The peak flux of long gamma-ray bursts in the E$_{\rm p,i}$--L$_{\rm iso}$ diagram and in the classification

Guangxuan Lan; Jean-Luc Atteia

REVIEW 4 major objections 5 minor 36 references

The peak flux of long gamma-ray bursts in the E$_{\rm p,i}$--L$_{\rm iso}$ diagram and in the classification

T0 review · 4 major / 5 minor · reviewed 2026-08-06 · deepseek-v4-flash

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

Pith's one-line read The paper claims that peak-flux selection significantly changes the observed ($E_{\rm p,i}$, $L_{\rm iso}$) distribution of long gamma-ray bursts, so the correlation's use as a standard candle requires correcting for this selection.

desk verdict Useful caution about peak-flux cuts in Ep,i–Liso fits, but the claim that the correlation is intrinsic is not yet supported by the simulation as constructed. read the letter →

arxiv 2506.20374 v1 pith:5BDL2BYJ submitted 2025-06-25 astro-ph.HE

Guangxuan Lan , Jean-Luc Atteia This is my paper · ORCID

classification astro-ph.HE

keywords gamma-rayburstslongGRBsEpi-LisocorrelationpeakfluxselectioneffectsGRBluminosityfunctionclassificationstandardcandles

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 argues that peak-flux selection—the observational filter that decides which long gamma-ray bursts (LGRBs) are detected and get redshifts—significantly shapes the observed joint distribution of rest-frame peak energy $E_{\rm p,i}$ and isotropic luminosity $L_{\rm iso}$. Because the best-fit $E_{\rm p,i}$–$L_{\rm iso}$ correlation is computed from that distribution, its slope and intercept change when samples are cut by peak flux, so the relation cannot be used as a standard candle or as a probe of GRB physics without modeling this selection. To show this, the authors simulate a 10,000-burst population calibrated to Swift observations. They also find the observed peak-flux distribution is reproduced only when an intrinsic $E_{\rm p,i}$–$L_{\rm iso}$ connection is included, strengthening the case that the correlation is real, and they identify two bursts in the low-luminosity corner whose likely merger origins suggest the diagram plus peak flux can flag non-collapsar LGRBs.

What carries the argument

The load-bearing instrument is a synthetic population of 10,000 LGRBs generated from the GRB world model of Lan et al. (2021): mock redshifts and luminosities are drawn from rate and luminosity functions that include trigger and redshift-measurement probabilities, mock rest-frame peak energies are sampled from the observed Swift ($E_{\rm p,i}$, $L_{\rm iso}$) distribution, mock spectral indices from the observed ($\alpha$, $E_{\rm p,o}$) distribution, and mock peak fluxes are then computed self-consistently from $z$, $L_{\rm iso}$, $E_{\rm p,o}$, and $\alpha$. The sample is retained only if one- and two-dimensional Kolmogorov-Smirnov tests fail to reject agreement with the observed Swift sample at the 5% significance level. The argument proceeds by comparing best-fit $E_{\rm p,i}$–$L_{\rm iso}$ relations across peak-flux bins and redshift bins, and by checking whether the simulated $P$ distribution matches observations only when an intrinsic $E_{\rm p,i}$–$L_{\rm iso}$ dependence is present.

What would settle it

One concrete check would be to take a large, redshift-complete sample of long GRBs with a well-understood peak-flux selection function, correct the observed ($E_{\rm p,i}$, $L_{\rm iso}$) distribution for that selection, and then re-fit the correlation in separate peak-flux bins. If the corrected distributions in different $P$ bins coincide, the claim that $P$ reshapes the ($E_{\rm p,i}$, $L_{\rm iso}$) plane is contradicted. A simpler version within current data is to restrict the mock comparison to $L_{\rm iso}\ge10^{50.5}$ erg s$^{-1}$ and test whether the predicted ordering of best-fit slopes across $\log P$ bins survives when the selection function is varied.

Watch

Extended reading notes

Core claim

On the paper's own terms, the central discovery is that the two-dimensional ($E_{\rm p,i}$, $L_{\rm iso}$) distribution of long GRBs is not a fixed population: it depends explicitly on the peak flux $P$. Fitting the $E_{\rm p,i}$–$L_{\rm iso}$ relation separately for different $\log P$ ranges yields slopes from $0.27\pm0.02$ to $0.37\pm0.01$ across the full simulated sample, and the low- and high-$P$ populations barely overlap. The same simulation shows the observed $P$ distribution cannot be matched unless an intrinsic $E_{\rm p,i}$–$L_{\rm iso}$ dependence is built in, which the authors take as evidence that the correlation is a crucial physical property of LGRBs. The paper further claims that high-peak-flux bursts in the low-$E_{\rm p,i}$, low-$L_{\rm iso}$ corner are not the simple extrapolation of the high-peak-flux population, and that selecting $L_{\rm iso}\le10^{50}$ erg s$^{-1}$, $E_{\rm p,i}\le10^{2.5}$ keV, and $P\ge10^{0.5}$ ph cm$^{-2}$ s$^{-1}$ picks out GRB 060614 and GRB 191019A, both plausibly of merger rather than massive-star origin.

Load-bearing premise

The load-bearing assumption is that the observed Swift two-dimensional ($E_{\rm p,i}$, $L_{\rm iso}$) distribution used to seed the simulation is itself an unbiased picture of the intrinsic GRB population; if that distribution is already distorted by the same peak-flux selection under study, the simulated $P$-dependence could be a circular artifact.

Editorial extensions

If this is right

Any flux-limited sample of LGRBs selects a specific slice of the ($E_{\rm p,i}$, $L_{\rm iso}$) plane, so the best-fit correlation from one sample should not be compared directly with another sample selected at a different peak-flux threshold.
Cosmological uses of the $E_{\rm p,i}$–$L_{\rm iso}$ relation, such as standardizing LGRB luminosities to build a Hubble diagram, need an explicit model of peak-flux selection; otherwise the derived distances can be biased.
The fact that the observed peak-flux distribution is reproduced only when an intrinsic $E_{\rm p,i}$–$L_{\rm iso}$ link is included supports the physical reality of the correlation rather than a purely selection-driven origin.
Selecting $L_{\rm iso}\le10^{50}$ erg s$^{-1}$, $E_{\rm p,i}\le10^{2.5}$ keV, and $P\ge10^{0.5}$ ph cm$^{-2}$ s$^{-1}$ isolates bursts such as GRB 060614 and GRB 191019A, suggesting the diagram combined with peak flux can identify long GRBs with non-collapsar progenitors.
Earlier estimates of the $E_{\rm p,i}$–$L_{\rm iso}$ relation were probably dominated by luminous bursts with moderate-to-high peak flux, so the full population may have a wider and differently sloped correlation.

Reading between the lines

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

Editorial extensions beyond the paper's claims: if the peak-flux dependence is real, the next necessary step is to invert the selection function and reconstruct the intrinsic two-dimensional distribution directly from data, rather than sampling the observed distribution as the simulation does.
A testable prediction follows for future samples with nearly complete redshift follow-up at lower $E_{\rm p,i}$ and $L_{\rm iso}$: the low-corner bursts should split into two populations, one with supernova associations and one without.
The same selection logic should apply to other GRB correlations such as $E_{\rm p,i}$–$E_{\rm iso}$ or multi-parameter relations, where peak-flux cuts may alter fitted slopes in an analogous way.
The paper's classification criterion is conditional on peak flux, which implies that proposed boundaries in the ($E_{\rm p,i}$, $L_{\rm iso}$) plane should be treated as functions of $P$, a concrete and checkable prediction.

Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

Colleague,

The paper makes one point I think is right and one that doesn't yet land. The right point: if you fit Ep,i–Liso on Swift-like samples, applying different peak-flux cuts gives you different best-fit slopes. Their Table 1 shows that cleanly in a mock, and it's a useful warning for anyone using this relation as a standard candle. The second point—that the Ep,i–Liso connection is a crucial intrinsic property because the mock can't reproduce the observed P distribution without it—is asserted but not demonstrated. Section 3.1 says the no-correlation version fails, but no CDF, no KS statistic, no figure. That's the load-bearing support for the "intrinsic" language, and it's missing.

The bigger problem is circularity. In step 3 of Section 2.1, mock Ep,i is drawn from the observed Swift (Ep,i, Liso) distribution of 259 bursts with P≥0.5. That observed distribution is already shaped by the very selection the paper studies. So when they bin the mock by P and see different slopes, they are re-discovering the selection effect they imported. It's a valid demonstration that P cuts matter for the observed correlation, but it doesn't tell you about the intrinsic relation. The no-correlation test, if shown properly with Ep,i drawn independent of Liso from a plausible marginal, could fix this—but it has to be shown, and the intrinsic distribution has to be constructed without using the biased sample.

What the paper does well: the simulation is carefully built on the Lan et al. (2021) world model, the KS checks are standard, and the authors are transparent about mock artifacts like the 4% faint-P excess and the Ep,o fitting jump. The four-burst subgroup (060614, 161219B, 191019A, 230328B) is a suggestive post-hoc selection; two of the four are known non-collapsars, which is interesting but a sample of four can't carry much weight. The references to Butler et al., Shahmoradi, and Palmerio & Daigne are appropriate; this is a quantitative extension of known selection concerns, not a wholly new effect.

Who's this for: anyone fitting spectral–luminosity correlations on Swift GRBs, and people building population models. It deserves peer review, but the referee should ask for the no-correlation baseline, a discussion of how the imported 2D distribution limits the intrinsic claim, and a softer framing of the subgroup result.

Referee Report

4 major / 5 minor

Summary. The paper builds a simulated population of 10,000 long GRBs from the Swift/BAT world model of Lan et al. (2021) in order to study how peak-flux (P) selection affects the observed Ep,i--Liso distribution and the best-fit Ep,i--Liso correlation. Redshifts and isotropic luminosities are drawn from a cosmic star-formation-rate model, a triple power-law luminosity function, and a trigger/redshift-measurement probability function; rest-frame peak energies are drawn from the observed Swift 2D (Ep,i, Liso) distribution; spectral indices are drawn from the observed (alpha, Ep,o) distribution; and P is computed self-consistently from the spectral model. The mock sample passes 1D and 2D KS tests against the 259-burst Swift sample with P >= 0.5 ph cm^-2 s^-1. The authors find that the best-fit Ep,i--Liso slope depends on the P range considered (Table 1), that the observed P distribution can be reproduced only if an Ep,i--Liso correlation is included in the simulation, and that a small group of low-Ep,i, low-Liso, high-P bursts contains objects such as GRB 060614 and GRB 191019A that may have non-collapsar origins. The paper concludes that peak-flux selection must be taken into account in applications of the Ep,i--Liso relation.

Significance. The practical message of the paper--that selection on peak flux can change the apparent Ep,i--Liso relation and that standard-candle applications need to model this selection--is important and timely for the growing use of GRB correlations in cosmology. The simulation pipeline is detailed, the construction is explicitly described, and the use of KS tests on both 1D and 2D distributions is a good validation practice that goes beyond what is often done in this literature. If the central claims hold, the paper would strengthen the case for correcting selection effects before fitting the Ep,i--Liso relation. However, the evidence for the strongest claim--that the Ep,i--Liso correlation is an intrinsic property required to reproduce the P distribution--is weakened by a circular construction: the intrinsic 2D distribution is imported from the very observed sample whose selection effects are being studied. The paper is therefore best viewed as a useful forward-modeling exercise whose conclusions need a more independent test before they can be fully accepted.

major comments (4)

[Section 3.1 and Section 4] The claim that the observed P distribution can be reproduced only if an Ep,i--Liso correlation is included in the simulation is asserted but never demonstrated. The paper states that the mock P distribution cannot be reproduced 'well' without the correlation, but it does not show the no-correlation variant: no P CDF, no KS statistic, and no description of what exactly was tried. This is a load-bearing point, since it is used to conclude that the Ep,i--Liso relation is a crucial intrinsic property of LGRBs. The authors should show the full comparison between the observed P distribution and the mock P distributions with and without an intrinsic Ep,i--Liso correlation, including the quantitative KS results.
[Section 2.1, step 3] The mock Ep,i values are drawn from the observed Swift 2D (Ep,i, Liso) distribution of the same P >= 0.5 ph cm^-2 s^-1 sample whose selection effects are under study. If that observed 2D distribution is already distorted by the P selection, then the simulation imports the very effect it claims to discover. Because P is computed directly from Liso, z, and the spectral parameters, splitting the mock sample by P naturally selects different Liso and z ranges, and the different best-fit slopes in Table 1 are a necessary consequence of coupling Ep,i to Liso. This does not independently demonstrate that the intrinsic relation changes with P. A more convincing test would generate the intrinsic (Ep,i, Liso) distribution from an assumed functional form (e.g., a bivariate lognormal or a physically motivated correlation), apply the same selection machinery, and show that the observed P and 2D distributions are recovered only when the intrinsic correlation is present, while a no-correlation intrinsic model fails even after applying the same trigger and redshift-selection probabilities.
[Section 3.3] The proposed identification of a distinct subgroup in the low-Ep,i, low-Liso, high-P region is based on four bursts selected by cuts that were chosen after inspecting the same diagram. The paper notes that two of the four (GRB 060614 and GRB 191019A) have been proposed to have non-collapsar origins, but it does not quantify the expected number of non-collapsar contaminants among LGRBs selected this way, nor does it apply the same cuts to a simulated collapsar-only population to estimate a false-positive rate. As a classifier, the proposed region needs a completeness and purity estimate; as evidence for a separate population, the present argument is anecdotal and should be either strengthened or explicitly labeled as a speculative illustration.
[Table 1 and Section 3.2] The reported differences in best-fit slopes across P bins are not accompanied by a statistical test of whether the slopes differ beyond what is expected from the different dynamic ranges and sample sizes. The 1-sigma uncertainties in Table 1 do not account for the strong covariance between the fitted slope a and intercept b, nor for the fact that low-P and high-P bins occupy very different regions of the (Ep,i, Liso) plane. Reporting the Liso range, sample size, and confidence contours (or a fit with a single relation plus a selection term) would make the claim that the P dependence is significant and not merely a boundary effect more convincing.

minor comments (5)

[Section 4] The word 'instrinsic' should be corrected to 'intrinsic'.
[Equations (1)-(2)] The selection probability function theta(P(L,z)) is used in the CDFs but is not explicitly defined in the text; a brief definition or a pointer to the corresponding Lan et al. (2021) equations would improve reproducibility.
[Figure 3] The caption states that the figure shows cumulative distributions of six quantities, but the text reproduction shows only one panel; if the published figure is multi-panel, the caption should clearly identify each panel, and if not, the caption should be revised.
[Section 3.4] The 4% of mock events with P below Plim are retained in the main analysis and then removed in a robustness check. It would be cleaner to exclude them from the beginning or to model the detection probability explicitly, rather than relying on a post-hoc removal.
[Section 2.1] The KS acceptance criterion at the 5% level is applied to many 1D and 2D distributions; reporting the number of tests performed and the resulting multiple-testing caveat would be useful.

Circularity Check

2 steps flagged · score 6.0 of 10

The simulation samples mock Ep,i from the observed (Ep,i,Liso) distribution and computes P from that same Ep,i,Liso, so the Section 3.1 'only if' proof of an intrinsic Ep,i–Liso correlation is a consistency check, not an independent prediction.

self definitional [Section 2.1 steps 3 and 5; Section 3.1]
"To obtain the mock observed peak energy Emock p,o , we first use Lmock iso to get the mock intrinsic peak energy Emock p,i based on the two-dimensional (Ep,i, Liso) distribution observed by Swift ... Finally, we complete the mock LGRB sample with Pmock being calculated from zmock,Lmock iso,Emock p,o, and αmock. ... To get mock P data that follow the observed distribution, it is mandatory to include in the simulation the correlation between the intrinsic peak energy Ep,i and the LGRB luminosity Liso."

The mock Ep,i is defined by sampling the observed (Ep,i,Liso) joint distribution, i.e. the very correlation under study. Mock P is then computed as a deterministic function of that same Ep,i (through Ep,o = Ep,i/(1+z)), Liso, z, and α. Therefore the statement that the observed P distribution 'can not be reproduced well' unless an Ep,i–Liso correlation is included is a consequence of the construction: P is computed from the input Ep,i and Liso. Reproducing the observed P distribution is a consistency check of the fitted input, not an independent test that the correlation is intrinsic. The no-correlation control is asserted but not shown, so the 'mandatory' conclusion has no independent evidentiary content.
fitted input called prediction [Section 3.2 and Table 1]
"To reveal the impact of P on the Ep,i–Liso correlation, we show in Fig 4 the Ep,i vs. Liso data with colors representing the log P values. Here we can see that the boundaries for data points with different colors (i.e. different values of log P) are significantly different."

Because Pmock is calculated from Lmock iso, zmock, Ep,o, and αmock (Section 2.1 step 5), binning the mock sample by P is almost equivalent to binning by Liso and z. The input Ep,i is drawn from the observed (Ep,i,Liso) distribution, which already contains the Ep,i–Liso correlation. The different best-fit slopes across P bins are therefore a forced consequence of the imported correlation and the luminosity function, not an independent demonstration that peak-flux selection biases an intrinsic relation. The practical warning to account for selection may be valid, but as a 'finding' it is built into the simulation input rather than derived from first principles.

full rationale

The paper's practical recommendation that peak-flux selection should be considered when fitting the Ep,i–Liso correlation is reasonable, and the identification of GRB 060614 and GRB 191019A as possible non-collapsar bursts is data-driven and independent of the simulation circularity. However, the central evidential claim in the abstract and Section 3.1—that the observed P distribution can only be reproduced if an Ep,i–Liso correlation is included, and that this proves the correlation is a crucial intrinsic property—reduces by construction. The mock Ep,i is sampled from the observed (Ep,i,Liso) joint distribution, and mock P is computed from that same Ep,i and Liso (and z,α). Thus the P distribution is a derived quantity of the very input distribution the paper claims to validate. The no-correlation variant is asserted but not shown; without it, the 'only if' statement is a consistency check of the fitted input, not a falsifiable prediction. The KS-test agreements with observed data are also partly by construction, since the same observed sample supplied the Ep,i and α distributions. Overall this is partial circularity affecting the central reality-of-correlation claim, while the practical selection-effect warning retains independent value. Score 6.

Assumptions & free parameters 5 free parameters · 4 assumptions · 1 invented entities

The central claim depends on the Lan et al. (2021) world model with its fitted luminosity function, redshift evolution, and trigger probabilities, plus empirical 2D distributions from the Swift sample. The paper introduces a hypothesized subgroup of LGRBs as an interpretation of the mock P distribution, with weak independent support.

free parameters (5)

Triple power-law luminosity function parameters = not given in this paper; from Lan et al. 2021
Used to simulate Liso in Eqs. 1 and 2; fitted to Swift observations in the cited model.
Redshift density evolution index delta = not given in this paper; from Lan et al. 2021
Modifies the star formation rate in the redshift distribution and affects the simulated z sample.
Trigger and redshift measurement probability parameters = not given in this paper; from Lan et al. 2021
Theta(P,L,z) enters the CDFs in Eqs. 1 and 2 and controls which simulated bursts would be observed by Swift.
KDE bandwidths for 2D (Ep,i,Liso) and (alpha,Ep,o) distributions
Not specified in the paper; affects the smoothness of the empirical distributions from which mock Ep,i and alpha are drawn.
Limiting luminosity Llim(z) derived from Plim=0.5 ph cm-2 s-1
Sets the lower bound in luminosity sampling and depends on average spectral parameters; a modeling choice that influences the mock sample.

assumptions (4)

standard math Flat ΛCDM cosmology with H0=70 km/s/Mpc, Omega_m=0.3, Omega_Lambda=0.7
Adopted for distance and volume computations; standard in the field.
domain assumption The cut-off power-law (CPL) spectral model describes the time-integrated Swift/BAT spectra of LGRBs
Used to compute peak flux P and rest-frame quantities; standard but not universally valid for all GRB spectra.
domain assumption The Swift observed sample (259 bursts with P>=0.5 and 15<=Ep,o<=9000 keV) is representative of the LGRB population after accounting for selection via the world model
The mock sample is validated against this sample with KS tests, and the 2D distributions are drawn from it.
ad hoc to paper The existence of a distinct subgroup of LGRBs in the low-Ep,i, low-Liso, high-P region
Hypothesized in Section 3.3 to explain the anomalous P distribution; not independently established, and only 4 observed bursts satisfy the selection.

invented entities (1)

Proposed low-Ep,i, low-Liso, high-P subgroup of LGRBs with possible non-collapsar origins independent evidence
purpose: Explains the anomalous peak flux distribution in the lower-left corner of the Ep,i-Liso diagram and identifies potential merger-origin GRBs.
The paper provides a falsifiable handle: future bursts with Liso<=1e50 erg/s, Ep,i<=1e2.5 keV, and P>=1e0.5 ph/cm2/s can be tested for supernova association. The two historical examples (GRB 060614 and GRB 191019A) are already known to lack supernovae.

how reviews work

0 comments

Cite this review

Pith. "Pith review of The peak flux of long gamma-ray bursts in the E$_{\rm p,i}$--L$_{\rm iso}$ diagram and in the classification." pith.science (2026). https://pith.science/paper/5BDL2BYJ

@misc{pith2026250620374,
  author       = {Pith},
  title        = {Pith review of: The peak flux of long gamma-ray bursts in the E$_\rm p,i$--L$_\rm iso$ diagram and in the classification},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/5BDL2BYJ}},
  note         = {Machine review of arXiv:2506.20374}
}

abstract

The E$_{\rm p,i}$--L$_{\rm iso}$ correlation of long gamma-ray bursts (LGRBs) is regarded as a fundamental correlation for standardizing LGRBs to probe cosmology and constrain LGRB physics. However, this correlation may be affected by potential selection effects which are likely overlooked in the current small LGRB redshift sample. In this work, we simulate a large LGRB sample that reflects the observed situation, aiming to study the impact of peak flux $P$ on the observed LGRB E$_{\rm p,i}$--L$_{\rm iso}$ correlation. We find that the overall (E$_{\rm p,i}$, L$_{\rm iso}$) distribution, which will directly affect the best-fit result of the correlation, is significantly dependent on the value of $P$. This indicates that the impact of peak flux selection should be carefully considered in the studies and applications of the E$_{\rm p,i}$--L$_{\rm iso}$ correlation. Notably, we show that our simulated data can reproduce the observed $P$ distribution only if some dependence of (E$_{\rm p,i}$, L$_{\rm iso}$) is included in the simulation. This is an indication that the (E$_{\rm p,i}$, L$_{\rm iso}$) connection is a crucial property of LGRBs. We also find that GRBs with high peak flux in the low-E$_{\rm p,i}$ & L$_{\rm iso}$ region are not the straightforward extrapolation of the GRB population in the higher-E$_{\rm p,i}$ & L$_{\rm iso}$ region. Selecting four bursts with $ L_{\rm iso}\le10^{50}$ erg s$^{-1}$, $E_{\rm p, i}\le10^{2.5}$ keV, and $P\ge10^{0.5}$ ph cm$^{-2}$ s$^{-1}$, we find two bursts, GRB 060614 and GRB 191019A, which may not be associated with the theoretical massive-star origin of LGRBs. This suggests that combining $P$ with the position in the E$_{\rm p,i}$--L$_{\rm iso}$ diagram may be used to indicate alternative LGRB origins.

Figures

Figures reproduced from arXiv: 2506.20374 by the authors.

**Figure 1.** The Ep,i vs. Liso distribution for 259 Swift observed GRBs with a measured redshift. The colors represent the different values of log P. The three fitted lines are bestfit results for the Ep,i–Liso correlation based on the sample in this work (solid), the total sample (dashed) and the complete sample (dash-dotted) in Nava et al. (2012), respectively. The dotted lines are 1σ confidence interval of the solid line.… view at source ↗

**Figure 2.** The joint distributions of parameters Liso vs. z (upper-left), Ep,i vs. Liso (upper-right), Ep,o vs. Liso (bottom-left) and α vs. Ep,o (bottom-right) for both simulated data (blue points) and observed data (red star symbols). In the upperleft panel, some observed points are located below the lower limit of simulated luminosity because the limiting luminosity is estimated with average spectral parameters which can o… view at source ↗

**Figure 3.** The cumulative distributions of peak flux P, redshift z, luminosity Liso, and spectral power-law index α, observed peak energy Ep,o, and rest-frame peak energy Ep,i of LGRBs. The blue curves represent the mock data, and the red curves represent the observed data from Swift catalog. In each diagram, the null hypothesis that both simulated and observed data sets were drawn from the same continuous distribution is not … view at source ↗

Figures from the paper (2 more)

**Figure 4.** Figure 4: The Ep,i vs. Liso distribution for the mock data. The colors represent the different levels of log P values. The four gray lines are best-fit Ep,i–Liso relations for the entire mock data with log P ≤ 0 (dotted), 0 ≤ log P ≤ 1 (dashdotted), 1 ≤ log P ≤ 2 (dashed) and l…

**Figure 5.** Figure 5: The Ep,i vs. Liso distribution for the mock data. Data with P > 2.6 are highlighted with colors representing the different levels of log z values. The four gray lines are best-fit Ep,i–Liso relations for bright data with z < 1 (solid), 1 < z < 3 (dashed), 3 < z < 5 (da…

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

36 extracted references · 4 canonical work pages

[1]

2019, MNRAS, 486, L46, doi: 10.1093/mnrasl/slz056

Tantalo, M. 2019, MNRAS, 486, L46, doi: 10.1093/mnrasl/slz056

doi:10.1093/mnrasl/slz056 2019
[2]

2002, A&A, 390, 81, doi: 10.1051/0004-6361:20020722

Amati, L., Frontera, F., Tavani, M., et al. 2002, A&A, 390, 81, doi: 10.1051/0004-6361:20020722

doi:10.1051/0004-6361:20020722 2002
[3]

Atteia, J. L. 2003, A&A, 407, L1, doi: 10.1051/0004-6361:20030958

doi:10.1051/0004-6361:20030958 2003
[4]

L., Cordier, B., & Wei, J

Atteia, J. L., Cordier, B., & Wei, J. 2022, International Journal of Modern Physics D, 31, 2230008, doi: 10.1142/S0218271822300087

doi:10.1142/s0218271822300087 2022
[5]

Band, D. L. 2003, ApJ, 588, 945, doi: 10.1086/374242

work page doi:10.1086/374242 2003
[6]

L., & Preece, R

Band, D. L., & Preece, R. D. 2005, ApJ, 627, 319, doi: 10.1086/430402

doi:10.1086/430402 2005
[7]

R., Bloom, J

Butler, N. R., Bloom, J. S., & Poznanski, D. 2010, ApJ, 711, 495, doi: 10.1088/0004-637X/711/1/495

doi:10.1088/0004-637x/711/1/495 2010
[8]

R., Kocevski, D., Bloom, J

Butler, N. R., Kocevski, D., Bloom, J. S., & Curtis, J. L. 2007, ApJ, 671, 656, doi: 10.1086/522492

doi:10.1086/522492 2007

Show all 36 references

[9]

C., Schaefer, B

Collazzi, A. C., Schaefer, B. E., Goldstein, A., & Preece, R. D. 2012, ApJ, 747, 39, doi: 10.1088/0004-637X/747/1/39

2012 doi
[10]

G., & Amati, L

Dainotti, M. G., & Amati, L. 2018, PASP, 130, 051001, doi: 10.1088/1538-3873/aaa8d7 peak flux in LGRB fundamental diagram 9

2018 doi
[11]

P., Barthelmy, S

Gehrels, N., Norris, J. P., Barthelmy, S. D., et al. 2006, Nature, 444, 1044, doi: 10.1038/nature05376 Heussaﬀ, V., Atteia, J. L., & Zolnierowski, Y. 2013, A&A, 557, A100, doi: 10.1051/0004-6361/201321528

2006 doi
[12]

2019, Nature Communications, 10, 1504, doi: 10.1038/s41467-019-09281-z

Ito, H., Matsumoto, J., Nagataki, S., et al. 2019, Nature Communications, 10, 1504, doi: 10.1038/s41467-019-09281-z

2019 doi
[13]

2012, ApJ, 747, 146, doi: 10.1088/0004-637X/747/2/146

Kocevski, D. 2012, ApJ, 747, 146, doi: 10.1088/0004-637X/747/2/146

2012 doi
[14]

2022, ApJ, 938, 129, doi: 10.3847/1538-4357/ac8fec

Lan, G.-X., Wei, J.-J., Li, Y., Zeng, H.-D., & Wu, X.-F. 2022, ApJ, 938, 129, doi: 10.3847/1538-4357/ac8fec

2022 doi
[15]

2021, MNRAS, 508, 52, doi: 10.1093/mnras/stab2508

Lan, G.-X., Wei, J.-J., Zeng, H.-D., Li, Y., & Wu, X.-F. 2021, MNRAS, 508, 52, doi: 10.1093/mnras/stab2508

2021 doi
[16]

2019, MNRAS, 488, 4607, doi: 10.1093/mnras/stz2011

Lan, G.-X., Zeng, H.-D., Wei, J.-J., & Wu, X.-F. 2019, MNRAS, 488, 4607, doi: 10.1093/mnras/stz2011

2019 doi
[17]

J., Malesani, D

Levan, A. J., Malesani, D. B., Gompertz, B. P., et al. 2023, Nature Astronomy, 7, 976, doi: 10.1038/s41550-023-01998-8

2023 doi
[18]

2007, MNRAS, 379, L55, doi: 10.1111/j.1745-3933.2007.00333.x

Li, L.-X. 2007, MNRAS, 379, L55, doi: 10.1111/j.1745-3933.2007.00333.x

2007
[19]

2005, MNRAS, 360, L73, doi: 10.1111/j.1745-3933.2005.00049.x

Nakar, E., & Piran, T. 2005, MNRAS, 360, L73, doi: 10.1111/j.1745-3933.2005.00049.x

2005
[20]

2008, MNRAS, 391, 639, doi: 10.1111/j.1365-2966.2008.13758.x

Nava, L., Ghirlanda, G., Ghisellini, G., & Firmani, C. 2008, MNRAS, 391, 639, doi: 10.1111/j.1365-2966.2008.13758.x

2008
[21]

2012, MNRAS, 421, 1256, doi: 10.1111/j.1365-2966.2011.20394.x

Nava, L., Salvaterra, R., Ghirlanda, G., et al. 2012, MNRAS, 421, 1256, doi: 10.1111/j.1365-2966.2011.20394.x

2012
[22]

T., & Daigne, F

Palmerio, J. T., & Daigne, F. 2021, A&A, 649, A166, doi: 10.1051/0004-6361/202039929

2021 doi
[23]

Peacock, J. A. 1983, MNRAS, 202, 615, doi: 10.1093/mnras/202.3.615

1983 doi
[24]

A., Kr¨ uhler, T., Schulze, S., et al

Perley, D. A., Kr¨ uhler, T., Schulze, S., et al. 2016, ApJ, 817, 7, doi: 10.3847/0004-637X/817/1/7

2016 doi
[25]

2016, A&A, 587, A40, doi: 10.1051/0004-6361/201526760

Pescalli, A., Ghirlanda, G., Salvaterra, R., et al. 2016, A&A, 587, A40, doi: 10.1051/0004-6361/201526760

2016 doi
[26]

2015, ApJ, 806, 44, doi: 10.1088/0004-637X/806/1/44

Petrosian, V., Kitanidis, E., & Kocevski, D. 2015, ApJ, 806, 44, doi: 10.1088/0004-637X/806/1/44

2015 doi
[27]

D., et al

Salvaterra, R., Campana, S., Vergani, S. D., et al. 2012, ApJ, 749, 68, doi: 10.1088/0004-637X/749/1/68

2012 doi
[28]

2013, ApJ, 766, 111, doi: 10.1088/0004-637X/766/2/111

Shahmoradi, A. 2013, ApJ, 766, 111, doi: 10.1088/0004-637X/766/2/111

2013 doi
[30]

2013, ApJL, 772, L8, doi: 10.1088/2041-8205/772/1/L8

Tan, W.-W., Cao, X.-F., & Yu, Y.-W. 2013, ApJL, 772, L8, doi: 10.1088/2041-8205/772/1/L8

2013 doi
[31]

2010, MNRAS, 406, 1944, doi: 10.1111/j.1365-2966.2010.16787.x

Wanderman, D., & Piran, T. 2010, MNRAS, 406, 1944, doi: 10.1111/j.1365-2966.2010.16787.x

2010
[32]

Y., Dai, Z

Wang, F. Y., Dai, Z. G., & Liang, E. W. 2015, NewAR, 67, 1, doi: 10.1016/j.newar.2015.03.001

2015 doi
[33]

2016, arXiv e-prints , arXiv:1610.06892, doi: 10.48550/arXiv.1610.06892

Wei, J., Cordier, B., Antier, S., et al. 2016, arXiv e-prints , arXiv:1610.06892, doi: 10.48550/arXiv.1610.06892

2016 doi arXiv
[34]

E., & Bloom, J

Woosley, S. E., & Bloom, J. S. 2006, ARA&A, 44, 507, doi: 10.1146/annurev.astro.43.072103.150558

2006 arXiv
[35]

2004, ApJ, 609, 935, doi: 10.1086/421285

Yonetoku, D., Murakami, T., Nakamura, T., et al. 2004, ApJ, 609, 935, doi: 10.1086/421285

2004 doi
[36]

2022, in Handbook of X-ray and Gamma-ray Astrophysics, ed

Yuan, W., Zhang, C., Chen, Y., & Ling, Z. 2022, in Handbook of X-ray and Gamma-ray Astrophysics, ed. C. Bambi & A. Sangangelo, 86, doi: 10.1007/978-981-16-4544-0 151-1

2022 doi
[37]

M., & Alaryani, O

Zitouni, H., Guessoum, N., AlQassimi, K. M., & Alaryani, O. 2018, Ap&SS, 363, 223, doi: 10.1007/s10509-018-3449-0

2018 doi

Pith tools

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

[1] [1]

2019, MNRAS, 486, L46, doi: 10.1093/mnrasl/slz056

Tantalo, M. 2019, MNRAS, 486, L46, doi: 10.1093/mnrasl/slz056

doi:10.1093/mnrasl/slz056 2019

[2] [2]

2002, A&A, 390, 81, doi: 10.1051/0004-6361:20020722

Amati, L., Frontera, F., Tavani, M., et al. 2002, A&A, 390, 81, doi: 10.1051/0004-6361:20020722

doi:10.1051/0004-6361:20020722 2002

[3] [3]

Atteia, J. L. 2003, A&A, 407, L1, doi: 10.1051/0004-6361:20030958

doi:10.1051/0004-6361:20030958 2003

[4] [4]

L., Cordier, B., & Wei, J

Atteia, J. L., Cordier, B., & Wei, J. 2022, International Journal of Modern Physics D, 31, 2230008, doi: 10.1142/S0218271822300087

doi:10.1142/s0218271822300087 2022

[5] [5]

Band, D. L. 2003, ApJ, 588, 945, doi: 10.1086/374242

work page doi:10.1086/374242 2003

[6] [6]

L., & Preece, R

Band, D. L., & Preece, R. D. 2005, ApJ, 627, 319, doi: 10.1086/430402

doi:10.1086/430402 2005

[7] [7]

R., Bloom, J

Butler, N. R., Bloom, J. S., & Poznanski, D. 2010, ApJ, 711, 495, doi: 10.1088/0004-637X/711/1/495

doi:10.1088/0004-637x/711/1/495 2010

[8] [8]

R., Kocevski, D., Bloom, J

Butler, N. R., Kocevski, D., Bloom, J. S., & Curtis, J. L. 2007, ApJ, 671, 656, doi: 10.1086/522492

doi:10.1086/522492 2007