Pith. sign in

REVIEW 4 major objections 5 minor 49 references

Cosmological $\gamma$-$\gamma$ Pair-Production Background

T0 review · 4 major / 5 minor · reviewed 2026-08-02 · deepseek-v4-flash

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

Pith's one-line read Cosmic photon background annihilates with itself to produce a measurable share of the gamma-ray background.

desk verdict A plausible bookkeeping calculation of a guaranteed process, but the headline 10-20% IC contribution is a fiducial, not a floor, given the authors' own 0.075-5.1 normalization band. read the letter →

arxiv 2607.14276 v1 pith:QESGBZQY submitted 2026-07-15 astro-ph.CO astro-ph.HE

Mika A. Gelowicz , Thomas Siegert , Saurabh Mittal , Laura Eisenberger , Dimitris Tsatsis , Niklas C. Bauer , Rudi Reinhardt , Patrik Ehrmann
show 5 more authors
Manja L. Zimmerer Hiroki Yoneda Tomohiko Oka Tristan Bouchet Manuel R. H. W. Skalka
This is my paper
classification astro-ph.COastro-ph.HE
keywords cosmicgamma-raybackgroundpairproductiongamma-gammaannihilationInverseComptonphotonelectron-positronpairsgray-bodydecompositionredshiftevolution
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 the cosmic photon background—the combined radiation from radio to TeV energies—interacts with itself through gamma-gamma pair production, creating electron-positron pairs throughout cosmic history. After accounting for how those pairs lose energy, the resulting Inverse Compton emission forms an unavoidable secondary component of the cosmic gamma-ray background. In the 1 MeV to 1 GeV range, this component can make up 10–20% of the measured emission, substantially narrowing the long-standing gap between observed MeV background and model predictions. The claim matters because, if correct, no model of the gamma-ray background can be complete without including this process.

What carries the argument

The calculation rests on decomposing the full cosmic photon background into 28 diluted blackbody (gray-body) components, fitting their temperatures and amplitudes to observational data. Each component is then evolved in redshift using source-type luminosity functions—pure density evolution, pure luminosity evolution, or luminosity-dependent density evolution—so that the CPB can be reconstructed for redshifts up to 10. The pair-injection spectrum is obtained by integrating the angle- and energy-dependent pair-production cross section (following Boettcher & Schlickeiser) over the evolving CPB, and the resulting electron/positron populations are propagated toward z=0 through a cosmological cont

What would settle it

Measure the cosmic gamma-ray background spectrum in the 1–100 MeV range with significantly better precision and compare it to the sum of established source contributions (Seyferts, FSRQs, supernovae, blazars, neutron stars). If the observed background is already fully explained by known sources alone, or if the sum of known sources plus this predicted Inverse Compton component exceeds the observed flux at the fiducial CPB amplitudes, the central 10–20% claim would be ruled out. Conversely, if the excess tracks the predicted double-peaked shape around 0.1 MeV and tens of MeV, the claim would be

Watch

Extended reading notes

Core claim

The paper's central claim is that electron-positron pairs produced by gamma-gamma annihilation of the cosmic photon background with itself, after Inverse Compton cooling, contribute 10–20% of the cosmic gamma-ray background between roughly 1 MeV and 1 GeV. The pair-production emissivity rises steeply from about 2×10⁻³⁶ e± cm⁻³ s⁻¹ at z=0 to a peak of 1.8×10⁻³¹ e± cm⁻³ s⁻¹ at z≈2.7, then declines, yielding a total cosmic pair-production rate on the order of 10⁵⁴ e± s⁻¹ up to redshift 10. Because the process is physically inevitable, the authors argue it sets a minimum level of secondary emission that any CGB study must include.

Load-bearing premise

The magnitude of the claimed effect depends on the assumption that the cosmic photon background at every redshift is accurately represented by 28 gray-body components, whose amplitudes at z=0 are uncertain by up to an order of magnitude and whose redshift evolution—especially beyond z=5—is described by luminosity functions the paper itself calls rather uncertain.

Editorial extensions

If this is right

  • Any future model of the cosmic gamma-ray background must include this pair-production secondary component as a minimum contribution, especially in the 1–100 MeV band.
  • If correct, roughly 10–20% of the measured MeV background could originate from the re-emission of pairs created by photon-photon absorption at higher energies, reducing the need for unknown sources.
  • The peak pair-production rate at z≈2.7 means most of this secondary emission is generated during the epoch of peak star formation, linking the gamma-ray background to the cosmic star-formation history.
  • The local (Galactic-scale) pair-production rate is about eight orders of magnitude below the Milky Way's positron annihilation rate, so this process does not solve the Galactic positron puzzle—but it does create a substantial intergalactic population of high-energy e± pairs above 1 GeV.

Reading between the lines

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

  • If the central claim holds, precise measurements of the MeV background could be inverted to constrain the amplitude of the cosmic UV/optical background and the GeV background, which are the dominant pair-production partners—offering a new observational probe of those fields.
  • The model assumes negligible intergalactic magnetic fields; if the IGMF is actually near 10⁻⁹ G, synchrotron losses would compete with Inverse Compton, shifting the predicted secondary spectrum and possibly producing a radio background—a testable alternative scenario.
  • The gray-body decomposition is a modeling choice; a power-law decomposition or an independently fitted CPB evolution could either confirm the 10–20% estimate or reveal how much of it is tied to the assumed 28-component functional form.
  • Because the emission peaks around 100 keV and tens of MeV, instruments with improved sensitivity in that band could directly search for the double-peaked spectral signature predicted here.
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.

Referee Report

4 major / 5 minor

Summary. This paper calculates the cosmological electron–positron pair-production rate from γ–γ interactions of the cosmic photon background (CPB) with itself for 0 ≤ z ≤ 10. The CPB is decomposed into 28 diluted blackbodies fitted to Hill et al. (2018), each evolved by an assumed source luminosity function. The authors integrate the Boettcher & Schlickeiser (1997) differential cross section over the evolving fields, solve a continuity equation with Coulomb/ionization, IC, bremsstrahlung, synchrotron, adiabatic, and annihilation losses, and line-of-sight integrate the resulting IC, bremsstrahlung, and annihilation emission. They find a peak pair emissivity of 1.8×10^-31 cm^-3 s^-1 at z≈2.7, a total rate ~10^54 e±/s, and conclude that IC emission from the pairs contributes 10–20% of the observed CGB in the 1 MeV–1 GeV range, making it an inevitable secondary component that should be included in CGB models.

Significance. If the quantitative claim held, this would be a valuable addition to CGB modeling: it identifies an unavoidable secondary channel operating on the known CPB alone, and it could help close the long-standing MeV-band gap. The use of the exact QED pair-production kernel, the explicit redshift-dependent propagation, and the careful treatment of the IGM cooling channels are strengths. The main limitation is not the formalism but the normalization: the input CPB amplitudes are uncertain by orders of magnitude, the high-z luminosity functions are extrapolated, and no fitted parameters or code are provided. The paper's own uncertainty band reaches values for which the IC contribution is below ~1% of the CGB, so the headline '10–20%' should be read as an upper-end estimate rather than a robust minimum.

major comments (4)
  1. [§3.1, §4, Fig. 10] The headline claim that the Inverse Compton component contributes 10–20% of the CGB between 1 MeV and 1 GeV is not robust to the input uncertainties stated in the paper itself. Section 3.1 notes that the fitted blackbody amplitudes in the COB and MeV-CGB ranges are “typically uncertain by one order of magnitude, or more”. Section 4 propagates COB/CUV (70%) and CGB (50%) amplitude uncertainties into a normalization range 0.075–5.1 times the fiducial IC prediction. Multiplying the 10–20% fiducial contribution by 0.075 gives ~0.75–1.5%, so the claimed “minimum level” and “sizable contribution” are not established at the low end. The paper should supply the fitted parameters with covariance and present the IC/CGB ratio as a function of the input amplitude uncertainties rather than a single curve.
  2. [§3.2, Eq. (29)] High-redshift source evolution is a second, unquantified normalization risk. Section 3.2 states that luminosity functions are “rather uncertain” beyond z=5, yet Eq. (29) integrates secondary emission to z_max=10. The peak pair-production rate occurs at z≈2.7, but the line-of-sight integral receives contributions from z>5 where the CPB model is extrapolated. The quoted 0.075–5.1 uncertainty band includes only COB/CGB amplitude and energy-loss factors, not this luminosity-function uncertainty. A sensitivity test with alternative high-z luminosity functions, or a truncated z_max=5 comparison, is needed to determine whether the 10–20% claim survives.
  3. [§3.1, Table 2] The calculation is not independently reproducible. Section 3.1 states that 54 parameters (27 temperatures and 27 amplitudes) were fit by χ²-minimization, but neither the fitted values nor the fitting residuals are given; Table 2 lists only source identifications and compositions. Since the pair-production emissivity is a direct integral (Eq. 5) over these fitted gray-body fields, the central result cannot be checked without the parameter table or code. Please provide a supplementary table with the fitted temperatures/amplitudes and, ideally, the propagation script.
  4. [§4, Eq. (27)] The IC emissivity uses the delta-approximation kernel (Dermer & Schlickeiser 1993). Because the secondary spectrum in the 1 MeV–1 GeV band is the quantity compared with CGB data, the delta approximation can shift the predicted spectral shape and the fraction of flux falling in that band. The authors should quantify the effect by comparing with the full IC kernel, at least for the dominant CMB target field; this is particularly relevant to the two-peak structure described in Section 4.
minor comments (5)
  1. [Eq. (29), Fig. 9] The text says Eq. (29) includes e^{-τ}, but the Fig. 9 caption calls the total spectrum “unabsorbed”. Clarify whether τ=0 is used in the figure; if not, state the attenuation treatment explicitly.
  2. [Abstract/§4/§5] The claimed band is stated variously as “1–100 MeV” and “1 MeV–1 GeV”, and “10–20%” vs. “20%”. Harmonize these statements and specify whether the percentage is a local maximum in a sub-band or an average over the stated range.
  3. [§5] The total systematic uncertainty is quoted as “about one order of magnitude”, but Section 4 gives a normalization range 0.075–5.1 (a factor of 68). Reconcile these statements.
  4. [Table 2] Row 22 lists “0.6 FSRQ+0.5 BL Lac”, which sums to 1.1; check and normalize the composition fractions.
  5. [§4] Using the total measured CGB as input includes the secondary component being computed. For a 10–20% contribution this is a second-order correction, but a brief self-consistency check, or an explicit statement that the effect is neglected, would strengthen the “minimum level” terminology.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the 10–20% IC contribution is a forward QED calculation from measured CPB fields, not a fit to the comparison data.

full rationale

The derivation is self-contained. The CPB is decomposed into 28 gray bodies fitted to Hill et al. (2018) data (Sec. 3.1, Eq. 7); the pair-injection spectrum is the QED integral of Eq. (5); the IC/annihilation emission follows from solving Eq. (21) and line-of-sight integration of Eq. (29). The claimed 10–20% CGB contribution (Sec. 4, Fig. 10) is not equal to any fitted parameter and is not statistically forced to the comparison data: it is a reshuffled, sub-dominant product of a nonlinear integral over the fitted photon fields. The paper's own caveats—amplitudes 'typically uncertain by one order of magnitude, or more' (Sec. 3.1), luminosity functions 'rather uncertain' beyond z=5 (Sec. 3.2), and an IC normalization range of 0.075–5.1× (Sec. 4)—are robustness/accuracy limitations, affecting the strength of the quantitative claim but not creating logical circularity. The z≈2.7 peak is inherited from the assumed SFR/luminosity-function evolution, which is an input dependence, not a tautology. Self-citations (Siegert 2023, Siegert et al. 2016) are background or rate comparisons and are not load-bearing. No uniqueness theorem or ansatz is imported from the authors' prior work. The only near-overlap is that the observed CGB is both part of the fitted input and the comparison target; because the predicted IC is not the same quantity as the input and is small relative to the dominant pair-production partners (COB/CUV with GeV CGB), this is a self-consistency consideration rather than a reduction by construction. Missing code/parameter tables hinder reproducibility but are not circularity.

Assumptions & free parameters 5 free parameters · 7 assumptions · 0 invented entities

The central result depends on a chain of external inputs: the QED cross-section, the measured CPB, the choice of gray-body decomposition, literature luminosity functions, IGM thermodynamics, and approximate cooling kernels. No new physical particles, forces, or dimensions are introduced; the 'thermal pool' is a numerical state variable, not a new entity.

free parameters (5)
  • 27 blackbody temperatures T_i = not given numerically; peak energies from 37 MHz to 236 GeV (Table 2)
    Shape parameters fitted by chi2 minimization to Hill+18 CPB; paper states temperature is 'a mere shape parameter and not necessarily physically meaningful'.
  • 27 blackbody dilution amplitudes A_i = not given numerically; amplitudes uncertain by order of magnitude or more in COB/CGB(MeV) ranges
    Scale each gray body; A_i enters Eq. (5) linearly, so the pair-production rate and IC spectrum inherit these uncertainties.
  • source-composition fractions per blackbody = e.g., 0.5 Gal+0.5 AGN, 0.25 SNe+0.75 FSRQ (Table 2)
    Hand-assigned weights determine which luminosity function evolves each component; some rows (BBs 22-24) sum to more than 1.
  • luminosity-function parameters (phi*, L*, slopes, evolution e(z)) = taken from cited AGN/blazar/SF galaxy surveys
    These literature parameters set the redshift evolution shown in Fig. 2; beyond z~5 the paper states they are 'rather uncertain'.
  • IGM magnetic field / synchrotron cooling = assumed negligible (B ~ 1e-15 G)
    Section 4: 'we assume negligible synchrotron cooling'; if B ~ 1e-9 G, synchrotron becomes as strong as IC and the predicted CGB contribution changes.
assumptions (7)
  • standard math QED gamma-gamma pair-production cross section and differential spectrum (Boettcher & Schlickeiser 1997; Jauch & Rohrlich 1976)
    Used via Eq. (5) as the unproved physics kernel; the paper refers to the reference for the analytical function F.
  • domain assumption The CPB is well represented by a sum of 28 diluted blackbodies
    Sect. 3.1; arbitrary functional choice, fitted to observed CPB data.
  • domain assumption Each blackbody can be assigned to specific source types and evolved by luminosity functions/redshift
    Sect. 3.2 and Table 2; required to get CPB(z), with large uncertainties beyond z=5.
  • domain assumption IGM density, temperature, ionization states from Puchwein+15, Silva+13; Ps formation coefficients from Wallyn+96
    Sect. 4; enters annihilation and cooling rates in the propagation equation.
  • domain assumption Delta-approximation for IC kernel and E^-1 bremsstrahlung kernel suffice
    Sect. 4; approximation is not benchmarked against exact kernels.
  • ad hoc to paper Negligible synchrotron cooling (small IGM magnetic field)
    Sect. 4; if false, IC flux is reduced and a radio background is added.
  • ad hoc to paper All pairs cool fully and only then annihilate; a global factor of 2 covers early annihilation
    Sect. 4; no detailed treatment of in-galaxy losses or partial cooling before annihilation.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Cosmological $\gamma$-$\gamma$ Pair-Production Background." pith.science (2026). https://pith.science/paper/QESGBZQY

@misc{pith2026260714276,
  author       = {Pith},
  title        = {Pith review of: Cosmological $\gamma$-$\gamma$ Pair-Production Background},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/QESGBZQY}},
  note         = {Machine review of arXiv:2607.14276}
}
abstract

The origin of positrons is one of the unsolved puzzles in astrophysics as the majority of sources are still unidentified. The Cosmic Photon Background (CPB) is the isotropic radiation spanning the entire electromagnetic spectrum. Interactions of the CPB with itself may pose a promising source of positrons and secondary emission. We calculate the electron-positron pair production rate from the $\gamma$-$\gamma$ pair-production of the CPB with itself for redshifts $z \leq 10$, and determine the annihilation spectrum, Inverse Compton emission, and bremsstrahlung. The CPB is decomposed into a sum of gray body functions, of which each is being evolved according to source type luminosity functions and redshift. We compute the pair-production rate by integrating the angle- and energy-dependent cross section over the evolving CPB. The pairs produced at each redshift are then propagated towards $z=0$, taking into account a cosmological, intergalactic, energy loss function. The photon emission is calculated per redshift and then line-of-sight integrated towards a contribution of the Cosmic Gamma-Ray Background (CGB) today. The resulting pair-production emissivity increases steeply from $z=0$ of about $2 \times 10^{-36}$ to a peak of $1.8 \times 10^{-31}\,\mathrm{e^\pm\,cm^{-3}\,s^{-1}}$ at $z=2.7$, then declines again. This yields a total cosmic pair-production rate on the order of $10^{54}\,\mathrm{e^\pm\,s^{-1}}$ up to redshift $10$. The secondary emission of pairs experiencing Inverse Compton scattering off the CPB results in a sizable contribution to the CGB. The pairs from cosmological $\gamma$-$\gamma$ absorption provide a minimum level of secondary emission which needs to be taken into account for any CGB study. Especially in the range from 1 MeV to 1 GeV, this background can make up 20% of the total CGB emission and may substantially reduce the gap between MeV observations and models.

Figures

Figures reproduced from arXiv: 2607.14276 by the authors.

Figure 1
Figure 1. CPB spectrum (black data points; data and uncertainties taken from Hill et al. 2018) together with decomposition into [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Evolution of amplitude relative to redshift 0 for the first [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. Redshift evolution for the CPB for z = 1, z = 3, z = 5, and z = 10 (blue) in comparison to z = 0 (red). Up to z ∼ 3, most blackbody components have reached peak amplitude. At z = 5, most amplitudes are comparable to z = 0, while at z = 10 most components decline again, except for some UV and soft gamma￾ray components that remain elevated. In contrast, there is the behavior of the CMB, which continues to increase in … view at source ↗
Figures from the paper (6 more)
Figure 4
Figure 4. Figure 4: Pair yield contribution from diluted blackbodies inter [PITH_FULL_IMAGE:figures/full_fig_p007_4.png]
Figure 5
Figure 5. Figure 5: Pair injection spectrum from γ-γ pair-production of the CPB with itself. The general shape (dashed gray line) can be described by a cutoff power-law with index −1 and cutoff energy around 0.1–1 TeV. The total local pair emissivity is 2×10−36 cm−3 s −1 . Then, the emiss…
Figure 8
Figure 8. Figure 8: Cosmological energy loss rates for different processes at redshift z = 0 (top) and z = 8.5 (bottom). losses, this is still sub-dominant. In general, the magnitude of the losses increases with redshift. Due to the low number densities of baryons and electrons as the low…
Figure 7
Figure 7. Figure 7: Intergalactic medium minimum particle densities accord [PITH_FULL_IMAGE:figures/full_fig_p008_7.png]
Figure 9
Figure 9. Figure 9: Secondary emission from pairs produced via [PITH_FULL_IMAGE:figures/full_fig_p009_9.png]
Figure 10
Figure 10. Figure 10: A composition of the CPB from 20 keV to 40 GeV. The individual contributions from established astrophysical source [PITH_FULL_IMAGE:figures/full_fig_p010_10.png]

Discussion (0). Sign in to comment.

Reference graph

Works this paper leans on

49 extracted references · 2 linked inside Pith

  1. [1]

    2015, The Astrophysical Journal, 799, 86

    Ackermann, M., Ajello, M., Albert, A., et al. 2015, The Astrophysical Journal, 799, 86

    2015

  2. [2]

    L., Georgakakis, A., et al

    Aird, J., Coil, A. L., Georgakakis, A., et al. 2015, Monthly Notices of the Royal Astronomical Society, 451, 1892

    2015

  3. [3]

    M., et al

    Ajello, M., Costamante, L., Sambruna, R. M., et al. 2009, The Astrophysical Journal, 699, 603

    2009

  4. [4]

    2015, The Astrophysical Journal Letters, 800, L27

    Ajello, M., Gasparrini, D., Sánchez-Conde, M., et al. 2015, The Astrophysical Journal Letters, 800, L27

    2015

  5. [5]

    D., Paliya, V

    Ajello, M., Mauro, M. D., Paliya, V . S., & Garrappa, S. 2020, The Astrophysical Journal, 894, 88

    2020

  6. [6]

    W., Gasparrini, D., et al

    Ajello, M., Romani, R. W., Gasparrini, D., et al. 2014, The Astrophysical Jour- nal, 780, 73

    2014

  7. [7]

    S., Romani, R

    Ajello, M., Shaw, M. S., Romani, R. W., et al. 2012, The Astrophysical Journal, 751, 108

    2012

  8. [8]

    2015, ApJ, 810, 74

    Aversa, R., Lapi, A., de Zotti, G., Shankar, F., & Danese, L. 2015, ApJ, 810, 74

    2015

Show all 49 references
  1. [9]

    & Schlickeiser, R

    Boettcher, M. & Schlickeiser, R. 1997, The Pair Production Spectrum from Photon-Photon Annihilation

    1997

  2. [10]

    & Totani, T

    Chen, J. & Totani, T. 2025, Monthly Notices of the Royal Astronomical Society, staf928

    2025

  3. [11]

    R., Crocker, R

    Das, S., Krumholz, M. R., Crocker, R. M., Siegert, T., & Eisenberger, L. 2025, arXiv e-prints, arXiv:2506.00847

    2025 arXiv

  4. [12]

    Dermer, C. D. & Schlickeiser, R. 1993, ApJ, 416, 458

    1993

  5. [13]

    & Krennrich, F

    Dwek, E. & Krennrich, F. 2013, Astroparticle Physics, 43, 112

    2013

  6. [14]

    Fixsen, D. J. 2009, The Astrophysical Journal, 707, 916

    2009

  7. [15]

    2022, The Astro- physical Journal, 931, 138

    Fukazawa, Y ., Matake, H., Kayanoki, T., Inoue, Y ., & Finke, J. 2022, The Astro- physical Journal, 931, 138

    2022

  8. [16]

    2007, A&A, 463, 79

    Gilli, R., Comastri, A., & Hasinger, G. 2007, A&A, 463, 79

    2007

  9. [17]

    & Reinhardt, J

    Greiner, W. & Reinhardt, J. 2008, Quantum electrodynamics (Springer Science & Business Media)

    2008

  10. [18]

    2013, Monthly Notices of the Royal Astronomical Society, 432, 23

    Gruppioni, C., Pozzi, F., Rodighiero, G., et al. 2013, Monthly Notices of the Royal Astronomical Society, 432, 23

    2013

  11. [19]

    2012, The Astrophysical Journal, 752, 113

    Helgason, K., Ricotti, M., & Kashlinsky, A. 2012, The Astrophysical Journal, 752, 113

    2012

  12. [20]

    W., & Scott, D

    Hill, R., Masui, K. W., & Scott, D. 2018, Applied Spectroscopy, 72, 663

    2018

  13. [21]

    Hogg, D. W. 1999, arXiv preprint astro-ph/9905116

    1999 arXiv

  14. [22]

    2014, Cosmic Gamma-ray Background Radiation

    Inoue, Y . 2014, Cosmic Gamma-ray Background Radiation

    2014

  15. [23]

    Jauch, J. M. & Rohrlich, F. 1976, The Theory of Photons and Electrons: the relativistic quantum field theory of charged particles with spin one-half, 2nd edn. (Berlin: Springer)

    1976

  16. [24]

    2009, A&A, 508, 1099

    Jean, P., Gillard, W., Marcowith, A., & Ferrière, K. 2009, A&A, 508, 1099

    2009

  17. [25]

    & Srianand, R

    Khaire, V . & Srianand, R. 2019, Monthly Notices of the Royal Astronomical Society, 484, 4174 Knödlseder, J., Sabri, K., Jean, P., et al. 2025, A&A, 700, A257

    2019

  18. [26]

    2005, Annual Review of Astronomy and Astrophysics, 43, 727

    Lagache, G., Puget, J.-L., & Dole, H. 2005, Annual Review of Astronomy and Astrophysics, 43, 727

    2005

  19. [27]

    & Liddle, A

    Lahav, O. & Liddle, A. R. 2024, The Cosmological Parameters (2023)

    2024

  20. [28]

    2021, A&A, 652, A80

    Locatelli, N., Vazza, F., Bonafede, A., et al. 2021, A&A, 652, A80

    2021

  21. [29]

    Longair, M. S. 2007, Galaxy formation (Springer Science & Business Media)

    2007

  22. [30]

    & Dickinson, M

    Madau, P. & Dickinson, M. 2014, Annual Review of Astronomy and Astro- physics, 52, 415

    2014

  23. [31]

    2015, The Astrophysical Journal, 810, 72

    Mancuso, C., Lapi, A., Cai, Z.-Y ., et al. 2015, The Astrophysical Journal, 810, 72

    2015

  24. [32]

    M., et al

    Marcotulli, L., Ajello, M., Urry, C. M., et al. 2022, The Astrophysical Journal, 940, 77

    2022

  25. [33]

    & V ovk, I

    Neronov, A. & V ovk, I. 2010, Science, 328, 73

    2010

  26. [34]

    & Powell, J

    Ore, A. & Powell, J. L. 1949, Physical Review, 75, 1696

    1949

  27. [35]

    A., Matteucci, F., Della Valle, M., & Spitoni, E

    Palicio, P. A., Matteucci, F., Della Valle, M., & Spitoni, E. 2024, A&A, 689, A203

    2024

  28. [36]

    Penzias, A. A. & Wilson, R. W. 1965, ApJ, 142, 419 Planck Collaboration, Aghanim, N., Akrami, Y ., et al. 2020, A&A, 641, A6

    1965

  29. [37]

    M., et al

    Prantzos, N., Boehm, C., Bykov, A. M., et al. 2011, Reviews of Modern Physics, 83, 1001

    2011

  30. [38]

    S., Haehnelt, M

    Puchwein, E., Bolton, J. S., Haehnelt, M. G., et al. 2015, MNRAS, 450, 4081

    2015

  31. [39]

    2019, Monthly Notices of the Royal Astronomical Society, 490, 758

    Qu, Y ., Zeng, H., & Yan, D. 2019, Monthly Notices of the Royal Astronomical Society, 490, 758

    2019

  32. [40]

    & Korobkin, O

    Ruiz-Lapuente, P. & Korobkin, O. 2020, The Astrophysical Journal, 892, 45

    2020

  33. [41]

    H., et al

    Ruiz-Lapuente, P., The, L.-S., Hartmann, D. H., et al. 2016, The Astrophysical Journal, 820, 142

    2016

  34. [42]

    1976, Astrophysical Journal, V ol

    Schechter, P. 1976, Astrophysical Journal, V ol. 203, p. 297-306, 203, 297

    1976

  35. [43]

    F., Faucher-Giguère, C.-A., et al

    Shen, X., Hopkins, P. F., Faucher-Giguère, C.-A., et al. 2020, Monthly Notices of the Royal Astronomical Society, 495, 3252

    2020

  36. [44]

    2023, Astrophysics and Space Science, 368, 27

    Siegert, T. 2023, Astrophysics and Space Science, 368, 27

    2023

  37. [45]

    2016, A&A, 586, A84

    Siegert, T., Diehl, R., Khachatryan, G., et al. 2016, A&A, 586, A84

    2016

  38. [46]

    B., Santos, M

    Silva, M. B., Santos, M. G., Gong, Y ., Cooray, A., & Bock, J. 2013, ApJ, 763, 132

    2013

  39. [47]

    A., Driver, S

    Tompkins, S. A., Driver, S. P., Robotham, A. S. G., et al. 2023, Monthly Notices of the Royal Astronomical Society, 521, 332

    2023

  40. [48]

    A., Durouchoux, P., & Chapuis, C

    Wallyn, P., Mahoney, W. A., Durouchoux, P., & Chapuis, C. 1996, ApJ, 465, 473

    1996

  41. [49]

    2017, The Astrophysical Jour- nal, 846, 78 Article number, page 11

    Yuan, Z., Wang, J., Zhou, M., Qin, L., & Mao, J. 2017, The Astrophysical Jour- nal, 846, 78 Article number, page 11

    2017

Pith tools

Reviewed August 2, 2026 · model on record in the stance chip above.