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The observed diversity of GRB X-ray plateau morphologies—rising, flat, and decaying—does not require distinct magnetar populations; a single population of millisecond magnetars with large intrinsic luminosity scatter can reproduce the data.

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2026-08-01 03:33 UTC pith:GJ2OJ6LI

load-bearing objection A credible first population-level hierarchical inference for GRB plateau magnetars, but the headline conclusion about morphology diversity is weaker than the abstract claims because the model never generates the morphology it compares.

arxiv 2607.23114 v1 pith:GJ2OJ6LI submitted 2026-07-25 astro-ph.HE

Diverse Morphologies of GRB X-Ray Plateaus within a Common Magnetar Framework

Xiao-Fei Dong , Yong-Feng Huang , Nurimangul Nurmamat , Chen Deng , Ze-Cheng Zou , Fan Xu , Abdusattar Kurban , Chen Du
show 2 more authors
Chen-Ran Hu Jin-Jun Geng
This is my paper
classification astro-ph.HE
keywords gamma-ray burstsX-ray plateausmagnetarshierarchical Bayesian inferencepopulation inferencedipole spin-downneutron starsafterglows
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

This paper tries to settle whether the different shapes of the X-ray plateau phase in gamma-ray bursts—rising, flat, or decaying—come from different kinds of central engines or from one common type. The authors perform the first hierarchical population-level inference of magnetar properties for 185 long GRBs with well-defined plateaus, using a conditional Poisson point-process likelihood that accounts for selection effects and measurement errors. They find that a single, physically plausible population of newborn millisecond magnetars (spin period around 6.8 ms, magnetic field around 3×10^15 G) reproduces the observed plateau population, and that the inferred parameter distributions for the three morphologies overlap substantially. The paper's central conclusion is that plateau diversity does not require distinct magnetar populations; instead, all subclasses require a large intrinsic luminosity scatter of roughly 0.5–1.0 dex, while duration scatter stays small. If true, this means the variety of plateau shapes can be understood as one engine seen under different conditions, not as evidence for separate classes of central engines.

Core claim

The paper's central claim is that the diversity of observed X-ray plateau morphologies can be reproduced by a single underlying magnetar population, so distinct magnetar populations are not required. Using a conditional Poisson point-process hierarchical model, the authors infer the population distribution of initial spin period P and dipole magnetic field B for a uniform sample of 185 long GRBs with plateaus, together with intrinsic scatter around the idealized spin-down relations. The inferred population has a characteristic spin period of about 6.8 ms and a magnetic field of about 3.3×10^15 G, matching expectations for newborn magnetars. Posterior comparisons among the rising, flat, and d

What carries the argument

The central mechanism is the conditional Poisson point-process (CPP) likelihood, a hierarchical Bayesian framework that treats the observed plateau sample as a filtered realization of a latent population, conditioning on the observed sample size. The forward model maps each latent magnetar parameter set (P, B, z) to an idealized plateau luminosity L0 and rest-frame spin-down timescale T0 through the standard magnetic-dipole spin-down relations (Eqs. 2–3), with independent log-normal intrinsic scatter (Eqs. 4–5) absorbing radiative-efficiency and geometry variations. Selection effects enter through a smooth logistic function of plateau flux and break time. Monte Carlo forward modeling approxi

Load-bearing premise

The load-bearing premise is that every plateau—including rising ones—is generated by the same magnetic-dipole spin-down mapping from (spin period, magnetic field, redshift) to plateau luminosity and break time, with any morphology-dependent physics absorbed into independent log-normal scatter; if rising plateaus actually require fallback accretion or propeller effects, the inferred magnetar parameters for that subclass lose physical meaning.

What would settle it

Conduct the same conditional Poisson point-process analysis on a sample of at least 30 well-measured rising plateaus: if the posterior for (P_c, B_c) of the rising subclass excludes the flat/decaying posteriors at high credibility, or if a three-population model is preferred over a single-population model by a decisive Bayes factor, the common-magnetar claim fails. A second falsifier: if adding an explicit fallback-accretion parameter to the forward model eliminates the need for large intrinsic luminosity scatter (σ_L,int drops well below 0.5 dex), then the current estimate of scatter is infla

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

  • If the common-population conclusion is right, the rising, flat, and decaying plateau classes should continue to show overlapping inferred magnetar parameters as more bursts are added; no separate 'engine taxonomy' is needed.
  • The characteristic parameters (P ≈ 6.8 ms, B ≈ 3.3×10^15 G) are physically plausible for newborn millisecond magnetars, supporting the magnetar energy-injection scenario for plateaus.
  • The required large intrinsic luminosity scatter (σ_L,int ≈ 0.5–1.0 dex) means that plateau luminosity is not a clean probe of spin-down physics alone; radiative efficiency or geometry must vary substantially from burst to burst.
  • Because pure dipole spin-down cannot produce a rising plateau, rising morphologies imply additional time-dependent processes (e.g., fallback accretion or propeller effects) acting within a common magnetar framework, not a different central engine.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • My inference: the no-separation result may be partly an artifact of the model's flexibility—the independent log-normal luminosity scatter can absorb morphology-dependent physics, so the convergence of inferred populations could reflect model adaptability rather than a truly common engine.
  • My inference: the weaker overlap (OVL 0.2–0.5) for spin-period centroid and luminosity scatter hints at residual differences among morphologies; a more sensitive test using explicit model comparison (e.g., Bayes factors for one vs. three populations) could reveal separation that the current overlap-coefficient analysis treats as not 'strong.'
  • My inference: a decisive check would be to add an explicit fallback-accretion or propeller term to the forward model for rising plateaus; if the rising subclass then moves to a distinct (P, B) region, the common-population conclusion would be endangered.
  • My inference: the framework could be extended to test whether the large σ_L,int correlates with known burst properties (e.g., prompt-emission energy or jet opening angle); if it does, the scatter is not 'intrinsic' to the magnetar population but encodes a missing parameter.

Editorial analysis

A structured set of objections, weighed in public.

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

Circularity Check

1 steps flagged

No central circularity: the main result is a fit comparing data-driven posteriors; only the Eq. (28) consistency check is circular by construction.

specific steps
  1. other [Section 5.1, Eq. (28) and Figure 5]
    "Following Zhang & Mészáros (2001) and Lü et al. (2015), we assume T = t_b/(1+z) and L_b ≃ ηL_0 ... B_{p,15} = 2.05 I_{45} R_6^{-3} L_{0,49}^{-1/2} T_3^{-1}, P_{0,-3} = 1.42 I_{45}^{1/2} L_{0,49}^{-1/2} T_3^{-1/2}. ... Despite methodological differences, the two approaches occupy similar regions."

    Eq. (28) is the algebraic inverse of the dipole spin-down mapping used as the CPP forward model, Eqs. (2)-(3). Therefore the overlap between the 'traditional inversion' estimates and the Bayesian posterior in Fig. 5 is expected from the shared mapping, rather than an independent population-level confirmation. The paper presents this overlap as a 'complementary check' of the common-population conclusion, but the check is largely by construction. This is not load-bearing for the main morphological comparison, hence mild.

full rationale

The paper is a hierarchical Bayesian fit rather than a derivation. Population parameters (Pc, sigma_P, Bc, sigma_B, sigma_L,int, sigma_T,int) are inferred from the 185 observed plateaus, so the 'reproduction' of observed distributions in Fig. 1 and the KS p-values are in-sample posterior predictive checks, not independent predictions; they are standard model diagnostics and not load-bearing. The central morphological conclusion compares posterior distributions of (Pc, Bc) across rising, flat, and decaying subclasses; these posteriors are data-driven and could in principle separate, so the no-separation result is not forced by construction. The admitted limitation in Sec. 5.2 that pure magnetic-dipole spin-down cannot by itself produce a pronounced rising plateau is a model-validity issue for the rising subclass, not circularity: the paper explicitly defers morphology-dependent physics to future work, and the likelihood never uses the subclass-defining slope alpha_1. Self-citations (Dong et al. 2026 sample, Dong et al. 2022 SFR parameters) provide data and fixed inputs, not self-supporting results. The only mild circularity is the comparison in Sec. 5.1, where Eq. (28) inverts the same Eqs. (2)-(3) used in the forward model, so agreement between the two methods is to a large extent by construction. Overall, no central circularity.

Axiom & Free-Parameter Ledger

11 free parameters · 7 axioms · 0 invented entities

The ledger contains the six fitted population parameters, the hand-set selection-function parameters, and the key modeling assumptions (dipole spin-down mapping, log-normal scatter, SFR redshift prior, separable selection function, CPP likelihood). No new particles, forces, or entities are introduced. The main burden of the paper is carried by the dipole spin-down forward model and the incompleteness of the selection function, both of which are stated in the text.

free parameters (11)
  • P_c (log10 ms) = 0.83 (total); 0.90 (rising); 0.92 (flat); 0.72 (decaying)
    Population mean of log10 initial spin period; fitted to the data in the CPP likelihood.
  • sigma_P (dex) = 0.27 (total); 0.46 (rising); 0.25 (flat); 0.19 (decaying)
    Population dispersion in log10 spin period; fitted to the data.
  • B_c (log10 G) = 15.52 (total); 15.46 (rising); 15.54 (flat); 15.49 (decaying)
    Population mean of log10 dipole magnetic field strength; fitted to the data.
  • sigma_B (dex) = 0.19 (total); 0.34 (rising); 0.18 (flat); 0.24 (decaying)
    Population dispersion in log10 magnetic field; fitted to the data.
  • sigma_L,int (dex) = 0.87 (total); 0.46 (rising); 1.06 (flat); 0.71 (decaying)
    Intrinsic log-normal luminosity scatter around the dipole spin-down relation; fitted to the data and central to the conclusion about luminosity diversity.
  • sigma_T,int (dex) = 0.12 (total); 0.24 (rising); 0.17 (flat); 0.23 (decaying)
    Intrinsic log-normal duration scatter around the spin-down timescale; fitted to the data.
  • F_th (log10 erg/cm2/s) = -12.76
    Effective flux threshold in the logistic selection function; fixed to the minimum observed plateau flux of the sample, i.e., chosen from the same data being fit rather than externally calibrated.
  • Delta_F = Delta_T = 0.5
    Width of the logistic selection transitions; chosen by hand, with robustness tested only over 0.3–0.7.
  • tmin, tmax (log10 s) = log10 t = 1, 6
    Plateau break-time selection boundaries; set from the observed range of plateau measurements.
  • Minimum effective uncertainty s_min = 0.05 dex
    Floor imposed on measurement uncertainties in the error kernel for numerical stability; robustness tested at 0.10 dex.
  • Radiative efficiency eta (traditional inversion) = 0.7
    Used only in the Section 5.1 event-by-event comparison, not in the central CPP inference; authors note varying eta from 0.1 to 1 preserves the overlap.
axioms (7)
  • domain assumption Idealized magnetic-dipole spin-down scalings L0(P,B) and T0(P,B) with canonical NS radius and moment of inertia (Eqs. 2–3).
    The forward model assumes the plateau luminosity and break time are set by pure dipole spin-down of a magnetar with R=10^6 cm and I=10^45 g cm^2.
  • domain assumption The observed plateau break time t_b equals the rest-frame spin-down timescale times (1+z), and the observed luminosity equals L0 times log-normal scatter (Eqs. 4–5).
    This mapping is central to translating (P,B,z) into observed (L,t_b); it is not derived from first principles and is known to be an idealization for internal plateaus and rising plateaus.
  • domain assumption The latent magnetar population is independent log-normal in P and B, with no redshift evolution (Eqs. 6 and 11).
    The population model factorizes p(P)p(B)p(z); this is motivated by previous fits but not independently justified.
  • domain assumption The intrinsic redshift distribution traces the cosmic star-formation history with fixed Hopkins & Beacom parameters (Eqs. 7–10).
    The SFR parameters are taken from Dong et al. 2022 and the consistency with the observed z distribution is checked but not used to calibrate them.
  • ad hoc to paper The catalog selection function is separable into smooth logistic flux and duration terms with fixed thresholds (Eqs. 12–14).
    The selection model is an effective approximation; it does not include observing cadence, light-curve quality, or redshift completeness, as the authors note in Section 2.3.
  • standard math The conditional Poisson likelihood equals the full point-process likelihood after marginalizing over a uniform-in-log rate prior (Eq. 20).
    This follows Fishbach et al. 2018 and Mandel et al. 2019; it is a standard Bayesian result used to remove the rate normalization.
  • ad hoc to paper Measurement errors are Gaussian with a floor of 0.05 dex in both luminosity and break-time dimensions (Eqs. 15 and 25).
    The floor is imposed for numerical stability and tested in robustness checks; it is not derived from instrument properties.

pith-pipeline@v1.3.0-alltime-deepseek · 13607 in / 12544 out tokens · 127565 ms · 2026-08-01T03:33:15.603639+00:00 · methodology

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read the original abstract

The origin of the X-ray plateau phase in gamma-ray bursts (GRBs) remains an open problem. In particular, it is unclear whether GRBs with different temporal morphologies (i.e., with a rising, flat, or decaying plateau) arise from a common underlying mechanism. Although magnetar energy injection is a leading explanation, previous studies have primarily inferred magnetar properties on a burst-by-burst basis and have not tested the model at the population level. Here we perform the first hierarchical population inference of magnetar parameters for a uniform sample of 185 long GRBs with X-ray plateaus within a conditional Poisson point-process framework. It is found that the observed plateau population is well reproduced by physically plausible magnetar populations. The inferred parameter distributions show no strong statistical separation among subclasses with different plateau morphologies. Nevertheless, all subclasses show a substantial intrinsic luminosity scatter, $\sigma_{L,\rm int}\sim0.5$--1.0 dex, whereas the intrinsic duration scatter remains considerably smaller. The results provide a population-level test of the magnetar interpretation of GRB X-ray plateaus, showing that the observed diversity of plateau morphologies does not require distinct magnetar populations.

Figures

Figures reproduced from arXiv: 2607.23114 by Abdusattar Kurban, Chen Deng, Chen Du, Chen-Ran Hu, Fan Xu, Jin-Jun Geng, Nurimangul Nurmamat, Xiao-Fei Dong, Yong-Feng Huang, Ze-Cheng Zou.

Figure 1
Figure 1. Figure 1: Parameter distributions of the observed sample and the CPP mock bursts. The three panels show the distributions in the LX − tb plane, the LX − z plane, and the redshift distribution. The simulated source sample includes all 185 plateau events used in this work. Following the CPP framework described in Section 2, we analyze the full sample of 185 plateau GRBs using the K-corrected plateau luminosities LX an… view at source ↗
Figure 2
Figure 2. Figure 2: Two-dimensional distribution of magnetar spin periods and magnetic fields for the full plateau sample, reconstructed from 15,000 Monte Carlo draws from the posterior population. The color scale indicates the number of samples in each bin. 3.2. CPP Analysis of the Rising, Flat, and Decaying Subsamples To investigate whether different plateau morphologies require distinct magnetar populations, we apply the C… view at source ↗
Figure 3
Figure 3. Figure 3: Two-dimensional posterior distribution of the three subclasses in the log10 Bc − log10 Pc plane. The color scale indicates the number of posterior samples in each bin. From left to right, the panels correspond to the rising, flat, and decaying samples, respectively. Each panel is constructed from 15,000 posterior samples for the corresponding plateau class [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Violin plots of the posterior distributions of the six CPP parameters inferred for the Rising, Flat, Decaying, and Total plateau samples. The panels show Pc, σP , Bc, σB, σL,int, and σT ,int, respectively. White markers and error bars denote the median values and 68% confidence intervals. The best-fit parameter estimates are listed in [PITH_FULL_IMAGE:figures/full_fig_p009_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Comparison of traditional inversion and Bayesian population inference in the B–P plane. The colored background shows the Bayesian-inferred population density, with the color bar indicating the normalized density. The superimposed points show the traditional inversion results, assuming η = 0.7. Triangles, crosses, and circles denote the rising, flat, and decaying plateau subsamples, respectively. The red do… view at source ↗

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Works this paper leans on

67 extracted references · 18 canonical work pages · 2 internal anchors

  1. [1]

    S., Narendra, A., Giovanna Dainotti, M., et al

    Bal, D. S., Narendra, A., Giovanna Dainotti, M., et al. 2025, ApJ, 994, 185, doi: 10.3847/1538-4357/ae1736

    work page doi:10.3847/1538-4357/ae1736 2025

  2. [2]

    W., Gaebel, S

    Barrett, J. W., Gaebel, S. M., Neijssel, C. J., et al. 2018, MNRAS, 477, 4685, doi: 10.1093/mnras/sty908

    doi:10.1093/mnras/sty908 2018

  3. [3]

    2020, MNRAS, 492, 2847, doi: 10.1093/mnras/staa070

    Beniamini, P., Duque, R., Daigne, F., & Mochkovitch, R. 2020, MNRAS, 492, 2847, doi: 10.1093/mnras/staa070

    doi:10.1093/mnras/staa070 2020

  4. [4]

    2017, A&A, 605, A60, doi: 10.1051/0004-6361/201730523

    Beniamini, P., & Mochkovitch, R. 2017, A&A, 605, A60, doi: 10.1051/0004-6361/201730523

    work page doi:10.1051/0004-6361/201730523 2017

  5. [5]

    G., Venkatesh, S., et al

    Bhardwaj, S., Dainotti, M. G., Venkatesh, S., et al. 2023, MNRAS, 525, 5204, doi: 10.1093/mnras/stad2593

    doi:10.1093/mnras/stad2593 2023

  6. [6]

    2020, ApJ, 893, 38, doi: 10.3847/1538-4357/ab7eaf Magnetar Origin of GRB Plateaus13

    Biscoveanu, S., Thrane, E., & Vitale, S. 2020, ApJ, 893, 38, doi: 10.3847/1538-4357/ab7eaf Magnetar Origin of GRB Plateaus13

    doi:10.3847/1538-4357/ab7eaf 2020

  7. [7]

    G., & Lu, T

    Dai, Z. G., & Lu, T. 1998a, A&A, 333, L87, doi: 10.48550/arXiv.astro-ph/9810402 —. 1998b, PhRvL, 81, 4301, doi: 10.1103/PhysRevLett.81.4301

    Pith/arXiv arXiv doi:10.48550/arxiv.astro-ph/9810402

  8. [9]

    G., Cardone, V

    Dainotti, M. G., Cardone, V. F., & Capozziello, S. 2008, MNRAS, 391, L79, doi: 10.1111/j.1745-3933.2008.00560.x

    arXiv 2008

  9. [10]

    2015, ApJ, 800, 31, doi: 10.1088/0004-637X/800/1/31 Dall’Osso, S., Stratta, G., Perna, R., De Cesare, G., &

    Capozziello, S. 2015, ApJ, 800, 31, doi: 10.1088/0004-637X/800/1/31 Dall’Osso, S., Stratta, G., Perna, R., De Cesare, G., &

    doi:10.1088/0004-637x/800/1/31 2015

  10. [11]

    2023, ApJL, 949, L32, doi: 10.3847/2041-8213/acccec

    Stella, L. 2023, ApJL, 949, L32, doi: 10.3847/2041-8213/acccec

    work page doi:10.3847/2041-8213/acccec 2023

  11. [12]

    2023, ApJ, 943, 126, doi: 10.3847/1538-4357/acaefd

    Deng, C., Huang, Y.-F., & Xu, F. 2023, ApJ, 943, 126, doi: 10.3847/1538-4357/acaefd

    doi:10.3847/1538-4357/acaefd 2023

  12. [13]

    2026, ApJ, 1000, 97, doi: 10.3847/1538-4357/ae486b Dereli-B´ egu´ e, H., Pe’er, A., Ryde, F., et al

    Deng, C., Huang, Y.-F., Kurban, A., et al. 2026, ApJ, 1000, 97, doi: 10.3847/1538-4357/ae486b Dereli-B´ egu´ e, H., Pe’er, A., Ryde, F., et al. 2022, Nature Communications, 13, 5611, doi: 10.1038/s41467-022-32881-1

    doi:10.3847/1538-4357/ae486b 2026

  13. [14]

    F., Li, X

    Dong, X. F., Li, X. J., Zhang, Z. B., & Zhang, X. L. 2022, MNRAS, 513, 1078, doi: 10.1093/mnras/stac949

    work page doi:10.1093/mnras/stac949 2022

  14. [15]

    2026, ApJ, 1003, 227, doi: 10.3847/1538-4357/ae66f1

    Dong, X.-F., Huang, Y.-F., Deng, C., et al. 2026, ApJ, 1003, 227, doi: 10.3847/1538-4357/ae66f1

    work page doi:10.3847/1538-4357/ae66f1 2026

  15. [16]

    Y., Zhen, H

    Du, X. Y., Zhen, H. Y., Liu, J. X., et al. 2024, ApJ, 960, 77, doi: 10.3847/1538-4357/ad0f24

    work page doi:10.3847/1538-4357/ad0f24 2024

  16. [17]

    2006, MNRAS, 369, 197, doi: 10.1111/j.1365-2966.2006.10280.x

    Fan, Y., & Piran, T. 2006, MNRAS, 369, 197, doi: 10.1111/j.1365-2966.2006.10280.x

    arXiv 2006

  17. [18]

    Farah, A., Essick, R., Doctor, Z., Fishbach, M., & Holz, D. E. 2020, ApJ, 895, 108, doi: 10.3847/1538-4357/ab8d26

    doi:10.3847/1538-4357/ab8d26 2020

  18. [19]

    M., Gair, J

    Farr, W. M., Gair, J. R., Mandel, I., & Cutler, C. 2015, PhRvD, 91, 023005, doi: 10.1103/PhysRevD.91.023005

    doi:10.1103/physrevd.91.023005 2015

  19. [20]

    E., & Farr, W

    Fishbach, M., Holz, D. E., & Farr, W. M. 2018, ApJL, 863, L41, doi: 10.3847/2041-8213/aad800

    doi:10.3847/2041-8213/aad800 2018

  20. [21]

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

    Foreman-Mackey, D., Hogg, D. W., Lang, D., & Goodman, J. 2013, PASP, 125, 306, doi: 10.1086/670067

    doi:10.1086/670067 2013

  21. [22]

    W., & Morton, T

    Foreman-Mackey, D., Hogg, D. W., & Morton, T. D. 2014, ApJ, 795, 64, doi: 10.1088/0004-637X/795/1/64

    doi:10.1088/0004-637x/795/1/64 2014

  22. [23]

    P., Barthelmy, S

    Gehrels, N., Norris, J. P., Barthelmy, S. D., et al. 2006, Nature, 444, 1044, doi: 10.1038/nature05376

    doi:10.1038/nature05376 2006

  23. [24]

    L., Wynn, G

    Gibson, S. L., Wynn, G. A., Gompertz, B. P., & O’Brien, P. T. 2017, MNRAS, 470, 4925, doi: 10.1093/mnras/stx1531 —. 2018, MNRAS, 478, 4323, doi: 10.1093/mnras/sty1363

    work page doi:10.1093/mnras/stx1531 2017

  24. [25]

    P., O’Brien, P

    Gompertz, B. P., O’Brien, P. T., & Wynn, G. A. 2014, MNRAS, 438, 240, doi: 10.1093/mnras/stt2165

    doi:10.1093/mnras/stt2165 2014

  25. [26]

    2013, MNRAS, 431, 1745, doi: 10.1093/mnras/stt293

    Rowlinson, A. 2013, MNRAS, 431, 1745, doi: 10.1093/mnras/stt293

    doi:10.1093/mnras/stt293 2013

  26. [27]

    2006, MNRAS, 366, L13, doi: 10.1111/j.1745-3933.2005.00121.x

    Granot, J., & Kumar, P. 2006, MNRAS, 366, L13, doi: 10.1111/j.1745-3933.2005.00121.x

    arXiv 2006

  27. [28]

    2024, A&A, 692, A73, doi: 10.1051/0004-6361/202451877

    Guglielmi, L., Stratta, G., Dall’Osso, S., et al. 2024, A&A, 692, A73, doi: 10.1051/0004-6361/202451877

    work page doi:10.1051/0004-6361/202451877 2024

  28. [29]

    2025, A&A, 703, A101, doi: 10.1051/0004-6361/202556663

    Guidorzi, C., Maccary, R., Maistrello, M., et al. 2025, A&A, 703, A101, doi: 10.1051/0004-6361/202556663

    doi:10.1051/0004-6361/202556663 2025

  29. [30]

    M., & Beacom, J

    Hopkins, A. M., & Beacom, J. F. 2006, ApJ, 651, 142, doi: 10.1086/506610

    doi:10.1086/506610 2006

  30. [31]

    2021, ApJ, 922, 102, doi: 10.3847/1538-4357/ac2c74

    Hou, S.-J., Du, S., Liu, T., Mu, H.-J., & Xu, R.-X. 2021, ApJ, 922, 102, doi: 10.3847/1538-4357/ac2c74

    work page doi:10.3847/1538-4357/ac2c74 2021

  31. [32]

    F., & Jr, E

    Inman, H. F., & Jr, E. L. B. 1989, Communications in Statistics - Theory and Methods, 18, 3851, doi: 10.1080/03610928908830127

    doi:10.1080/03610928908830127 1989

  32. [33]

    Kelly, B. C. 2007, ApJ, 665, 1489, doi: 10.1086/519947

    doi:10.1086/519947 2007

  33. [34]

    S., Dainotti, M

    Khatiya, N. S., Dainotti, M. G., Narendra, A., et al. 2025, ApJ, 990, 69, doi: 10.3847/1538-4357/adf219

    doi:10.3847/1538-4357/adf219 2025

  34. [35]

    2025, ApJS, 280, 45, doi: 10.3847/1538-4365/adefe4

    Lan, L., Gao, H., Ai, S., et al. 2025, ApJS, 280, 45, doi: 10.3847/1538-4365/adefe4

    work page doi:10.3847/1538-4365/adefe4 2025

  35. [36]

    M., & Prakash, M

    Lattimer, J. M., & Prakash, M. 2004, Science, 304, 536, doi: 10.1126/science.1090720

    doi:10.1126/science.1090720 2004

  36. [37]

    L., Dainotti, M

    Lenart, A. L., Dainotti, M. G., Khatiya, N., et al. 2025, Journal of High Energy Astrophysics, 47, 100384, doi: 10.1016/j.jheap.2025.100384

    arXiv 2025

  37. [38]

    2018, ApJS, 236, 26, doi: 10.3847/1538-4365/aabaf3

    Li, L., Wu, X.-F., Lei, W.-H., et al. 2018, ApJS, 236, 26, doi: 10.3847/1538-4365/aabaf3

    doi:10.3847/1538-4365/aabaf3 2018

  38. [39]

    2012, ApJ, 758, 27, doi: 10.1088/0004-637X/758/1/27

    Li, L., Liang, E.-W., Tang, Q.-W., et al. 2012, ApJ, 758, 27, doi: 10.1088/0004-637X/758/1/27

    doi:10.1088/0004-637x/758/1/27 2012

  39. [40]

    2026, arXiv e-prints, arXiv:2607.18698

    Li, Q.-M., Sun, Q.-B., Qian, S.-B., et al. 2026, arXiv e-prints, arXiv:2607.18698. https://arxiv.org/abs/2607.18698

    Pith/arXiv arXiv 2026

  40. [41]

    2007, ApJ, 670, 565, doi: 10.1086/521870

    Liang, E.-W., Zhang, B.-B., & Zhang, B. 2007, ApJ, 670, 565, doi: 10.1086/521870

    doi:10.1086/521870 2007

  41. [42]

    2014, ApJ, 783, 24, doi: 10.1088/0004-637X/783/1/24

    Lien, A., Sakamoto, T., Gehrels, N., et al. 2014, ApJ, 783, 24, doi: 10.1088/0004-637X/783/1/24

    doi:10.1088/0004-637x/783/1/24 2014

  42. [43]

    J., & Hendry, M

    Loredo, T. J., & Hendry, M. A. 2019, arXiv e-prints, arXiv:1911.12337, doi: 10.48550/arXiv.1911.12337

    Pith/arXiv arXiv doi:10.48550/arxiv.1911.12337 2019

  43. [44]

    J., & Wasserman, I

    Loredo, T. J., & Wasserman, I. M. 1995, ApJS, 96, 261, doi: 10.1086/192119 —. 1998a, ApJ, 502, 75, doi: 10.1086/305870 —. 1998b, ApJ, 502, 108, doi: 10.1086/305871 L¨ u, H.-J., & Zhang, B. 2014, ApJ, 785, 74, doi: 10.1088/0004-637X/785/1/74 L¨ u, H.-J., Zhang, B., Lei, W.-H., Li, Y., & Lasky, P. D. 2015, ApJ, 805, 89, doi: 10.1088/0004-637X/805/2/89

    work page doi:10.1086/192119 1995

  44. [45]

    T., Zhang, B., et al

    Lyons, N., O’Brien, P. T., Zhang, B., et al. 2010, MNRAS, 402, 705, doi: 10.1111/j.1365-2966.2009.15538.x 14Dong et al

    arXiv 2010

  45. [46]

    M., & Gair, J

    Mandel, I., Farr, W. M., & Gair, J. R. 2019, MNRAS, 486, 1086, doi: 10.1093/mnras/stz896

    doi:10.1093/mnras/stz896 2019

  46. [47]

    2011, MNRAS, 413, 2031, doi: 10.1111/j.1365-2966.2011.18280.x

    Bucciantini, N., & Quataert, E. 2011, MNRAS, 413, 2031, doi: 10.1111/j.1365-2966.2011.18280.x

    arXiv 2011

  47. [48]

    2020, ApJ, 893, 88, doi: 10.3847/1538-4357/ab8221 Planck Collaboration, Ade, P

    Oganesyan, G., Ascenzi, S., Branchesi, M., et al. 2020, ApJ, 893, 88, doi: 10.3847/1538-4357/ab8221 Planck Collaboration, Ade, P. A. R., Aghanim, N., et al. 2014, A&A, 571, A16, doi: 10.1051/0004-6361/201321591 Planck Collaboration, Aghanim, N., Akrami, Y., et al. 2020, A&A, 641, A6, doi: 10.1051/0004-6361/201833910

    work page doi:10.3847/1538-4357/ab8221 2020

  48. [49]

    2026, arXiv e-prints, arXiv:2601.03861, doi: 10.48550/arXiv.2601.03861

    Pracchia, M., & Sharan Salafia, O. 2026, arXiv e-prints, arXiv:2601.03861, doi: 10.48550/arXiv.2601.03861

    Pith/arXiv arXiv doi:10.48550/arxiv.2601.03861 2026

  49. [50]

    2023, A&A, 675, A117, doi: 10.1051/0004-6361/202245348

    Ronchini, S., Stratta, G., Rossi, A., et al. 2023, A&A, 675, A117, doi: 10.1051/0004-6361/202245348

    doi:10.1051/0004-6361/202245348 2023

  50. [51]

    P., Dainotti, M., et al

    Rowlinson, A., Gompertz, B. P., Dainotti, M., et al. 2014, MNRAS, 443, 1779, doi: 10.1093/mnras/stu1277

    doi:10.1093/mnras/stu1277 2014

  51. [52]

    T., Metzger, B

    Rowlinson, A., O’Brien, P. T., Metzger, B. D., Tanvir, N. R., & Levan, A. J. 2013, MNRAS, 430, 1061, doi: 10.1093/mnras/sts683

    doi:10.1093/mnras/sts683 2013

  52. [53]

    S., Ravasio, M

    Salafia, O. S., Ravasio, M. E., Ghirlanda, G., & Mandel, I. 2023, A&A, 680, A45, doi: 10.1051/0004-6361/202347298

    doi:10.1051/0004-6361/202347298 2023

  53. [54]

    Shahmoradi, A., & Nemiroff, R. J. 2015, MNRAS, 451, 126, doi: 10.1093/mnras/stv714

    doi:10.1093/mnras/stv714 2015

  54. [55]

    P., Dainotti, M

    Srinivasaragavan, G. P., Dainotti, M. G., Fraija, N., et al. 2020, ApJ, 903, 18, doi: 10.3847/1538-4357/abb702

    doi:10.3847/1538-4357/abb702 2020

  55. [56]

    G., Dall’Osso, S., Hernandez, X., & De Cesare, G

    Stratta, G., Dainotti, M. G., Dall’Osso, S., Hernandez, X., & De Cesare, G. 2018, ApJ, 869, 155, doi: 10.3847/1538-4357/aadd8f

    doi:10.3847/1538-4357/aadd8f 2018

  56. [57]

    2019, ApJS, 245, 1, doi: 10.3847/1538-4365/ab4711

    Tang, C.-H., Huang, Y.-F., Geng, J.-J., & Zhang, Z.-B. 2019, ApJS, 245, 1, doi: 10.3847/1538-4365/ab4711

    doi:10.3847/1538-4365/ab4711 2019

  57. [58]

    2019, PASA, 36, e010, doi: 10.1017/pasa.2019.2

    Thrane, E., & Talbot, C. 2019, PASA, 36, e010, doi: 10.1017/pasa.2019.2

    doi:10.1017/pasa.2019.2 2019

  58. [59]

    2024, ApJ, 974, 133, doi: 10.3847/1538-4357/ad6e85

    Tian, X., L¨ u, H., Yuan, Y., et al. 2024, ApJ, 974, 133, doi: 10.3847/1538-4357/ad6e85

    work page doi:10.3847/1538-4357/ad6e85 2024

  59. [60]

    T., et al

    Troja, E., Cusumano, G., O’Brien, P. T., et al. 2007, ApJ, 665, 599, doi: 10.1086/519450

    doi:10.1086/519450 2007

  60. [61]

    Reassessing high-energy emission correlations in gamma-ray bursts using a large, homogeneous sample of X-ray afterglows

    Vigliano, A. A., Longo, F., & Boˇ snjak,ˇZ. 2026, arXiv e-prints, arXiv:2605.25644, doi: 10.48550/arXiv.2605.25644

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.48550/arxiv.2605.25644 2026

  61. [62]

    2026, Fast Radio Bursts Trace Cosmic Star Formation with Little Delay

    Wang, Y.-Y., Li, Y.-J., & Fan, Y.-Z. 2026, Fast Radio Bursts Trace Cosmic Star Formation with Little Delay. https://arxiv.org/abs/2607.09109

    Pith/arXiv arXiv 2026

  62. [63]

    2009, ApJL, 690, L118, doi: 10.1088/0004-637X/690/2/L118

    Yamazaki, R. 2009, ApJL, 690, L118, doi: 10.1088/0004-637X/690/2/L118

    work page doi:10.1088/0004-637x/690/2/l118 2009

  63. [64]

    B., Wu, X

    Yu, Y. B., Wu, X. F., Huang, Y. F., et al. 2015, MNRAS, 446, 3642, doi: 10.1093/mnras/stu2336

    work page doi:10.1093/mnras/stu2336 2015

  64. [65]

    S., & Cao, X.-F

    Yu, Y.-W., Cheng, K. S., & Cao, X.-F. 2010, ApJ, 715, 477, doi: 10.1088/0004-637X/715/1/477 Y¨ uksel, H., Kistler, M. D., Beacom, J. F., & Hopkins, A. M. 2008, ApJL, 683, L5, doi: 10.1086/591449

    work page doi:10.1088/0004-637x/715/1/477 2010

  65. [66]

    Z., Dyks, J., et al

    Zhang, B., Fan, Y. Z., Dyks, J., et al. 2006, ApJ, 642, 354, doi: 10.1086/500723

    doi:10.1086/500723 2006

  66. [67]

    2001, ApJL, 552, L35, doi: 10.1086/320255

    Zhang, B., & M´ esz´ aros, P. 2001, ApJL, 552, L35, doi: 10.1086/320255

    doi:10.1086/320255 2001

  67. [68]

    Magnetar-powered long gamma-ray bursts and connection to superluminous supernovae and fast radio bursts

    Zhou, Y.-Q., Yi, S.-X., Yang, Y.-P., et al. 2026, arXiv e-prints, arXiv:2605.13440, doi: 10.48550/arXiv.2605.13440

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.48550/arxiv.2605.13440 2026