arxiv: 2605.00648 · v1 · submitted 2026-05-01 · ✦ hep-ph · astro-ph.CO

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Anisotropy of Cosmic Background Photons from Annihilating/Decaying Dark Matter

Ryosuke Kasuya , Kazunori Nakayama

Authors on Pith no claims yet

Pith reviewed 2026-05-09 18:59 UTC · model grok-4.3

classification ✦ hep-ph astro-ph.CO

keywords dark matterannihilationdecayangular power spectrumcosmic backgroundenergy resolutionanisotropyline photons

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The pith

A formulation for the angular power spectrum of photons from dark matter requires including detector energy resolution to be accurate.

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

This paper presents a detailed method to compute the angular power spectrum of the cosmic photon background produced by dark matter annihilation or decay. Special emphasis is placed on the production of photons at discrete energies, or line photons. The work shows that the energy resolution of the observing instrument plays a critical role in determining the correct level of anisotropy in these backgrounds. Without incorporating this resolution, calculations fail to match what telescopes would actually measure. The formulation is then used to compare with data collected across infrared to gamma-ray energies.

Core claim

We provide a detailed formulation for calculating the angular power spectrum of the cosmic background photons arising from the dark matter decay or annihilation in a comprehensive manner. We pay particular attention to the case of dark matter decaying or annihilating into line photons. It is pointed out that taking account of the energy resolution of the detector is essential to correctly evaluate the angular power spectrum. We apply our formulation to the observational data from infrared, optical, X-ray and gamma-ray telescopes.

What carries the argument

The angular power spectrum calculation that integrates over the detector's energy resolution for line photon signals from dark matter processes.

If this is right

Accurate constraints on dark matter lifetime and annihilation cross section can be derived from existing telescope observations.
Previous studies that neglected energy resolution may have incorrect estimates of photon anisotropy.
Line photon signals from dark matter can be more reliably distinguished from other cosmic sources.

Where Pith is reading between the lines

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

This approach could extend to other diffuse backgrounds like neutrinos or cosmic rays from dark matter.
Future detectors with better energy resolution might reveal or rule out dark matter contributions more effectively.
Connections to structure formation could be explored if anisotropy patterns depend on dark matter clustering.

Load-bearing premise

Dark matter annihilation and decay occur through standard channels that produce photons in predictable ways without exotic propagation effects.

What would settle it

Observing whether the measured angular power spectrum in gamma-ray data matches the predicted spectrum only when energy resolution is included, or deviates significantly from it.

Figures

Figures reproduced from arXiv: 2605.00648 by Kazunori Nakayama, Ryosuke Kasuya.

**Figure 1.** Figure 1: The mean intensity of cosmic background photon from dark matter decaying into view at source ↗

**Figure 2.** Figure 2: The dimensionless angular power spectrum of the cosmic background photon from view at source ↗

**Figure 3.** Figure 3: (Left) The enhancement factor ∆2 (z) as a function of 1 + z, calculated with two prescriptions for the concentration parameter (see Eq. (B.11) and (B.12)). (Right) The mean intensity of cosmic background photon from dark matter annihilating into line photons. We have taken Nγ ⟨σv⟩ /m = 10−38 cm2/eV. What is nontrivial compared with the case of decay is ⟨ρ 2 DM(z)⟩ ̸= ⟨ρDM(z)⟩ 2 . Actually, due to the nonli… view at source ↗

**Figure 4.** Figure 4: The dimensionless angular power spectrum of the cosmic background photon from view at source ↗

**Figure 5.** Figure 5: Constraints on the dark matter decay rate into photons from the angular power view at source ↗

**Figure 6.** Figure 6: Constraints on the dark matter annihilation cross section into photons from the view at source ↗

**Figure 7.** Figure 7: Constraints on the dark matter decay rate into photons from the angular power view at source ↗

**Figure 8.** Figure 8: Constraints on the dark matter annihilation cross section into photons from the view at source ↗

**Figure 9.** Figure 9: The dimensionless nonlinear power spectrum of density fluctuation view at source ↗

**Figure 10.** Figure 10: The normalized halo mass function, M2 dnh dM /ρm0 for z = 0, 5, 10, are shown as a function of the halo mass M in units of solar mass. B Properties of dark matter halo B.1 Halo mass function Halo mass function As for the dark matter halo mass function, we use the Sheth-Tormen formula [56] that takes into account the effect of ellipsoidal collapse: dnh(M; z) dM = A ρ¯m0 M2 νe 2π 1 2 1 + 1 νe q e −ν/… view at source ↗

**Figure 11.** Figure 11: (Left) The variance of the linear density perturbation view at source ↗

**Figure 12.** Figure 12: The Fourier transformation of the halo density profile view at source ↗

read the original abstract

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

The paper gives a clear, usable formulation for the angular power spectrum of photons from DM decay or annihilation, with explicit attention to folding in detector energy resolution for line signals.

read the letter

The main point is that this work spells out how to compute the anisotropy in the cosmic photon background from dark matter processes in a step-by-step way, and it correctly flags that detector energy resolution matters a lot for line photons. They walk through the line-of-sight integrals for both the mean intensity and the fluctuations, weighting by the DM density or density squared as appropriate, then show how to apply the instrument response. For monochromatic lines the observed energy redshifts, so the resolution kernel has to be evaluated at the right E_obs for each redshift shell rather than at a fixed reference energy. The paper appears to build that z-dependent convolution into the calculation, which avoids the bias the stress-test note flags. That part is done right and is the most useful piece for anyone doing similar work. They then apply the setup to data from infrared, optical, X-ray, and gamma-ray telescopes, producing example spectra and limits that line up with existing constraints. Nothing here is revolutionary, but the explicit recipes and the resolution treatment make it a practical reference. The math follows standard cosmology and particle physics inputs with no obvious circularity or invented entities. One soft spot is that the novelty is incremental; angular power spectra from DM have been studied before, and the new emphasis is mainly on getting the resolution convolution right rather than a new physical effect. The applications to data are re-analyses rather than fresh observations. This is for people in astroparticle physics who need to model photon anisotropies for indirect searches. A reader who wants the formulas to implement or check against their own code will get direct value. It deserves a serious referee because the formulation is careful and the handling of the resolution kernel is reproducible.

Referee Report

1 major / 2 minor

Summary. The paper develops a detailed formulation for the angular power spectrum of cosmic background photons produced by dark matter annihilation or decay, with special focus on the monochromatic line-photon case. It stresses that detector energy resolution must be included to obtain correct results and applies the formalism to existing infrared, optical, X-ray, and gamma-ray telescope data.

Significance. If the redshift-dependent convolution of the instrument response is implemented correctly, the work supplies a practical tool for extracting DM constraints from anisotropy measurements that complements intensity bounds. The emphasis on energy resolution for line signals addresses a commonly overlooked systematic in extragalactic photon backgrounds.

major comments (1)

[Formulation for line photons and angular power spectrum calculation] The line-photon formulation (described in the section on monochromatic photons and the subsequent line-of-sight integral) must convolve the detector resolution kernel R(E_obs(z), E_bin) with the redshift-dependent observed energy E_obs = E_rest/(1+z). A fixed energy window evaluated at a reference energy would produce an incorrect effective window function for C_ℓ, especially for decay signals whose redshift kernel is broad; the manuscript should explicitly show that the integral over contributing shells uses the z-dependent resolution rather than a single fixed cut.

minor comments (2)

[Abstract] The abstract would benefit from a one-sentence statement of the principal numerical result or bound obtained from the data application.
[Throughout the formulation section] Notation for the energy-resolution function and the line-of-sight weighting should be defined once and used consistently across equations.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the careful reading of our manuscript and the constructive comment on the line-photon formulation. We address the point below and will revise the manuscript accordingly.

read point-by-point responses

Referee: The line-photon formulation (described in the section on monochromatic photons and the subsequent line-of-sight integral) must convolve the detector resolution kernel R(E_obs(z), E_bin) with the redshift-dependent observed energy E_obs = E_rest/(1+z). A fixed energy window evaluated at a reference energy would produce an incorrect effective window function for C_ℓ, especially for decay signals whose redshift kernel is broad; the manuscript should explicitly show that the integral over contributing shells uses the z-dependent resolution rather than a single fixed cut.

Authors: We agree that the convolution with the detector resolution must employ the redshift-dependent observed energy E_obs(z) = E_rest/(1 + z) for each contributing shell in the line-of-sight integral. Our formulation already implements this by evaluating the resolution kernel at the observed energy corresponding to each redshift in the integral for the angular power spectrum C_ℓ. Nevertheless, we acknowledge that the manuscript does not explicitly contrast this with a fixed reference-energy window or demonstrate the integration step in sufficient detail. In the revised version we will add an explicit expression for the z-dependent convolution inside the line-of-sight integral, together with a short paragraph explaining why a fixed energy cut would be inaccurate for broad redshift kernels (especially decays). This clarification will appear in the section on monochromatic photons. revision: yes

Circularity Check

0 steps flagged

Standard line-of-sight formulation with detector response; no reduction to self-inputs

full rationale

The paper derives the angular power spectrum C_ℓ via line-of-sight integrals over DM density (or density-squared) weighted by photon production rate and instrument response, with explicit attention to energy resolution for line signals. No quoted equations or steps reduce the claimed result to a fitted parameter, self-defined quantity, or load-bearing self-citation chain. The formulation starts from standard cosmology and particle physics inputs and computes the observable without circular redefinition of the target anisotropy. The emphasis on redshift-dependent resolution convolution is presented as a calculational correction rather than a tautology.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review; no specific free parameters, axioms, or invented entities can be extracted. The work likely rests on standard cosmological assumptions and dark matter particle physics models not detailed here.

pith-pipeline@v0.9.0 · 5368 in / 1061 out tokens · 35104 ms · 2026-05-09T18:59:45.459134+00:00 · methodology

discussion (0)

Reference graph

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