Pith. sign in

REVIEW 4 major objections 5 minor 124 references

The redshift distribution of 118 bright gamma-ray bursts implies a warm dark matter particle mass of at least 1.3 keV, tightening to 3.4 keV if the burst rate exactly traces the star formation rate.

Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →

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

T0 review · deepseek-v4-flash

2026-08-01 02:55 UTC pith:VN67JT2J

load-bearing objection Conscientious data update of de Souza et al. (2013), but the title is misleading: the free-alpha bound loosens to 1.3 keV and the 3.4 keV limit depends on an alpha=0 prior their own fit disfavors. the 4 major comments →

arxiv 2607.25261 v1 pith:VN67JT2J submitted 2026-07-28 astro-ph.HE astro-ph.COastro-ph.GA

Tightening Bounds on Warm Dark Matter with High-Redshift Gamma-Ray Bursts

Jun-Jie Wei , Jing-Meng Hao , Ding-Fang Hu , Yang Liu , Bao Wang , Xi Kang , Xue-Feng Wu This is my paper
classification astro-ph.HE astro-ph.COastro-ph.GA
keywords warm dark mattergamma-ray burstsstar formation ratehigh-redshift universestructure formationSheth-Tormen mass functionmaximum likelihoodcosmological constraints
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.

The paper tries to establish a lower limit on the mass of warm dark matter particles by using gamma-ray bursts as high-redshift probes. It models how the cosmic star formation rate depends on the WDM particle mass through hierarchical structure formation, then predicts the redshift distribution of GRBs that trace that star formation. Comparing this prediction to 118 luminous Swift GRBs with redshifts below 10, the authors find that WDM masses below 1.3 keV are excluded at 95% confidence; assuming the GRB rate exactly follows the star formation rate tightens the bound to 3.4 keV. A sympathetic reader would care because these limits test a leading alternative to cold dark matter that resolves small-scale tensions.

Core claim

The paper claims that the observed redshift distribution of luminous gamma-ray bursts, when interpreted with a model where the GRB rate traces the cosmic star formation rate with a redshift-evolution factor (1+z)^alpha, excludes warm dark matter particle masses below 1.3 keV at 95% confidence. If the GRB rate is assumed to exactly trace the SFR (alpha=0), the limit strengthens to 3.4 keV. These constraints are derived from 118 bursts with z<10 and luminosity above 4×10^52 erg/s, selected to avoid instrumental selection effects, and they are robust to a free evolution index alpha.

What carries the argument

The central machinery is the hierarchical structure-formation model that computes the cosmic star formation rate as a function of the WDM particle mass. It uses a Sheth-Tormen halo mass function with a sharp-k filter, a WDM transfer function that suppresses small-scale power, and an effective Jeans mass that sets the minimum halo mass for star formation. The resulting SFR is then fed into a maximum-likelihood fit of the GRB redshift distribution, with the GRB rate proportional to the SFR times (1+z)^alpha and a constant luminosity threshold to minimize selection biases.

Load-bearing premise

The central assumption is that the comoving GRB formation rate is exactly proportional to the cosmic star formation rate times a single power law (1+z)^alpha over all redshifts from 0 to 10, with one index alpha absorbing all metallicity, luminosity-function, and selection effects; if this proportionality breaks down at high redshift, the predicted high-z tail that drives the mass limit is miscalibrated.

What would settle it

A redshift-complete sample of GRBs at z>4 with well-characterized selection effects could test whether the (1+z)^alpha parameterization holds; alternatively, a direct, model-independent measurement of the cosmic SFR at z>6 (e.g., from deep galaxy surveys) that disagrees with the model's predicted SFR would falsify the derived mass bounds.

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

If this is right

  • If correct, WDM models with particle masses below 1.3 keV are ruled out, narrowing the allowed parameter space for sterile neutrinos and other keV-scale dark matter candidates.
  • The 3.4 keV limit under the alpha=0 prior strengthens the case that high-redshift structure formation is incompatible with very warm dark matter, should the GRB-SFR relation be truly unbiased.
  • The method demonstrates that gamma-ray bursts, despite their rarity, are competitive probes of the high-redshift universe and can complement galaxy-based constraints on dark matter.
  • The bounds depend on the assumed GRB-SFR relation, so any improvement in understanding that relation will directly translate into tighter WDM limits from the same sample.
  • The framework can be extended to larger GRB samples as they accumulate, potentially pushing the lower limit above 3.4 keV and into the range preferred by other observations.

Where Pith is reading between the lines

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

  • The author's own fit finds alpha=1.29 with a 95% interval that excludes 0, so the alpha=0 prior used for the 3.4 keV bound is disfavored by the data; the more conservative 1.3 keV limit is likely the more reliable one.
  • The single power-law parameterization of GRB evolution may be too simplistic at z>6, where metallicity and luminosity-function evolution could deviate; a broken power law or a redshift-dependent alpha would test the robustness of the bound.
  • A direct measurement of the high-z cosmic SFR (e.g., from JWST galaxies) would provide an independent check of the model's predicted SFR, and if it disagrees, the WDM limits would need revision.
  • The same likelihood framework could be applied to other star-formation tracers, such as high-z quasars or superluminous supernovae, to cross-check the WDM mass limit without relying solely on GRBs.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

4 major / 5 minor

Summary. The paper derives lower bounds on the warm dark matter particle mass from the redshift distribution of bright Swift long GRBs. It constructs a cosmic star formation history in a WDM model using the Sheth-Tormen mass function, a WDM transfer function and effective Jeans mass, and calibrates the model to low-redshift SFR measurements. It then assumes a comoving GRB formation rate proportional to the SFR with an additional redshift dependence (1+z)^α, and applies a maximum-likelihood analysis to 118 GRBs with L ≥ 4.0×10^52 erg/s and z < 10. The main results are m_x ≳ 1.3 keV at 95% CL when α is free, and m_x ≳ 3.4 keV at 95% CL when α = 0 is imposed. The paper presents these as robust, improved WDM constraints from two decades of Swift data.

Significance. If the assumptions are accepted, the free-α 1.3 keV lower limit provides an independent GRB-based bound on WDM that is complementary to Lyman-α and high-z galaxy constraints, and the α=0 case reaches 3.4 keV. The analysis has notable strengths: the luminosity cut L ≥ 4×10^52 erg/s is designed to avoid modeling the GRB luminosity function and trigger/redshift completeness; the expected redshift distribution is compared directly to the data; and the likelihood framework is standard. However, the central limits are built on a single power-law extrapolation of the GRB–SFR relation out to z ≈ 10, while α is constrained mostly by bursts at z ≲ 3. The paper also does not state the prior range over which α is marginalized, and the α=0 bound is presented without noting that the same data prefer α close to 1.3 and exclude 0 at about 95% CL. These issues make the quantitative bounds less robust than the paper claims, although the free-α 1.3 keV result is a defensible point estimate.

major comments (4)
  1. [§4.2, Eq. (27)] The assumed GRB–SFR relation, ρ_GRB(z) = η0(1+z)^α ρ_*(z), is a single power law over 0 < z < 10. The likelihood is sensitive to the high-redshift tail—9 of the 118 bursts lie at z ≥ 6—but α is effectively pinned by bursts at lower redshifts. There is no evidence that the same power law extends to z ≈ 10, and mechanisms such as metallicity-dependent GRB production, luminosity-function evolution, or high-z selection effects could change its slope. If the effective α at z > 6 differs from the extrapolated value, the expected high-z counts in Eq. (30) and hence the m_x limits shift. Please provide a robustness test with a broken power law or a high-z-only fit, or clearly state the result as conditional on the assumed extrapolation.
  2. [§4.3, Fig. 3] The paper does not specify the prior range or shape used for α. Figure 3 and the quoted 95% interval 1 keV/m_x ≲ 0.76 are posterior quantities; without knowing how α was marginalized, the 95% CL is not reproducible. This is load-bearing because the lower limit on m_x is obtained from the joint posterior. State the prior (e.g., flat in α over a specified interval, or Gaussian) and show how the m_x lower limit depends on its range.
  3. [§4.3, Fig. 5] The α=0 case yields the stronger bound m_x ≳ 3.4 keV, but the data in Fig. 3 prefer α = 1.29 with a 95% interval that excludes 0. Thus α = 0 is a disfavored assumption, not a conservative choice. The abstract and conclusions should not present the 3.4 keV limit as a similarly robust constraint. I recommend reporting m_x ≳ 1.3 keV as the main model-agnostic bound and explicitly labeling the 3.4 keV value as conditional on the assumption that the GRB rate exactly traces the SFR with no redshift evolution.
  4. [§3, Fig. 1] The SFR model used in the likelihood is calibrated at z ≲ 4, and its high-z predictions depend on several fixed parameters: τ1 = 3.5 Gyr, f1 set by the z=0 normalization, f2 = 4.5%, τ2 = 0.1 Gyr, ε = 10^-3, and the IMF choices. The WDM bounds are driven by the model's SFR at z > 6, where none of these parameters are directly tested. A sensitivity analysis to these parameters (or at least to the Pop III efficiency and the minimum halo mass M_min) is needed to support the claim that the resulting m_x limits are robust.
minor comments (5)
  1. [§4.2, Eq. (33)] The text says K is 'marginalized' by setting ∂lnL/∂K = 0, which is a profile maximum-likelihood step rather than a Bayesian marginalization. The point estimate is unaffected, but the terminology should be corrected.
  2. [§4.2, Eq. (28)] The integration is truncated at z_max = 10 because all sample bursts have z < 10. This is acceptable if the analysis is explicitly conditioned on z < 10, but the paper should state this conditioning rather than simply setting z_max = 10.
  3. [§4.3, text after Eq. (35)] The notation '1 keV/m_x ≲ 0.76' mixes units with the mass ratio; it would be clearer to state m_x > 1.3 keV directly.
  4. [Abstract/Title] The title and abstract emphasize 'tightening' bounds, but the free-α 1.3 keV limit is weaker than the earlier de Souza et al. (2013) limit of 1.6–1.8 keV quoted in the introduction. Please clarify whether the tightening refers to the α=0 case or to the overall constraints from the larger sample.
  5. [Data Availability] The data availability statement says data will be shared 'on reasonable request'. For a result that depends on a specific 118-GRB subsample and a multi-parameter SFR model, releasing the final sample table and analysis code would improve reproducibility.

Circularity Check

0 steps flagged

No circularity: the WDM bound is obtained from a forward-model likelihood with a marginalized nuisance parameter, not from a fitted input renamed as a prediction.

full rationale

The derivation chain is not circular. The WDM-dependent ingredients (transfer function, Jeans mass, halo mass function) are imported from external literature (Eqs. 6–10). The cosmic SFR model is built from the baryon accretion formalism and calibrated to the observed low-redshift SFR of Madau & Dickinson (2014), independent of the GRB sample. The GRB rate model (Eq. 27) introduces a phenomenological (1+z)^alpha term, but alpha is explicitly treated as a free, marginalized nuisance parameter, and K is fixed analytically from the total count. The expected GRB distribution (Eqs. 30–35) is then compared with the 118 observed GRBs; mx enters only through the SFR model before the likelihood is evaluated, so the bound on mx is not defined in terms of the GRB data by construction. Self-citations (e.g., Wei et al. 2014/2016/2025; Lan et al. 2021/2022) supply data compilations, background references, and parameterization context; none is a load-bearing uniqueness theorem or an ansatz imported solely from the authors. The paper itself notes that constraints above about 4 keV are not robust (Section 2), and the alpha prior range is not stated (Section 4.3); these are reproducibility/robustness gaps, not circularity. Overall, the central claim has independent content and is not forced by self-citation or by construction.

Axiom & Free-Parameter Ledger

7 free parameters · 8 axioms · 0 invented entities

The paper introduces no new entities. It leans on a long chain of literature-calibrated astrophysical assumptions: ST mass function, sharp-k filter, WDM transfer function, effective WDM Jeans mass, cooling threshold, and a semi-analytic SFR model. The only parameters fitted to the GRB data are the WDM mass and the index alpha; the SFR model constants are calibrated to low-redshift SFR observations. The central 1.3/3.4 keV bounds inherit uncertainty from every link in this chain, and the paper does not propagate those systematics into the quoted confidence intervals.

free parameters (7)
  • tau1 (Pop II/I star formation timescale) = 3.5 Gyr
    Chosen so the model SFR reproduces the observed SFR at z<4 (Sec. 3, after Eq. 17); the high-z SFR extrapolation that shapes the WDM bound inherits this calibration.
  • f1 (Pop II/I efficiency normalization) = normalized to SFR = 0.016 Msun yr^-1 Mpc^-3 at z=0
    Determined by matching the total SFR at z=0 (Sec. 3). Affects the absolute SFR, though the GRB redshift-shape likelihood partly cancels the normalization through K.
  • f2 and tau2 (Pop III SFR parameters) = f2=4.5%, tau2=0.1 Gyr
    Adopted from Daigne et al. (2004) (Eq. 19); Pop III stars can dominate the high-z SFR, so these constants influence the predicted high-z GRB tail.
  • epsilon (outflow efficiency) = 1e-3
    Used in the outflow term of the baryon gas equation (Eq. 24); taken from prior literature, not fitted to the GRB sample.
  • alpha (GRB-SFR redshift evolution index) = 1.29 +1.30/-0.64 (95% CL)
    Free parameter fitted to the 118 GRBs (Eq. 27, Sec. 4.3); the WDM bound is obtained after marginalizing over it, so the result depends on its (unstated) prior range.
  • 1/mx (inverse WDM mass) = 1/mx ≤ 0.76 keV^-1 (95% CL); mx ≥ 1.3 keV
    The parameter of interest in the maximum-likelihood fit (Sec. 4.3); constrained by the shape of the GRB redshift distribution.
  • F_lim (assumed bolometric flux threshold) = 3.0e-8 erg cm^-2 s^-1
    Assumed instrument threshold used to define Llim(z) and the L>=4e52 luminosity cut (Eq. 29); a different threshold or energy band can change sample selection.
axioms (8)
  • standard math Sheth-Tormen halo mass function with A_ST=0.3222, a1=0.707, p1=0.3, delta_c=1.686 (Eq. 1) is accurate for WDM halo abundances.
    Standard analytic fitting function from Sheth & Tormen (1999), used to compute the baryon collapse fraction.
  • domain assumption Sharp-k filter with ks=2.5/R (Eq. 4) is the correct window function for WDM power-spectrum cutoffs.
    Adopted following Benson et al. (2013) and Kennedy et al. (2014); the choice affects the halo mass function and hence the SFR.
  • domain assumption WDM transfer function T(k) and free-streaming scale follow the Bode/Viel form (Eqs. 6-9).
    Standard WDM parameterization mapping mx to the linear power spectrum cutoff; different thermal histories (sterile neutrinos vs. thermal relics) would change this mapping.
  • domain assumption Effective WDM Jeans mass M_WDM = 1.8e10 (Omega_x h^2/0.15)^1/2 (mx/keV)^-4 Msun (Eq. 10) sets the minimum halo mass for star formation.
    From Barkana et al. (2001)/de Souza et al. (2013); a key semi-empirical bridge from mx to SFR suppression, not a first-principles result.
  • domain assumption Minimum cooling halo mass M_gal(z) = 1e8 ((1+z)/10)^-3/2 Msun (Eq. 13) describes the gas cooling threshold.
    From Sobacchi & Mesinger (2013); combined with M_WDM in Eq. (12) to define M_min.
  • domain assumption Long GRBs originate from massive-star core collapse, so their comoving rate is proportional to the cosmic SFR times (1+z)^alpha (Eq. 27).
    The collapsar model (Woosley 1993; Totani 1997) is the basis of the analysis; alpha is fitted but a single power law may not capture metallicity, luminosity-function evolution, or selection effects.
  • domain assumption SFR follows the Schmidt law with the baryon-reservoir equations of Daigne et al. (2006) (Eqs. 16-19).
    The high-z SFR is computed from this semi-analytic model with parameters calibrated to low-z data; the model is adopted from the literature, not derived here.
  • domain assumption For the bright subsample, the trigger plus redshift completeness factor F(z) is constant F0 (Kistler et al. 2008).
    The luminosity cut is intended to justify this, but redshift completeness is not demonstrated; selection bias would alter the high-z tail that drives the constraint.

pith-pipeline@v1.3.0-alltime-deepseek · 17281 in / 19265 out tokens · 181915 ms · 2026-08-01T02:55:59.915149+00:00 · methodology

0 comments
read the original abstract

The cold dark matter paradigm successfully explains large-scale structure but faces persistent tensions on small scales. Warm dark matter (WDM) with $\mathrm{keV}$-scale particles can alleviate these issues by suppressing small-scale structure formation. The presence of collapsed structures at high redshifts places strong lower limits on the WDM particle mass $m_x$. Gamma-ray bursts (GRBs) are ideal high-redshift probes due to their extreme brightness. Using the most recent \emph{Swift} GRB data accumulated over the past two decades, we derive robust constraints on $m_x$ by conservatively assuming that the comoving GRB formation rate is proportional to the cosmic star formation rate (SFR), with an additional redshift evolution parameterized as $(1+z)^\alpha$. Applying a maximum-likelihood analysis to 118 GRBs with redshift $z<10$ and luminosity $L\ge 4.0\times10^{52}\,\mathrm{erg\,s^{-1}}$, we obtain $m_x \gtrsim 1.3\,\mathrm{keV}$ at the 95\% confidence level (CL). When the GRB rate is assumed to exactly trace the SFR (i.e., $\alpha=0$), the lower limit tightens to $m_x \gtrsim 3.4\,\mathrm{keV}$ at the same CL. These robust constraints demonstrate that GRBs are a powerful probe of the early Universe. A better understanding of the relationship between the GRB rate and the SFR would enable even tighter limits on WDM models.

Figures

Figures reproduced from arXiv: 2607.25261 by Bao Wang, Ding-Fang Hu, Jing-Meng Hao, Jun-Jie Wei, Xi Kang, Xue-Feng Wu, Yang Liu.

Figure 1
Figure 1. Figure 1: Redshift evolution of the cosmic SFR. The solid lines show the predicted total SFR (including contributions from both Pop II/I and Pop III stars) for different WDM particle masses: mx = 1 keV (blue), 2 keV (orange), and 3 keV (green). The corresponding dot-dashed and dashed lines indicate the SFRs of Pop II/I and Pop III stars, respectively. Data points represent SFR determinations from IR (black dots) and… view at source ↗
Figure 2
Figure 2. Figure 2: Luminosity–redshift distribution of 496 Swift GRBs. The gray shaded region approximates the luminosity threshold (Equation 29), and the green diagonal region marks the luminosity cut L ≥ 4.0 × 1052 erg s−1 that defines our subsample. for the evolutionary trend captured by α, including cosmic metal￾licity evolution (Langer & Norman 2006; Li 2008; Campisi et al. 2010; Wei et al. 2014), an evolving GRB lumino… view at source ↗
Figure 3
Figure 3. Figure 3: 1D and 2D marginalized probability distributions for the inverse WDM particle mass, 1/mx, and the evolutionary index α, with 68%, 95%, and 99% confidence contours. The plus sign masks the best-fit parameter combination. value of K along with the best-fit parameter combination {mx , α}. In practice, we use 1/mx as the free parameter for the likelihood analysis to avoid numerical divergences when approaching… view at source ↗
Figure 4
Figure 4. Figure 4: Redshift distribution of 118 Swift GRBs with L ≥ 4.0×1052 erg s−1 . Data points show the observed number of bursts in each redshift bin, with Poisson error bars. The solid line represents the redshift distribution pre￾dicted by the best-fit model, and the shaded region indicates the 95% confi￾dence interval of the best-fit model. 0.1 0.2 0.3 0.4 1 [keV] / mx 0 1 2 3 4 5 Probability Density α = 0 [PITH_FUL… view at source ↗
Figure 5
Figure 5. Figure 5: 1D marginalized probability distribution of the inverse WDM par￾ticle mass, 1/mx, under a prior α = 0 (i.e., assuming the GRB formation rate strictly traces the SFR). The dark and light shaded regions mark the 68% and 95% confidence intervals, respectively. by strongly suppressing small-scale structure formation. The high￾redshift Universe provides a powerful testbed for such WDM mod￾els, as the mere prese… view at source ↗

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

124 extracted references · 4 canonical work pages

  1. [1]

    , keywords =

    Warm dark matter model with a few keV mass is bad for the too-big-to-fail problem. , keywords =. doi:10.1093/mnras/stz3118 , archivePrefix =. 1911.05257 , primaryClass =

    Pith/arXiv arXiv 1911

  2. [2]

    Methods and application to warm dark matter

    Dark matter halo merger histories beyond cold dark matter - I. Methods and application to warm dark matter. , keywords =. doi:10.1093/mnras/sts159 , archivePrefix =. 1209.3018 , primaryClass =

    Pith/arXiv arXiv

  3. [3]

    , keywords =

    Constraining the warm dark matter particle mass with Milky Way satellites. , keywords =. doi:10.1093/mnras/stu719 , archivePrefix =. 1310.7739 , primaryClass =

    Pith/arXiv arXiv

  4. [4]

    , keywords =

    The Effects of an Early Galactic Wind on the Evolution of D, ^ 3 He, and Z. , keywords =. doi:10.1086/303665 , archivePrefix =. astro-ph/9607106 , primaryClass =

    Pith/arXiv arXiv

  5. [5]

    , keywords =

    Cosmic Star Formation, Reionization, and Constraints on Global Chemical Evolution. , keywords =. doi:10.1086/425649 , archivePrefix =. astro-ph/0405355 , primaryClass =

    Pith/arXiv arXiv

  6. [6]

    , keywords =

    The Effect of Warm Dark Matter on Galaxy Properties: Constraints from the Stellar Mass Function and the Tully-Fisher Relation. , keywords =. doi:10.1088/0004-637X/767/1/22 , archivePrefix =. 1208.0008 , primaryClass =

    Pith/arXiv arXiv

  7. [7]

    , keywords =

    Constraining the luminosity function and delay-time distribution of short gamma-ray bursts for multimessenger gravitational-wave detection rate estimation. , keywords =. doi:10.1093/mnras/staf1368 , archivePrefix =. 2501.03614 , primaryClass =

    Pith/arXiv arXiv

  8. [8]

    , keywords =

    The Evolution of Swift/BAT Blazars and the Origin of the MeV Background. , keywords =. doi:10.1088/0004-637X/699/1/603 , archivePrefix =. 0905.0472 , primaryClass =

    Pith/arXiv arXiv

  9. [9]

    , keywords =

    The Luminosity Function of Fermi-detected Flat-spectrum Radio Quasars. , keywords =. doi:10.1088/0004-637X/751/2/108 , archivePrefix =. 1110.3787 , primaryClass =

    Pith/arXiv arXiv

  10. [10]

    , keywords =

    The Luminosity Function of the EGRET Gamma-Ray Blazars. , keywords =. doi:10.1086/305403 , adsurl =

    work page doi:10.1086/305403

  11. [11]

    , keywords =

    The luminosity function and formation rate of a complete sample of long gamma-ray bursts. , keywords =. doi:10.1093/mnras/stz2011 , archivePrefix =. 1907.08342 , primaryClass =

    Pith/arXiv arXiv 1907

  12. [12]

    , keywords =

    Revisiting the luminosity and redshift distributions of long gamma-ray bursts. , keywords =. doi:10.1093/mnras/stab2508 , archivePrefix =. 2109.00766 , primaryClass =

    Pith/arXiv arXiv

  13. [13]

    , keywords =

    The Stellar-mass Function of Long Gamma-Ray Burst Host Galaxies. , keywords =. doi:10.3847/1538-4357/ac8fec , archivePrefix =. 2209.02175 , primaryClass =

    Pith/arXiv arXiv

  14. [14]

    , keywords =

    Analysis of complete quasar samples to obtain parameters of luminosity and evolution functions. , keywords =. doi:10.1086/161016 , adsurl =

    work page doi:10.1086/161016

  15. [15]

    , keywords =

    Gamma-Ray Luminosity Function of Blazars and the Cosmic Gamma-Ray Background: Evidence for the Luminosity-Dependent Density Evolution. , keywords =. doi:10.1086/502708 , archivePrefix =. astro-ph/0602178 , primaryClass =

    Pith/arXiv arXiv

  16. [16]

    Journal of High Energy Astrophysics , keywords =

    Long GRBs as a tool to investigate star formation in dark matter halos. Journal of High Energy Astrophysics , keywords =. doi:10.1016/j.jheap.2015.11.001 , archivePrefix =. 1511.04483 , primaryClass =

    Pith/arXiv arXiv 2015

  17. [17]

    , keywords =

    Gamma-ray bursts and the history of star formation. , keywords =. doi:10.1046/j.1365-8711.2000.03318.x , archivePrefix =. astro-ph/9911468 , primaryClass =

    arXiv 2000

  18. [18]

    , keywords =

    Gamma-Ray Bursts as a Probe of the Very High Redshift Universe. , keywords =. doi:10.1086/308918 , archivePrefix =. astro-ph/9909002 , primaryClass =

    Pith/arXiv arXiv

  19. [19]

    , keywords =

    The Cosmic History of Long Gamma-Ray Bursts. , keywords =. doi:10.3847/1538-4357/ac6e43 , adsurl =

    doi:10.3847/1538-4357/ac6e43

  20. [20]

    , keywords =

    On the Collapsar Model of Long Gamma-Ray Bursts:Constraints from Cosmic Metallicity Evolution. , keywords =. doi:10.1086/500363 , archivePrefix =. astro-ph/0512271 , primaryClass =

    Pith/arXiv arXiv

  21. [22]

    , keywords =

    Selection Effects on the Observed Redshift Dependence of Gamma-Ray Burst Jet Opening Angles. , keywords =. doi:10.1088/0004-637X/745/2/168 , archivePrefix =. 1110.4943 , primaryClass =

    Pith/arXiv arXiv

  22. [24]

    A Complete Sample of Bright Swift Long Gamma-Ray Bursts. I. Sample Presentation, Luminosity Function and Evolution. , keywords =. doi:10.1088/0004-637X/749/1/68 , archivePrefix =. 1112.1700 , primaryClass =

    Pith/arXiv arXiv

  23. [25]

    , keywords =

    Cosmological Gamma-Ray Bursts and Evolution of Galaxies. , keywords =. doi:10.1086/310853 , archivePrefix =. astro-ph/9707051 , primaryClass =

    Pith/arXiv arXiv

  24. [26]

    , keywords =

    An Evolving Stellar Initial Mass Function and the Gamma-ray Burst Redshift Distribution. , keywords =. doi:10.1088/2041-8205/727/2/L34 , archivePrefix =. 1101.3633 , primaryClass =

    Pith/arXiv arXiv 2041

  25. [27]

    , year = 2009, month = apr, volume =

    The Effect of the Initial Mass Function of Stars on the Burst Rate of GRBs. , year = 2009, month = apr, volume =. doi:10.1016/j.chinastron.2009.03.003 , adsurl =

    work page doi:10.1016/j.chinastron.2009.03.003 2009

  26. [28]

    , keywords =

    Redshift distribution and luminosity function of long gamma-ray bursts from cosmological simulations. , keywords =. doi:10.1111/j.1365-2966.2010.17044.x , archivePrefix =. 1005.3700 , primaryClass =

    arXiv 2010

  27. [29]

    , keywords =

    Cosmological tests using gamma-ray bursts, the star formation rate and possible abundance evolution. , keywords =. doi:10.1093/mnras/stu166 , archivePrefix =. 1306.4415 , primaryClass =

    Pith/arXiv arXiv

  28. [30]

    , keywords =

    Where are the missing gamma-ray burst redshifts?. , keywords =. doi:10.1111/j.1365-2966.2008.13006.x , archivePrefix =. 0711.0242 , primaryClass =

    arXiv 2008

  29. [31]

    , keywords =

    The Swift gamma-ray burst redshift distribution: selection biases and optical brightness evolution at high z?. , keywords =. doi:10.1093/mnras/stt537 , archivePrefix =. 1210.2488 , primaryClass =

    Pith/arXiv arXiv

  30. [32]

    , keywords =

    Postlaunch Analysis of Swift's Gamma-Ray Burst Detection Sensitivity. , keywords =. doi:10.1086/503326 , archivePrefix =. astro-ph/0602267 , primaryClass =

    Pith/arXiv arXiv

  31. [33]

    , keywords =

    Is the Redshift Clustering of Long-Duration Gamma-Ray Bursts Significant?. , keywords =. doi:10.1086/374945 , archivePrefix =. astro-ph/0302249 , primaryClass =

    Pith/arXiv arXiv

  32. [34]

    , keywords =

    An Unexpectedly Swift Rise in the Gamma-Ray Burst Rate. , keywords =. doi:10.1086/527671 , archivePrefix =. 0709.0381 , primaryClass =

    Pith/arXiv arXiv

  33. [35]

    BATSE Observations of Gamma-Ray Burst Spectra. I. Spectral Diversity. , keywords =. doi:10.1086/172995 , adsurl =

    doi:10.1086/172995

  34. [36]

    , keywords =

    The Complete Spectral Catalog of Bright BATSE Gamma-Ray Bursts. , keywords =. doi:10.1086/505911 , archivePrefix =. astro-ph/0601188 , primaryClass =

    Pith/arXiv arXiv

  35. [37]

    The BATSE Gamma-Ray Burst Spectral Catalog. I. High Time Resolution Spectroscopy of Bright Bursts Using High Energy Resolution Data. , keywords =. doi:10.1086/313289 , archivePrefix =. astro-ph/9908119 , primaryClass =

    Pith/arXiv arXiv

  36. [38]

    , year = 1974, month = feb, volume =

    Formation of Galaxies and Clusters of Galaxies by Self-Similar Gravitational Condensation. , year = 1974, month = feb, volume =. doi:10.1086/152650 , adsurl =

    doi:10.1086/152650 1974

  37. [39]

    , keywords =

    Large-scale bias and the peak background split. , keywords =. doi:10.1046/j.1365-8711.1999.02692.x , archivePrefix =. astro-ph/9901122 , primaryClass =

    arXiv 1999

  38. [40]

    , keywords =

    Halo Formation in Warm Dark Matter Models. , keywords =. doi:10.1086/321541 , archivePrefix =. astro-ph/0010389 , primaryClass =

    Pith/arXiv arXiv

  39. [41]

    , keywords =

    Large-Scale Structure Tests of Warm Dark Matter. , keywords =. doi:10.1086/176788 , archivePrefix =. astro-ph/9505029 , primaryClass =

    Pith/arXiv arXiv

  40. [42]

    , keywords =

    Constraining warm dark matter candidates including sterile neutrinos and light gravitinos with WMAP and the Lyman- forest. , keywords =. doi:10.1103/PhysRevD.71.063534 , archivePrefix =. astro-ph/0501562 , primaryClass =

    Pith/arXiv arXiv

  41. [43]

    , keywords =

    Constraints on Warm Dark Matter from Cosmological Reionization. , keywords =. doi:10.1086/322393 , archivePrefix =. astro-ph/0102304 , primaryClass =

    Pith/arXiv arXiv

  42. [44]

    , keywords =

    Constraints on the Small-Scale Power Spectrum of Density Fluctuations from High-Redshift Gamma-Ray Bursts. , keywords =. doi:10.1086/428770 , archivePrefix =. astro-ph/0501233 , primaryClass =

    Pith/arXiv arXiv

  43. [45]

    , keywords =

    The depletion of gas in high-redshift dwarf galaxies from an inhomogeneous reionization. , keywords =. doi:10.1093/mnrasl/slt035 , archivePrefix =. 1301.6776 , primaryClass =

    Pith/arXiv arXiv

  44. [46]

    , keywords =

    Constraints on warm dark matter models from high-redshift long gamma-ray bursts. , keywords =. doi:10.1093/mnras/stt674 , archivePrefix =. 1303.5060 , primaryClass =

    Pith/arXiv arXiv

  45. [47]

    , keywords =

    Hierarchical Growth and Cosmic Star Formation: Enrichment, Outflows, and Supernova Rates. , keywords =. doi:10.1086/503092 , archivePrefix =. astro-ph/0509183 , primaryClass =

    Pith/arXiv arXiv

  46. [48]

    , keywords =

    Stochastic background of gravitational waves generated by pre-galactic black holes. , keywords =. doi:10.1111/j.1365-2966.2009.15774.x , archivePrefix =. 0909.4252 , primaryClass =

    arXiv 2009

  47. [49]

    , year = 1955, month = jan, volume =

    The Luminosity Function and Stellar Evolution. , year = 1955, month = jan, volume =. doi:10.1086/145971 , adsurl =

    doi:10.1086/145971 1955

  48. [50]

    , year = 1959, month = mar, volume =

    The Rate of Star Formation. , year = 1959, month = mar, volume =. doi:10.1086/146614 , adsurl =

    doi:10.1086/146614 1959

  49. [51]

    The Rate of Star Formation. II. The Rate of Formation of Stars of Different Mass. , year = 1963, month = apr, volume =. doi:10.1086/147553 , adsurl =

    doi:10.1086/147553 1963

  50. [52]

    , keywords =

    A Stochastic Approach to Chemical Evolution. , keywords =. doi:10.1086/304627 , archivePrefix =. astro-ph/9610224 , primaryClass =

    Pith/arXiv arXiv

  51. [53]

    , keywords =

    The Nucleosynthetic Signature of Population III. , keywords =. doi:10.1086/338487 , archivePrefix =. astro-ph/0107037 , primaryClass =

    Pith/arXiv arXiv

  52. [54]

    , keywords =

    The Stellar Initial Mass Function. , keywords =

  53. [55]

    , keywords =

    On the Evolution of Star-forming Galaxies. , keywords =. doi:10.1086/424032 , archivePrefix =. astro-ph/0407170 , primaryClass =

    Pith/arXiv arXiv

  54. [56]

    , year = 2007, month = jan, volume =

    Erratum: ``On the Evolution of Star-forming Galaxies`` (<A href=''/abs/2004ApJ...615..209H''>ApJ, 615, 209 [2004]</A>). , year = 2007, month = jan, volume =. doi:10.1086/509654 , adsurl =

    work page doi:10.1086/509654 2004

  55. [57]

    Planck 2018 results. VI. Cosmological parameters. , keywords =. doi:10.1051/0004-6361/201833910 , archivePrefix =. 1807.06209 , primaryClass =

    Pith/arXiv arXiv 2018

  56. [58]

    , keywords =

    The large-scale structure of the Universe. , keywords =. doi:10.1038/nature04805 , archivePrefix =. astro-ph/0604561 , primaryClass =

    Pith/arXiv arXiv

  57. [59]

    , keywords =

    Cosmological constraints from the SDSS luminous red galaxies. , keywords =. doi:10.1103/PhysRevD.74.123507 , archivePrefix =. astro-ph/0608632 , primaryClass =

    Pith/arXiv arXiv

  58. [60]

    , keywords =

    Galaxy formation theory. , keywords =. doi:10.1016/j.physrep.2010.06.001 , archivePrefix =. 1006.5394 , primaryClass =

    Pith/arXiv arXiv 2010

  59. [62]

    , keywords =

    Where Are the Missing Galactic Satellites?. , keywords =. doi:10.1086/307643 , archivePrefix =. astro-ph/9901240 , primaryClass =

    Pith/arXiv arXiv

  60. [63]

    , keywords =

    Dark Matter Substructure within Galactic Halos. , keywords =. doi:10.1086/312287 , archivePrefix =. astro-ph/9907411 , primaryClass =

    Pith/arXiv arXiv

  61. [64]

    , keywords =

    Born to be Starless: Revisiting the Missing Satellite Problem. , keywords =. doi:10.3847/1538-4357/ade2e0 , archivePrefix =. 2506.09152 , primaryClass =

    Pith/arXiv arXiv

  62. [65]

    Galaxies , keywords =

    Review of Solutions to the Cusp-Core Problem of the CDM Model. Galaxies , keywords =. doi:10.3390/galaxies9040123 , archivePrefix =. 2209.14151 , primaryClass =

    Pith/arXiv arXiv

  63. [66]

    , keywords =

    Mass Density Profiles of Low Surface Brightness Galaxies. , keywords =. doi:10.1086/320262 , archivePrefix =. astro-ph/0103102 , primaryClass =

    Pith/arXiv arXiv

  64. [67]

    , year = 1994, month = aug, volume =

    Evidence against dissipation-less dark matter from observations of galaxy haloes. , year = 1994, month = aug, volume =. doi:10.1038/370629a0 , adsurl =

    doi:10.1038/370629a0 1994

  65. [68]

    , keywords =

    Small-Scale Challenges to the CDM Paradigm. , keywords =. doi:10.1146/annurev-astro-091916-055313 , archivePrefix =. 1707.04256 , primaryClass =

    Pith/arXiv arXiv

  66. [69]

    Proceedings of the National Academy of Science , keywords =

    Cold dark matter: Controversies on small scales. Proceedings of the National Academy of Science , keywords =. doi:10.1073/pnas.1308716112 , archivePrefix =. 1306.0913 , primaryClass =

    Pith/arXiv arXiv

  67. [70]

    , keywords =

    Too big to fail? The puzzling darkness of massive Milky Way subhaloes. , keywords =. doi:10.1111/j.1745-3933.2011.01074.x , archivePrefix =. 1103.0007 , primaryClass =

    arXiv 2011

  68. [73]

    Science , keywords =

    Stellar Feedback in Dwarf Galaxy Formation. Science , keywords =. doi:10.1126/science.1148666 , archivePrefix =. 0711.4803 , primaryClass =

    Pith/arXiv arXiv

  69. [74]

    , keywords =

    Reionization and the Abundance of Galactic Satellites. , keywords =. doi:10.1086/309279 , archivePrefix =. astro-ph/0002214 , primaryClass =

    Pith/arXiv arXiv

  70. [76]

    , keywords =

    Cold dark matter heats up. , keywords =. doi:10.1038/nature12953 , archivePrefix =. 1402.1764 , primaryClass =

    Pith/arXiv arXiv

  71. [77]

    Nature Astronomy , keywords =

    Baryonic solutions and challenges for cosmological models of dwarf galaxies. Nature Astronomy , keywords =. doi:10.1038/s41550-022-01689-w , archivePrefix =. 2206.05295 , primaryClass =

    Pith/arXiv arXiv

  72. [78]

    , keywords =

    Composite dark matter from a model with composite Higgs boson. , keywords =. doi:10.1103/PhysRevD.78.065040 , archivePrefix =. 0806.1191 , primaryClass =

    Pith/arXiv arXiv

  73. [79]

    , keywords =

    The haloes of bright satellite galaxies in a warm dark matter universe. , keywords =. doi:10.1111/j.1365-2966.2011.20200.x , archivePrefix =. 1104.2929 , primaryClass =

    arXiv 2011

  74. [80]

    , keywords =

    The properties of warm dark matter haloes. , keywords =. doi:10.1093/mnras/stt2431 , archivePrefix =. 1308.1399 , primaryClass =

    Pith/arXiv arXiv

  75. [81]

    , keywords =

    Halo Substructure and the Power Spectrum. , keywords =. doi:10.1086/378797 , archivePrefix =. astro-ph/0304292 , primaryClass =

    Pith/arXiv arXiv

  76. [82]

    , keywords =

    The mass of the dark matter particle: Theory and galaxy observations. , keywords =. doi:10.1016/j.newast.2012.04.001 , archivePrefix =. 1004.1908 , primaryClass =

    Pith/arXiv arXiv 2012

  77. [84]

    , keywords =

    The edge of galaxy formation III: the effects of warm dark matter on Milky Way satellites and field dwarfs. , keywords =. doi:10.1093/mnras/stz327 , archivePrefix =. 1902.02047 , primaryClass =

    Pith/arXiv arXiv 1902

  78. [85]

    , keywords =

    THESAN-HR: galaxies in the Epoch of Reionization in warm dark matter, fuzzy dark matter, and interacting dark matter. , keywords =. doi:10.1093/mnras/stad3397 , archivePrefix =. 2304.06742 , primaryClass =

    Pith/arXiv arXiv

  79. [86]

    Testing warm dark matter cosmologies with galaxy scaling relations: A joint simulation─observation study using DREAMS simulations

    CASCO: Cosmological and AStrophysical parameters from Cosmological simulations and Observations: IV. Testing warm dark matter cosmologies with galaxy scaling relations: A joint simulation─observation study using DREAMS simulations. , keywords =. doi:10.1051/0004-6361/202556698 , archivePrefix =. 2601.07543 , primaryClass =

    arXiv

  80. [87]

    , keywords =

    Non-linear evolution of cosmological structures in warm dark matter models. , keywords =. doi:10.1111/j.1365-2966.2012.21252.x , archivePrefix =. 1112.0330 , primaryClass =

    arXiv 2012

Showing first 80 references.