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REVIEW 4 major objections 5 minor 21 references

Constraining GRBs pseudo-redshift using different empirical correlations

T0 review · 4 major / 5 minor · reviewed 2026-08-14 · deepseek-v4-flash

Pith's one-line read This paper applies two empirical correlations, the Amati peak-energy/isotropic-energy relation and the Guiriec non-thermal luminosity/peak-energy relation, to six Fermi gamma-ray bursts.

desk verdict Useful cautionary table showing Amati and Guiriec pseudo-redshifts diverge for faint Fermi bursts, but the paper needs fixes for a likely copy-paste, a redshift inconsistency, and a circular validation before the result can be trusted. read the letter →

arxiv 1909.00887 v1 pith:YEX4NPHV submitted 2019-09-02 astro-ph.HE

classification astro-ph.HE
keywords gamma-rayburstsGRBpseudo-redshiftsAmaticorrelationGuiriecrelationnon-thermalspectralcomponentfine-timeanalysisFermiGBMTeVdetectability
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

Distances to gamma-ray bursts are hard to measure because they require multi-wavelength follow-up, so empirical redshift estimators matter. This paper takes six bright Fermi bursts and applies two estimators: the Amati correlation between rest-frame peak energy $E_{peak}$ and isotropic energy $E_{iso}$, and the Guiriec relation between the luminosity $L_i^{NT}$ and rest-frame peak energy $E_{peak,i}^{rest,NT}$ of the non-thermal component in fine-time fits. For the three bursts with measured redshifts, GRB080916C, GRB090926A and GRB150314A, both correlations reproduce the reported values. For the three fainter bursts without measured redshifts, the Amati correlation gives modest pseudo-redshifts while the Guiriec relation gives much larger ones, for example $z = 14.31 \pm 0.8$ for GRB170114A. The paper concludes that the two correlations agree for bright bursts, and that for less luminous bursts the Guiriec relation predicts higher pseudo-redshifts.

What carries the argument

The carrying object is the Guiriec correlation (equation 2.3), a power-law relation between the luminosity of the non-thermal (cutoff power-law) spectral component and its rest-frame peak energy in fine-time spectral fits: $L_i^{NT} = (9.6 \pm 1.1)\,10^{51}\,(E_{peak,i}^{rest,NT}/100\,\mathrm{keV})^{1.38 \pm 0.04}\,\mathrm{erg\,s^{-1}}$. Pseudo-redshifts are obtained by varying the redshift until each burst's $E_{peak}^{NT}$-$L^{NT}$ pairs minimize their distance to this relation. The comparison baseline is the Amati correlation, $E_p = 80\,E_{iso}^{0.57}$ keV with dispersion $\sigma = 0.18$, evaluated with $H_0 = 70\,\mathrm{km\,s^{-1}\,Mpc^{-1}}$, $\Omega_m = 0.3$, and $\Omega_\Lambda = 0.7$. Both correlations are cosmology-dependent, and the same cosmology is used for both.

What would settle it

Direct spectroscopic redshifts for GRB150105A, GRB160113A and GRB170114A from afterglow or host-galaxy observations would settle the disagreement. If, for example, GRB170114A turns out to be at $z\lesssim1$ rather than $z\approx14.3$, the universality of the Guiriec relation is falsified; if it is near $z\approx14$, the Amati correlation is the one that fails for faint bursts.

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Extended reading notes

Core claim

The central claim is that the Guiriec relation, $L_i^{NT} = (9.6 \pm 1.1)\,10^{51}\,(E_{peak,i}^{rest,NT}/100\,\mathrm{keV})^{1.38 \pm 0.04}\,\mathrm{erg\,s^{-1}}$, can be inverted to estimate a pseudo-redshift for any Fermi burst by varying $z$ until the burst's rest-frame non-thermal peak-energy/luminosity pairs fall on this relation. Applied to the sample, the inversion reproduces the measured redshifts of GRB080916C (inferred $3.96 \pm 0.24$ versus reported $4.15 \pm 0.15$), GRB090926A ($2.12 \pm 0.16$ versus $2.106$), and GRB150314A ($1.9 \pm 0.13$ versus $1.758$). For the three bursts without measured redshifts, GRB150105A, GRB160113A and GRB170114A, the Guiriec estimator gives $z = 3.21 \pm 0.25$, $2.71 \pm 0.2$, and $14.31 \pm 0.8$, while the Amati correlation gives ranges $0.1$-$0.5$, $0.2$-$1.7$, and $>0.7$ respectively. The paper's conclusion is that the two correlations are in agreement for bright bursts, and that for less luminous bursts the $E_{peak,i}^{NT}$-$L_i$ correlation predicts higher pseudo-redshifts.

Load-bearing premise

The load-bearing premise is that the Guiriec relation between the non-thermal component's peak energy and luminosity is universal for all Fermi bursts, so varying the redshift until data land on that single curve gives the true distance; if the relation does not hold for fainter, less luminous bursts, the extreme pseudo-redshifts (e.g. $z\approx14.3$) and the disagreement with Amati are artifacts.

Editorial extensions

If this is right

  • For bright bursts, the Guiriec relation can serve as a pseudo-redshift estimator consistent with the Amati correlation and with optical redshifts.
  • For less luminous bursts, the two estimators disagree: the Guiriec relation returns higher pseudo-redshifts, for example $z=3.21\pm0.25$ versus an Amati range of $0.1$ to $0.5$ for GRB150105A.
  • For the faint bursts, the Amati correlation yields only broad ranges while the Guiriec relation gives narrower values; for GRB170114A the Amati range ($z>0.7$) includes the Guiriec value.
  • When the Guiriec values are taken at face value, none of the six bursts in this sample would be expected to be detected by TeV instruments.

Reading between the lines

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

  • The three bright bursts used for validation are the same kind of objects that were used to establish the Guiriec relation, so part of the agreement may reflect the calibration sample; a decisive test needs faint bursts with measured redshifts.
  • The divergence for faint bursts is consistent with a luminosity-dependent normalization or slope of the $E_{peak}^{NT}$-$L^{NT}$ relation, a possibility that could be tested by stacking a larger Fermi sample with direct redshifts.
  • If the Guiriec pseudo-redshift for GRB170114A ($z \approx 14.3$) is correct, that burst would be among the most distant transients known; independent checks like the optical depth of the high-energy emission or late-time afterglow observations could test this.
  • The results also assume that the three-component spectral decomposition (black body, cutoff power law, power law) is the right model for every burst; misidentification of components in fainter, noisier spectra could create part of the reported offset.
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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. The paper applies two empirical GRB correlations to six Fermi/GBM bursts: the Amati E_peak–E_iso relation (eq. 2.1) and the Guiriec E^{NT}_peak,i–L^{NT}_i relation (eq. 2.3). For each burst, the authors infer a pseudo-redshift range by (for the Amati relation) adjusting z until the measured Band-function parameters satisfy eq. 2.1, and (for the Guiriec relation) varying z until a fine-time three-component spectral analysis places the burst's non-thermal component on eq. 2.3. They report that the two methods agree for three bright bursts with measured redshifts (GRB080916C, GRB090926A, GRB150314A) and disagree for three fainter bursts (GRB150105A, GRB160113A, GRB170114A), for which the Guiriec relation yields considerably higher pseudo-redshifts, including z = 14.31 ± 0.8 for GRB170114A. The paper concludes that the two correlations agree for bright bursts but that the E^{NT}_peak,i–Luminosity relation predicts higher pseudo-redshifts for less luminous bursts.

Significance. If the central claim were established, the paper would provide a useful cross-check of two pseudo-redshift estimators and suggest that the Guiriec relation may overestimate distances for fainter bursts. The paper is transparent in stating its key assumption that eq. 2.3 is universal for all Fermi bursts, and it presents a clear table and figures that display the claimed bright/faint dichotomy. However, the evidence is weakened by the likely circularity of the bright-burst checks, the absence of any validation for fainter bursts, and an apparent data duplication in the Band parameters. The paper's value is therefore currently more as a suggestive case study than as a definitive constraint on either correlation.

major comments (4)
  1. [Section 2, end of Section 4] The central claim about faint bursts rests entirely on the assumption, stated at the end of Section 2, that eq. (2.3) is universal for all Fermi bursts. No test is performed for the three fainter bursts to check that their inferred E^{NT}_peak,i and L^{NT}_i values lie within the luminosity and energy range of the sample from which eq. (2.3) was calibrated. Applying a relation calibrated on bright Fermi bursts to much fainter objects is an extrapolation; without such a check, the higher pseudo-redshifts reported in Table 1 for GRB150105A, GRB160113A, and especially GRB170114A (z = 14.31 ± 0.8) may be artifacts of extrapolation rather than measurements.
  2. [Section 4, first paragraph] The validation of eq. (2.3) on GRB080916C and GRB090926A is circular, because the text itself states that these bursts 'were used to validate the correlation presented in eq.2.3' and that the spectral analysis follows the procedure of [12], from which eq. (2.3) was derived. If these two bursts are part of the calibration sample, their consistency with the relation is not an independent test. The only potentially independent bright-burst check is GRB150314A, and a single object is insufficient to support the claimed general bright/faint dichotomy.
  3. [Section 3] The Band-function parameters quoted for GRB150105A are identical to those quoted for GRB090926A: E_peak = 296 ± 7 keV, α = -0.78 ± 0.02, β = -2.43 ± 0.04. This appears to be a copy-paste error. If the actual parameters for GRB150105A differ, the Amati redshift range in Table 1 (0.1 < z < 0.5) is invalid, and the claimed one-order-of-magnitude discrepancy with the Guiriec pseudo-redshift (3.21 ± 0.25) is not meaningful as printed.
  4. [Section 2 and Section 4] The procedure for obtaining pseudo-redshifts from eq. (2.3) is described only as 'varying the redshift until the relation ... becomes the relation 2.3' and as finding the correlation 'more alike to relation 2.3' (Figure 3 caption). No figure of merit, fitting statistic, or confidence-interval construction is specified, so the quoted uncertainties in Table 1 (e.g., 3.96 ± 0.24, 14.31 ± 0.8) are not reproducible from the text. The paper should define the minimization criterion and the method used to propagate errors.
minor comments (5)
  1. [Section 4] The text reports 'z = 2.12± 016' for GRB090926A; the uncertainty should read ±0.16.
  2. [Figure 4 caption] The caption gives the reported redshift of GRB080916C as 4.35 ± 0.15, while the text and Table 1 give 4.15 ± 0.15; one of these values is a typo and should be corrected.
  3. [Section 4] The burst is referred to as 'GRB170114' in the text while Table 1 and Section 3 use 'GRB170114A'; the notation should be made consistent.
  4. [Section 4] The sentence 'the two correlations seems to be in agreement' contains a subject-verb agreement error; it should be 'seem to be in agreement.'
  5. [Figure 3] The left panel is described in the caption as the E_peak–flux correlation, but the text in Section 4 refers to 'E_peak-Flux correlation as it is seen in left panel'; the axes and quantities plotted should be labeled explicitly so the reader can verify which quantity corresponds to the non-thermal component.

Circularity Check

1 steps flagged · score 6.0 of 10

The bright-burst 'validation' of Eq. 2.3 is in-sample, while the faint-burst pseudo-redshifts are an extrapolation under an explicit universality assumption.

  1. fitted input called prediction [Section 4, Results and discussion (validation of Eq. 2.3; Table 1)]
    "Burst GRB080916C and GRB090926A present clear deviations from the Band function as reported by [12] and both have been used to test theoretical models. These bursts were used to validate the correlation presented in eq.2.3. In particular, for GRB 090926A we find the correlation shown in figure 2 which is in agreement with equation 2.3."

    Equation 2.3 is imported from [12] as the E^NT_peak,i-Luminosity correlation, and the paper's positive check of the bright-burst pseudo-redshifts rests on GRB080916C and GRB090926A. The text itself says these bursts 'were used to validate the correlation presented in eq.2.3.' Recovering z ~ 3.96 for GRB080916C (reported 4.15) and z ~ 2.12 for GRB090926A (reported 2.106) is therefore an in-sample consistency check, not an independent prediction. The statement that 'the two correlations seems to be in agreement for bright bursts' is thus partly supported by data that were already used to validate the same relation in the prior work establishing Eq. 2.3.

full rationale

The paper's two correlation inversions are, on their face, normal uses of empirical relations. For the Amati correlation, fixed parameters from [10] are applied to independently fitted Band spectra, and the resulting redshift ranges are compared with the Guiriec-relation results. For the E^NT_peak,i-Luminosity relation, the procedure is to vary z until each burst satisfies Eq. 2.3; this is an inversion, not a circularity, provided Eq. 2.3 is independent of the target burst. The problem is located in the validation of that relation. Eq. 2.3 is taken from [12], and the paper's bright-burst checks are GRB080916C and GRB090926A. Section 4 states that these two bursts 'were used to validate the correlation presented in eq.2.3.' Therefore their recovered pseudo-redshifts (3.96 vs 4.15 and 2.12 vs 2.106) are in-sample consistency checks, not independent predictions. This makes the 'agreement for bright bursts' conclusion partly circular. The third bright burst, GRB150314A, provides independent support, and the faint-burst numbers are new extrapolations; they are not forced by construction but rest on the paper's explicit universality assumption. The exact duplication of the GRB090926A Band parameters for GRB150105A is a separate data-integrity problem, not a circularity, but it weakens the printed Amati comparison for that burst. Overall this is partial circularity, hence 6.

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

The paper's central results rest on five empirical constants adopted from two prior correlation papers (Amati 2006; Guiriec et al. 2015) and on four modeling assumptions about the GRB spectral decomposition and cosmology. It introduces no new entities or hand-chosen parameters of its own; the pseudo-redshifts are solved quantities. The burden is therefore not in what the paper fits, but in trusting the two external relations, especially their extrapolation to fainter bursts, and in accepting the manuscript's reported spectral parameters and redshifts.

free parameters (5)
  • Amati normalization K = 80.0
    Adopted from Amati (2006) [10] in eq 2.1 without refitting; the Amati-based pseudo-redshift ranges depend on it.
  • Amati slope m = 0.57
    Adopted from Amati (2006) [10] in eq 2.1; a fitted empirical constant from prior literature.
  • Amati dispersion sigma = 0.18
    Adopted from [10] to define the pseudo-redshift ranges in Table 1; the paper never explains how the dispersion is converted into a redshift range.
  • Guiriec normalization L0 = (9.6 +/- 1.1) x 10^51 erg/s
    Adopted from Guiriec et al. 2015 [12] in eq 2.3; central input for all luminosity-peak energy pseudo-redshifts.
  • Guiriec slope gamma = 1.38 +/- 0.04
    Adopted from Guiriec et al. 2015 [12] in eq 2.3; central input for all luminosity-peak energy pseudo-redshifts.
assumptions (5)
  • domain assumption Standard flat Lambda-CDM cosmology with H0 = 70 km/s/Mpc, Omega_m = 0.3, Omega_Lambda = 0.7
    Used to compute luminosity distance in eq 2.2 for both correlations (Section 2).
  • domain assumption Universality of the Guiriec relation, eq 2.3, for all Fermi bursts
    Section 2 states 'We assume that the relation 2.3 is universal for all Fermi bursts'; this is the core premise for all luminosity-peak energy pseudo-redshifts.
  • domain assumption Three-component spectral decomposition (BB, NT, PL) is applicable to every burst in the sample
    Section 2 and 3; the fine-time analysis assumes this decomposition for faint bursts without testing alternatives.
  • domain assumption Band function adequately models the time-integrated spectra for the Amati analysis
    Section 3; all Amati Epeak values come from single Band-function fits, while the cited literature reports spectral deviations in bright bursts [12].
  • domain assumption Reported redshift of GRB080916C is z = 4.15
    Used in Table 1 and Section 4 as the validation reference; the Fig. 4 caption and the cited GROND measurement [18] give 4.35, so the assumption as printed appears erroneous.

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Cite this review

Pith. "Pith review of Constraining GRBs pseudo-redshift using different empirical correlations." pith.science (2026). https://pith.science/paper/YEX4NPHV

@misc{pith2026190900887,
  author       = {Pith},
  title        = {Pith review of: Constraining GRBs pseudo-redshift using different empirical correlations},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/YEX4NPHV}},
  note         = {Machine review of arXiv:1909.00887}
}
abstract

The determination of distances is highly constrained to a small number of Gamma-Ray Bursts (GRBs) because it requires observations at different wavelengths. Some empirical functions to estimate redshifts have been identified using populations of GRBs with reported redshifts. For example, the Amati correlation relates $E_{peak}$ of the spectrum when modeled with a Band function and the total energy emitted $E_{iso}$ in a time integrated analysis. A multiple-component scenario has been proposed in order to explain GRBs spectra, and in this context when a fine-time spectral analysis is performed a correlation between the non-thermal component's peak energy and the luminosity ($E_{peak,i} - L_i$) appears. This correlation is also used to infer distances to GRBs. In this work we present a sample of bright GRBs and apply these empirical correlations to constrain the pseudo-redshift of the selected burst sample. Our results for GRB080916C, GRB090926A and GRB150214A with reported redshift are totally consistent. Another three bursts with lower luminosities were selected. For these bursts, the pseudo-redshift range obtained with the two correlations are not totally in agreement.

Figures

Figures reproduced from arXiv: 1909.00887 by the authors.

Figure 1
Figure 1. GRB080916C, GRB090926A and GRB150314A with reported redshifts follow the Am [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗
Figure 2
Figure 2. E NT peak,i - L NT i correlation for GRB090926A in a fine time spectral analysis following the procedure presented in [12]. To obtain the pseudo-redshift of these bursts using the E NT peak,i - L NT i correlation we followed the procedure described in section 2. First, we obtain the Epeak-Flux correlation as it is seen in left panel of figure 3. Then, we obtain the E NT peak,i - L NT i correlation that is more alike… view at source ↗
Figure 3
Figure 3. In the left panel the plot of Epeak-Flux of the non thermal component when fitting a three component scenario in a fine time analysis is presented. In the right panel in dotted lines the best E NT peak,i -Luminosity at the rest frame that minimize the distance to the relation 2.3 used to obtain pseudo-redshifts [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figures from the paper (2 more)
Figure 4
Figure 4. Figure 4: The two correlations applied to GRB090926A, GRB080916C and GRB150314A. The [PITH_FULL_IMAGE:figures/full_fig_p007_4.png]
Figure 5
Figure 5. Figure 5: The two correlations applied to GRB150105A, GRB160113A and GRB170114A. The [PITH_FULL_IMAGE:figures/full_fig_p008_5.png]

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