
  • Absolute normalization of ρ(z) = unstated
    The c- method yields the rate up to an overall constant; the paper plots it on the same absolute axis as SFR (in M_sun yr^-1 Mpc^-3) but does not say how the constant was chosen.
  • SFR fit parameters = a = 0.12 ± 0.02, b = 0.14 ± 0.02, c = 4.61 ± 0.20, d = 5.55 ± 0.23, h = 0.7
    Empirical fit to 17 binned SFR data points (Hopkins & Beacom 2006 formula); used as the comparison baseline.
  • Flux thresholds Flim,1 through Flim,5 = 1e-7, 2e-8, 5e-8, 1e-8, 2.35e-6, 2.65e-7 erg cm^-2 s^-1
    Hand-chosen thresholds from prior literature (Dong et al. 2022, Pescalli et al. 2016) used to define truncated samples and subsamples; the paper tests several and claims insensitivity, but each choice shapes the truncation.
assumptions (5)
  • domain assumption The 115 GRBs form a flux-limited sample after applying the stated flux cuts.
    Redshift measurements require follow-up, which may introduce redshift-dependent incompleteness; the paper assumes the flux cuts remove this bias (Sections 2 and 4.2).
  • domain assumption Luminosity evolution follows a single power law (1+z)^k.
    Adopted from earlier works (Yu et al. 2015, Dainotti et al. 2015, Dong et al. 2022); no physical model is given, and k is fitted.
  • domain assumption The truncation boundaries zmax_i and Lmin_0,i are known correctly.
    The c- method requires the exact maximum redshift at which each burst could be detected; the paper never specifies how these are computed from the flux limits (Eqs. 1-2).
  • standard math Flat ΛCDM cosmology with H0 = 70, ΩM = 0.27, ΩΛ = 0.73.
    Standard cosmology for luminosity distance and comoving volume (Section 2).
  • domain assumption The cumulative flux distribution is well described by a triple power law.
    Used to define bright/medium/faint groups; the first break has a very large uncertainty (Section 4.3).

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Pith. "Pith review of The Event Rate and Luminosity Function of Fermi/GBM Gamma-Ray Bursts." pith.science (2026). https://pith.science/paper/GNJOYALQ

@misc{pith2026250716595,
  author       = {Pith},
  title        = {Pith review of: The Event Rate and Luminosity Function of Fermi/GBM Gamma-Ray Bursts},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/GNJOYALQ}},
  note         = {Machine review of arXiv:2507.16595}
}
abstract

Luminosity function and event rate of Gamma-Ray Bursts (GRBs) are easily biased by the instrument and selection effects. We select 115 Fermi/GBM GRBs with good spectra fitted by a smoothly broken power-law function. The $\tau$-statistic method is used to describe how the luminosity evolves with redshift. The non-parametric Lynden-Bell's c$^{-}$ method has been applied to get the cumulative luminosity function and event rate which is compared with the star formation history. How the selection and instrument effects bias the deduced event rate has been carefully studied. We find that the event rate always exceeds the star formation rate (SFR) at lower redshift and matches with each other at higher redshift, which is independent of energy bands and consistent with previous findings of other satellites. Furthermore, it is found that sample completeness does not affect the deduced event rate too much as mentioned for the Swift lGRBs in Dong et al.. A triple power-law function has been used to fit the cumulative flux distribution and categorize the total sample into three subsamples of bright, medium and faint GRBs. We find that the event rates of bright GRBs, unlike medium and faint ones, comply with the SFR ideally, which indicates that these bright GRBs with higher luminosity are possibly produced from the core-collapse of massive stars.

Figures

Figures reproduced from arXiv: 2507.16595 by the authors.

Figure 1
Figure 1. Luminosity is plotted against redshift for 115 Fermi/GBM GRBs. The dashed line represents the lower limit of luminosities constrained by the instrumental sensitivity of Flim,2 = 2 × 10−8 erg cm−2 s −1 . Several peculiar GRBs are marked in the insert. 4 RESULTS 4.1 The instrument effect To check how the sensitivity affects the deduced event rate of GRBs, we choose two flux cuts of Flim,1 = 1 × 10−7 erg cm−2 s −1 and … view at source ↗
Figure 2
Figure 2. Comparison of the GRB event rates with the SFR. The blue and green step lines are the GRB rates given by the sensitivities of Flim,1 and Flim,2, respectively. The magenta, purple and orange step lines denote the Swift lGRB rates for diverse samples in D22. The black circles and the solid curve stand for the average SFR in each bin and the best fitting curve with 1σ and 3σ confidence levels. respectively 3.29, 3.85, … view at source ↗
Figure 3
Figure 3. Comparison of the GRB rate versus the SFR between P16 and this work. The gray step line is the observed GRB rate given by the Flim,3 of P16, the magenta step line shows the GRB rate in the case of Flim,3/5. The blue and green step lines are the GRB rates for Subsample I and II, correspondingly. The black dashed line represents the best fitting curve with 1σ and 3σ confidence levels.     ( L 0 ) L0 (erg s -1 )… view at source ↗
Figures from the paper (4 more)
Figure 4
Figure 4. Figure 4: Luminosity distributions of diverse GRB samples. The dashed line shows the best fit with a broken power-law form to the luminosity function constrained by the Flim,3 in P16. MNRAS 000, 1–11 (2025) [PITH_FULL_IMAGE:figures/full_fig_p005_4.png]
Figure 5
Figure 5. Figure 5: The cumulative peak flux distribution of 115 Fermi/GBM GRBs. The solid line is the best fit with a TPL function (χ 2 ν ≈ 1.51).      [PITH_FULL_IMAGE:figures/full_fig_p006_5.png]
Figure 6
Figure 6. Figure 6: Left panel: luminosity histograms of the bright, medium and faint GRBs. Right panel: luminosity versus redshift for three kinds of GRBs. Two luminosity thresholds estimated by Flim,4 and Flim,5 are drawn by the dashed and solid lines in each. MNRAS 000, 1–11 (2025) [P…
Figure 7
Figure 7. Figure 7: Comparison of the event rate with the SFR for three GRBs categories of this work. The estimated event rates of bright, medium and faint GRBs are marked by the green, blue and red step lines, respectively. The black dashed line is the best fitted curve together with con…

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Pith tools

Reviewed August 6, 2026 · model on record in the stance chip above.