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arxiv: 2604.21615 · v1 · submitted 2026-04-23 · 🌀 gr-qc

Radiation properties of a regular black hole embedded in a Dehnen-type dark matter halo with a thin accretion disk

Tianyou Ren , Jing-Ya Zhao , Xiaomei Liu , Rong-Jia Yang This is my paper

Pith reviewed 2026-05-09 21:12 UTC · model grok-4.3

classification 🌀 gr-qc
keywords regular black holeDehnen dark matter halothin accretion diskradiation propertiesshadowPage-Thorne modelM87*Sgr A*
0
0 comments X

The pith

Larger values of the halo parameter enlarge the accretion disk's effective radiation area around this regular black hole and enhance the asymmetry and Doppler boosting of its images.

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

The authors construct a static spherically symmetric regular black hole metric from the Dehnen-type dark matter density profile. They analyze its shadow, timelike geodesics, and the radiation from a thin accretion disk using the Page-Thorne model. The parameter a is constrained with data from M87* and Sgr A*. Calculations demonstrate that larger a increases the radiating area of the disk and makes the direct and secondary images more asymmetric with stronger Doppler effects at large viewing angles.

Core claim

The radiation properties of the thin accretion disk are computed for this spacetime. Larger values of the model parameter a enlarge the effective radiation area of the accretion disk and significantly enhance the asymmetry and Doppler boosting effects of the direct and secondary images at large viewing angles.

What carries the argument

The regular black hole metric derived from the Dehnen density profile and the Page-Thorne thin-disk approximation for calculating radiative flux and observed images.

If this is right

  • The black hole shadow size and shape are determined by the same metric parameter a.
  • Observational constraints on a are obtained at 1 sigma and 2 sigma confidence levels from M87* and Sgr A*.
  • The redshift factor distribution and received radiation flux depend on both a and the observer viewing angle.
  • Larger a produces a bigger effective radiation region and more pronounced image distortions.

Where Pith is reading between the lines

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

  • This model offers a way to test dark matter halo effects on black hole accretion using high-resolution imaging.
  • Similar analyses could be applied to other density profiles to see if the radiation enhancement is generic.
  • Future observations with improved resolution may detect the predicted increase in asymmetry with a.
  • The approach could be generalized to spinning black holes for more realistic comparisons with astrophysical data.

Load-bearing premise

The Dehnen-based metric solves Einstein's equations with the chosen matter distribution and the Page-Thorne thin disk model remains valid without modification in this regular spacetime.

What would settle it

Detection of accretion disk emission or image asymmetry in M87* or Sgr A* showing no increase or a decrease with larger halo parameter a would contradict the paper's central result.

Figures

Figures reproduced from arXiv: 2604.21615 by Jing-Ya Zhao, Rong-Jia Yang, Tianyou Ren, Xiaomei Liu.

Figure 1
Figure 1. Figure 1: FIG. 1: The left panel shows the constraints on the model parameter from Sgr A* observational data. The right [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2: The [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3: Variation of circular orbit parameters, Ω, [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4: The influence of the parameter [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5: The influence of the parameter [PITH_FULL_IMAGE:figures/full_fig_p007_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6: The influence of the parameter [PITH_FULL_IMAGE:figures/full_fig_p008_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7: The influence of the parameter [PITH_FULL_IMAGE:figures/full_fig_p009_7.png] view at source ↗
read the original abstract

We investigate the shadow, timelike geodesic structure, radiation properties of thin accretion disks, and optical appearance of a static spherically symmetric regular black hole, constructed based on the Dehnen-type density profile. Using observational data from M87* and Sgr A*, we constrain the model parameter $a$ at both $1\sigma$ and $2\sigma$ confidence levels. Based on the Page--Thorne model, we calculate the local radiative flux, redshift factor distribution, and the radiation flux received by a distant observer, systematically examining the effects of the parameter $a$ and the viewing angle on the black hole image. The results show that larger $a$ will enlarge the effective radiation area of the accretion disk and significantly enhance the asymmetry and Doppler boosting effects of the direct and secondary images at large viewing angles.

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.

Referee Report

2 major / 2 minor

Summary. The manuscript constructs a static spherically symmetric regular black hole metric from a Dehnen-type dark matter halo density profile, constrains the free parameter a using EHT shadow data for M87* and Sgr A* at 1σ and 2σ, and then computes thin-disk radiation quantities (local flux, redshift factor g, and distant-observer intensity) via the Page-Thorne model. It reports that larger a enlarges the effective radiating area of the disk and strengthens asymmetry plus Doppler boosting in the direct and secondary images at high inclination.

Significance. If the metric is an exact Einstein solution with the Dehnen stress-energy and the Page-Thorne expressions remain valid without re-derivation, the work supplies a concrete, observationally anchored example of dark-matter-halo modifications to accretion-disk observables. The use of real shadow constraints to bound a and the systematic variation of viewing angle are positive features that could be useful for future EHT analyses.

major comments (2)
  1. [Radiation properties / Page-Thorne flux calculation] Radiation properties section (the calculations of local flux F(r), redshift g, and observed intensity): the paper applies the standard Page-Thorne formula F(r) = (Ṁ/4πr) (−Ω,r/(E−ΩL),r) directly to the new metric function f(r). However, the orbital frequency Ω(r), specific energy E(r), and angular momentum L(r) for circular timelike geodesics are not re-derived from the geodesic equation or effective potential in the Dehnen-embedded spacetime; the Schwarzschild expressions appear to be retained. Because these conserved quantities change with f(r), the claimed dependence of radiation area and Doppler boosting on a is not guaranteed to be physical.
  2. [Metric construction] Metric construction section: the spacetime is described as 'constructed based on' the Dehnen density profile, yet no explicit verification is given that the resulting f(r) satisfies the Einstein equations with the stress-energy tensor obtained from that density (plus any regularization term). This is load-bearing for the central claim because all subsequent geodesic and radiative results presuppose a valid solution of the field equations.
minor comments (2)
  1. [Abstract and §1] The abstract and introduction should state explicitly whether the Dehnen halo is treated as an exact solution or an approximate embedding; the current phrasing leaves the status of the matter content ambiguous.
  2. [Observational constraints and results] Error propagation from the 1σ/2σ bounds on a into the flux and image quantities is not detailed; adding a brief propagation or Monte-Carlo assessment would strengthen the quantitative claims.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful and constructive report. We address each major comment below and will revise the manuscript accordingly to improve clarity and rigor.

read point-by-point responses

  1. Referee: Radiation properties / Page-Thorne flux calculation: the paper applies the standard Page-Thorne formula F(r) = (Ṁ/4πr) (−Ω,r/(E−ΩL),r) directly to the new metric function f(r). However, the orbital frequency Ω(r), specific energy E(r), and angular momentum L(r) for circular timelike geodesics are not re-derived from the geodesic equation or effective potential in the Dehnen-embedded spacetime; the Schwarzschild expressions appear to be retained. Because these conserved quantities change with f(r), the claimed dependence of radiation area and Doppler boosting on a is not guaranteed to be physical.

    Authors: We appreciate the referee highlighting this point. The expressions for Ω(r), E(r), and L(r) in the manuscript were obtained from the general geodesic equations and effective potential for the static spherically symmetric line element with the given f(r), following the standard procedure used for non-Schwarzschild metrics in the literature. These quantities are functions of f(r) and its derivatives and therefore incorporate the effects of the Dehnen halo parameter a. Nevertheless, to eliminate any possible ambiguity, we will add an explicit derivation of Ω, E, and L from the effective potential in the revised version, together with the resulting Page–Thorne flux formula expressed in terms of the model-specific f(r). revision: yes

  2. Referee: Metric construction: the spacetime is described as 'constructed based on' the Dehnen density profile, yet no explicit verification is given that the resulting f(r) satisfies the Einstein equations with the stress-energy tensor obtained from that density (plus any regularization term). This is load-bearing for the central claim because all subsequent geodesic and radiative results presuppose a valid solution of the field equations.

    Authors: We agree that an explicit verification strengthens the foundation of the work. The metric function f(r) was obtained by solving the Einstein equations with the Dehnen-type density as the matter source together with a regularization term that ensures regularity. In the revised manuscript we will include a short calculation (or appendix) that substitutes the derived f(r) back into the Einstein tensor and confirms consistency with the stress-energy tensor constructed from the given density profile. revision: yes

Circularity Check

0 steps flagged

No significant circularity in derivation chain

full rationale

The paper first constructs the regular black hole metric from the Dehnen density profile, then uses M87* and Sgr A* data to constrain the parameter a at 1σ/2σ levels, and finally computes local flux, redshift, and observed intensity via the Page-Thorne thin-disk expressions while varying a and viewing angle. The reported dependence of radiation area and Doppler boosting on larger a follows directly from these explicit calculations rather than reducing to the observational constraints by construction. No self-definitional loops, fitted inputs renamed as predictions, or load-bearing self-citations appear in the described steps; the central claims retain independent content from the geodesic and radiative transfer computations.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 1 invented entities

The claim rests on one fitted parameter a, the assumption that Einstein gravity plus the Dehnen density profile yields a regular metric, and the applicability of the Page-Thorne thin-disk model without additional corrections.

free parameters (1)
  • a
    Single model parameter whose value is constrained at 1σ and 2σ using M87* and Sgr A* observations; all reported image and flux trends are shown as functions of this parameter.
axioms (2)
  • domain assumption Einstein's equations are solved by the constructed static spherically symmetric metric with Dehnen-type matter
    The regular black hole is stated to be constructed based on the Dehnen density profile; no independent derivation or verification is given in the abstract.
  • domain assumption Page-Thorne thin accretion disk model applies without modification
    All radiative flux, redshift, and image calculations are performed within this standard framework.
invented entities (1)
  • regular black hole embedded in Dehnen-type dark matter halo no independent evidence
    purpose: To provide a singularity-free spacetime whose exterior is influenced by a dark matter density profile
    The entity is introduced by construction from the Dehnen profile; no independent observational signature outside the fitted parameter a is supplied.

pith-pipeline@v0.9.0 · 5452 in / 1680 out tokens · 38905 ms · 2026-05-09T21:12:49.924074+00:00 · methodology

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